f
fabric A flexible mesh of fibres or threads of natural or artificial materials, including metals, which may be manufactured by knitting, weaving, knotting (in the form of nets) or felting (compacting fibres). See also drape; screen mesh.
fabrication 1. The manufacture of components from metal, plastic, silicon, wood, etc. 2. The building up of components into complete or sub-assemblies.
fabric filter A fabric mounted in a frame for removing particulate material from a flow. See also screen mesh.
face 1. See toothed gearing. 2. The part of a valve that contacts the seat. 3. Any large flat area of a component such as the surfaces of a pipeflange. 4. The dial of a clock gauge.
face-centred cubic See crystal structure.
face cone See toothed gearing.
face gear See toothed gearing.
face plate An attachment for a lathe, consisting of a large circular plate having holes and slots to which workpieces may be bolted.
face velocity See Darcy’s law.
face width See toothed gearing.
factor of safety (design factor, safety factor, f) If σA is the actual strength of a component and σR is the required strength, the factor of safety f = σA/σR. The margin of safety is (σA − σR)/σR = f −1.
FAD See free-air delivery.
Fahrenheit scale (T) A largely obsolete, non-SI, relative-temperature scale now defined in terms of the Rankine absolute temperature scale as T(°F) = T(R) − 459.67, where °F is the Fahrenheit degree symbol. The conversion to SI is 
. The scale was originally defined with the melting point of ice (the ice point) as 32°F and the boiling point of water (the steam point) as 212°F. See also Celsius temperature scale.
fail-safe design The design methodology whereby failure of one part of a component or structure does not lead to failure of the whole assembly. This can be achieved through, for example, redundancy. In control systems, the philosophy is called ‘fail soft’. See also damage tolerance.
fail-safe system A system designed so that the failure of one or more components does not result in danger. For example, air-operated brakes on a heavy-goods vehicle are applied by springs and released by air pressure. A leak causing a pressure loss will thus result in the brakes being applied rather than causing them to become inoperative.
failure The result when a body, component, or structure is incapable of performing the task for which it was designed. The term is often used without reference to what causes failure, such as fracture, buckling, excessive deformation, wear, or erosion. Failure criteria (failure theories, theories of strength) are mathematical expressions for the combinations of stress, strain, or strain energy at which materials fail, which are employed in design to dimension components. See also damage; strength; stress.
failure-assessment diagram A diagram displaying different possible modes of failure of a body, component, or structure from which it is possible to ascertain which mode is likely to be controlling. See also design methodologies; rivet; R6 failure assessment diagram.
fairing A streamlined, smooth, thin-walled shell of metal, plastic, or composite material, placed around part of a vehicle, such as an aeroplane, motorcycle, motor vehicle, or train, in order to reduce aerodynamic drag. See also cowl.
Falkner–Skan solutions Exact similarity solutions (numerical) to the boundary layer equations for flows with a variation of free-stream velocity U∞ according to U∞ = Kxm where K is a dimensional constant, x is the distance along the surface, and m is a constant. The Blasius solution corresponds to m = 0. See also wedge flow.
falling-ball viscometer (falling-sphere viscometer) An instrument for determining the viscosity of a liquid by measuring the time for a sphere, typically of glass, stainless steel, or tantalum, to fall between two fiduciary lines in a glass tube containing the liquid.
falling-film cooler A type of heat exchanger in which a film of the liquid to be cooled flows down either the inside or the outside of vertical tubes or over flat surfaces while a refrigerant or chilled liquid, such as water or brine, flows on the other side of the cooling surface.
falling-film evaporator A type of heat exchanger in which a thin film of the liquid to be evaporated flows either down the inside of vertical tubes heated by steam or subjected to vacuum, or over the outside of an array of horizontal or vertical tubes through which there is a flow of hot fluid.
fan 1. (blower) A device with vanes or blades attached to a hub on a shaft that rotates to produce an airflow. There are both axial and centrifugal designs. The fan rating is the volumetric flow rate of air (i.e. the fan delivery, 
) a fan delivers at a particular rotation speed, and the fan static-pressure rise Δp is the average increase in static pressure across the blades of a fan at that speed. The fan total-pressure rise (fan total-head rise) is the average increase in stagnation pressure across the blades of a fan at a particular rotation speed, and the fan dynamic-pressure rise (fan velocity-pressure rise) the corresponding average increase in dynamic pressure. The overall fan efficiency (ηE) is the ratio of the power delivered to the air divided by the power provided by the driving motor PSHAFT, i.e. ηE = Δp/PSHAFT. The fan characteristics, measured in a fan test, are curves of Δp, PSHAFT, and ηE vs . 2. In a turbofan engine for a civil aircraft, a single-stage compressor at the front of the engine operating on the bypass air stream. For military applications there may be two or three stages.
fan brake A type of dynamometer in which the torque is provided by a fan.
Fanning friction factor (fF) For pipe or duct flow, a non-dimensional measure of the surface shear stress defined by 
where τS is the circumferential average surface shear stress at any axial location, ρ is the fluid density, and V is the bulk flow velocity. See also Darcy friction factor.
Fanno flow One-dimensional adiabatic gas flow through a constant-area duct with wall friction. For a perfect gas, tabulated results are available from a one-dimensional analysis assuming a constant friction factor. A Fanno line is curve of enthalpy or temperature vs specific volume or specific entropy for Fanno flow. See also Rayleigh flow.
fantail A ducted version of a helicopter tail rotor.
farfield In fluid mechanics and acoustics, used to indicate conditions far away from a specified source or disturbance.
fast coupling See quick coupling.
fastener A device for the permanent or temporary joining of components or structures, including bolts, screws, nails, pins, clamps, and circlips.
fast Fourier transform A mathematical technique for producing a Fourier transform from sampled data, i.e. for producing the discrete Fourier transform. It is particularly efficient (i.e. fast) when the number of sampled values is a power of 2.
fast pyrolysis A process in which organic materials, especially biomass, are rapidly heated to between 450°C and 600°C in the absence of air to produce gases, char, and organic vapours. The latter are condensed to yield bio oils. See also bioenergy.
fathom (fath) A non-SI, imperial unit of length used primarily for measuring water depth. 1 fath = 6 ft.
fatigue A term referring, in components and structures subjected to either random or cyclic periodically-varying loads, to a progressive reduction in strength leading to failure at stresses lower than those that cause failure under monotonic loading. Variable loads arise from out-of-balance machinery and other vibration sources, wind gusts, etc., and a large proportion of service failures is caused by fatigue. Fatigue results from the initiation and slow propagation of cracks. In manufactured components, crack initiation usually occurs at a point of stress concentration. After a period, often of millions of stress cycles, the crack reaches a critical length at which the next peak load causes sudden brittle or ductile fracture. Fracture surfaces resulting from fatigue display characteristic striations or progression marks emanating from the crack initiation site during the slow crack growth period, with a different surface appearance for the final fracture.
fatigue failure surface
There are various ways of determining the fatigue behaviour of materials. One of the earliest is the rotating cantilever (Wöhler) test, in which a cylindrical specimen is gripped in a chuck and rotated. At its free end the specimen has a bearing below which a dead weight is hung that bends the testpiece.
Wöhler testing machine
Surface elements experience the maximum sinusoidal variation of tensile and compressive bending stress (s) as the testpiece rotates, the magnitude of which depends on the hanging load. The machine records the number of cycles N at the instant of fracture. Typical results for alloys of steel and aluminium are plotted as s–N curves, using a log scale on the abscissa.
s–N fatigue curve
When s is high, failure occurs in fewer cycles than when s is low (low-cycle and high-cycle fatigue, respectively). The arbitrary dividing line between the two occurs at about 103 or 104 cycles. Low-cycle fatigue data are used in the design of components either having relatively short lives or likely to be overloaded. The diagram demonstrates that for N > 106 cycles there is a stress se (the fatigue limit or endurance limit) below which failure does not occur in plain carbon and low-alloy steels, and titanium, no matter how many cycles the testpiece is subjected to. Components designed so that stresses are lower than the endurance limit operate in the so-called infinite-life regime. Designs based on the higher fatigue stresses for N < 106 cycles have finite lives. In contrast, aluminium and other non-ferrous alloys, polymers, and composites do not exhibit a fatigue limit, so that for design purposes a fatigue strength is defined as the stress at 107 or 108 cycles. Mandatory requirements are often specified for periodic crack inspection of highly-stressed aluminium components and structures, such as airframes. The safe fatigue life is the period of time during which repeated applications of a load to a component or structure are unlikely to result in its failure. Unless stresses are oscillated above 104 Hz, frequency has no effect on the s–N curves for metals. This is not true for polymers where localized heating of testpieces occur.
The ratio of the endurance limit to the ultimate tensile strength of the material is called the endurance ratio or endurance-limit, ratio. For many steels whose UTS < 1.4 GPa, it is found empirically that the endurance ratio is about 0.5 ∼ 0.7. The ratio of the fatigue strength to the ultimate tensile strength of a material is called the fatigue ratio.
Relations for low-cycle fatigue failure may be expressed in terms of stress or strain amplitudes. Basquin’s equation is S = Sf Nf−b where S is the stress amplitude (given by (smax − smin)/2 where smax is the maximum stress in a cycle and smin the minimum, in which compressive stresses are negative), Nf is the number of cycles to failure, Sf is called the fatigue-strength coefficient, and b is the fatigue-strength exponent. Writing Δεp for the applied fluctuating plastic-strain amplitude, given by (εmax − εmin)/2 where εmax is the maximum strain in a cycle and εmin the minimum in which compressive strains are negative, the Coffin–Manson–Tavernelli relation is Δεp/2Ncf = εf′ where εf′ is called the fatigue ductility coefficient and c is the fatigue ductility exponent that ranges from 0.1 for magnesium and some stainless steels to 0.9 for other stainless steels, nickel alloys, and aluminium alloys. A simplified version is 
. In structures subjected to pulsating loads, shakedown can be important. When the shakedown stress range is exceeded, the small plastic strains produced in every cycle may accumulate to lead to fatigue failure.
Ordinary screw-driven machines may be used for fatigue testing in which the axial load is arranged to cycle from positive to negative (push–pull fatigue); others work like a vibrating tuning fork with the specimen attached to one of the arms. Yet other machines apply fluctuating torsional stresses, or combined stresses. Machines can be programmed to vary the amplitude and frequency of loading during a test, including random loading. Such information is necessary since practical operating conditions for components and structures are rarely the constant-frequency, constant-amplitude patterns of most laboratory testing. In addition to plain samples, specimens containing different sorts of notches may be tested, and even actual machine components rather than material testpieces.
Fatigue data show much scatter, as results are sensitive to surface finish and other factors such as stress concentrations, size of testpiece and the surrounding environment. Specimens are often highly polished to achieve the highest s–N curves (and greatest endurance limits for steels). The endurance limit in reversed-bending and torsion fatigue of round bars depends on the diameter, other factors (such as surface finish) being equal; for non-circular components an equivalent diameter based on the same cross-sectional area has to be found. In corrosion fatigue, aggressive chemical environments shorten the crack-initiation period and accelerate crack-growth rates leading to a shorter component life. In consequence there are various empirical correction factors (all < 1) that are applied to the endurance limit of polished-steel samples to arrive at a value for design; they include surface, size, temperature, and environment factors. Note that the fatigue-strength reduction factor Kf is the ratio of the fatigue limits of notched and un-notched testpieces, and is the stress-concentration factor to employ in fatigue instead of the usual stress-concentration factor Kt employed for monotonic loading. Kf varies with notch or discontinuity geometry. The notch-sensitivity factor (index or ratio) defined as q = (Kf − 1)/(Kt − 1) indicates the extent to which a body containing a notch is sensitive to fatigue. Notch-sensitive materials have q = 1; notch-insensitive materials have q = 0.
The mean stress in fatigue is defined as smean = (smax + smin )/2. In reversed bending, smax = −smin, so smean = 0. The stress ratio R = smin/smax is also employed as a parameter in fatigue. In many applications a fluctuating stress is superimposed upon a static load and it is found that increasing smean reduces the permissible fatigue-stress amplitude (limiting range of stress). The diagrams show different versions of Goodman (or fatigue) diagrams that show how S and smean are related to ensure different specified lives (Ne). The locus marked Nf is for an infinite fatigue life for materials having an endurance limit. The regions between the dashed lines are of little practical significance for infinite-life design, as smax exceeds the yield stress. In the diagram, 
where se for fully-reversed alternating stress is assumed to be 
.
Goodman diagram
Goodman diagram (alternative version)
The modified Goodman diagram sets se as the actual limiting stress range. The Goodman relation was preceded by Gerber’s equation in which the (smean/UTS) term was squared. Later Soderberg proposed an even more conservative relationship where UTS is replaced by the yield stress.
Components and structures may be subjected to an accumulation of stress cycles of varying amplitude and varying frequency, or load fluctuations that are random. The Palmgren–Miner or Miner empirical rule states that ΣiNi/Nf,i = 1 where Nf,i is the fatigue life of the component under maximum stress si, and Ni (< Nf,i) is the actual number of cycles spent at stress si. In practice the constant of unity varies widely, typically between 0.7 and 2, and depends on whether high stress amplitudes occur before or after low. Rainflow analysis is employed in the analysis of fatigue data obtained under random loading, in which random stress cycles may be represented in terms of a number of regular sine waves of different amplitude in order that the Palmgren–Miner rule may be applied to determine the life of a component or structure.
Fatigue loads arise from many sources. Acoustic fatigue concerns components exposed to intense sound, such as from the supersonic exhaust jet of an aeroengine or a high-speed turbulent boundary layer. The endurance limit of surfaces in cyclic contact (gear teeth, etc.) is called the contact-fatigue strength, the safety factor for the design of which is called the life factor. Failure of a ductile material due to repeated temperature cycling is called thermal fatigue. Two thermal-fatigue factors are used to quantify the ability of a material to withstand thermal-strain cycling, and are defined by Δσk/αE and ΔεPk/α where Δσ is the stress range to which the material is subjected, ΔεP is the corresponding range of plastic strain, k is the coefficient of thermal conductivity, α is the coefficient of thermal expansion, and E is Young’s modulus.
Complications in fatigue behaviour arise at high homologous temperatures TM in metals, and in other materials such as polymers having time-dependent behaviour, leading to creep fatigue.
Design based on s–N fatigue curves in which a statistical mean life is determined for the expected service load spectrum is safe-life design. Fail-safe design relies on redundancies in a structure such that failure of one member does not lead to a cascade of fractures and hence complete failure. Damage-tolerant design employs fracture mechanics to take into account initial imperfections (starter cracks), crack-growth rates and the conditions of final fracture. The Paris equation relates the crack growth per cycle in fatigue da/dN to the range of applied-stress intensity ΔK by da/dN = C(ΔK)n where a is crack length and 
and in which C and n are material-dependent, experimentally-determined constants and Y(a/W) are non-dimensional correction factors to take into account different geometries and loadings, with W a representative dimension of the body. Integration of this relation between a = ai (the length of a crack found by non-destructive inspection) and a = af the critical crack length at which the body fails, gives
in which Y is assumed to be constant. In this way the fatigue life Nf of a component is determined. As with s–N curves, there are modifications to the Paris equation to account for mean stress effects. See also flow-induced vibration; pitting; static fatigue; threshold stress-intensity factor.
FATT See ductile–brittle transition temperature.
fault monitoring The process of automatically checking the performance of a system to detect the occurrence of faults. Often applied to detect both hardware and software faults in computer-control systems.
fault tolerance The ability of a system to continue correct operation despite the failure of one or more components of the system. See also fail-safe design.
favourable pressure gradient (Unit Pa/m) In boundary-layer theory, a streamwise pressure gradient that accelerates the flow of a fluid, increases the wall shear stress, and delays transition to turbulence. If very strong, it can lead to laminarization of a turbulent boundary layer. See also adverse pressure gradient.
Favre averaging A method of time averaging used in the analysis of a turbulent flow in which density variations are significant. For a flow parameter u, the Favre average is defined by
where t is time, T is the averaging time, ρ is the fluid density, and the straight overbar indicates a Reynolds-averaged quantity.
faying surface The part of the surface of a component that is in contact with another surface to which it is joined, for example by welding, brazing, soldering, bonding, or riveting.
FBD See free-body diagram.
FCC See crystal structure.
f-chart A computer programme for the analysis and design of solar-heating systems.
FDM See fused deposition modelling.
feasibility study The determination of the viability and benefits of a proposal with particular emphasis on identifying potential problems.
feathering Adusting a controllable-pitch propeller to a position of minimum drag in the event of power failure.
feather key A metal bar of rectangular cross section, with both ends radiused, that fits into a keyslot on a shaft to allow torque to be transmitted to a wheel, gear, or other cylindrical component.
Fe-C phase diagram See steel microstructures.
Federation of European Producers of Abrasives See abradant.
feedback The process of taking a signal representing the output of a plant and using this with other signals to determine the input to the plant. In a control system, the feedback control loop (feedback loop) is formed by the plant, sensors measuring the plant output, feedback path, summing junction, and controller. The transfer function of the feedback path (feedback transfer function) includes the transfer function of the sensor measuring the plant output and the transfer function of the feedback compensation (the use of a compensator in the feedback branch, rather than in series with the plant as would be the case in cascade compensation). The signal fed back to the plant input through the feedback branch (feedback path) to the summing junction to produce the error signal is the feedback control signal. A feedback control system is one using one or more closed loops, i.e. where the output from the controlled plant is used by the controller to modify the plant input. Negative feedback is where the plant input is reduced by the feedback signal; positive feedback is where the plant input is increased. A feedback regulator uses feedback control so as to maintain the desired plant output.
feedforward control system A control system that uses one or more sensors to detect disturbances affecting the plant and then applies an additional input to the plant so as to minimize the effect of the disturbance. This requires a mathematical model of the plant so that the effect of disturbances can be predicted and the necessary additional input calculated.
feed gear The means by which, in a machine tool, a tool is fed to the workpiece or vice versa.
feed nut The means by which, in an automatic drill, a drill bit is fed to the workpiece.
feed pipe The pipe that connects a feed pump to a component or machine.
feed pressure (Unit Pa) The pressure provided by a feed pump.
feed pump A pump that supplies liquid to a component or machine, such as feedwater to a boiler, fuel or oil to an engine.
feed screw The screw that controls feed mechanisms in a machine tool, such as the drive for the saddle in a lathe. See also lead screw.
feedstock Workpiece material in bulk that is fed into a process, or into the deformation zone of a machine such as an automatic bolt-heading machine, a capstan lathe, etc.
feedwater The water supplied to a steam boiler.
feedwater heater A heat exchanger used to preheat feedwater before it enters a boiler. The energy required is usually derived from the flue gas or steam extracted between the stages of the steam turbine. See also economizer; extraction turbine.
feeler gauge An array of flat fingers of hardened steel of accurately-known thickness, pinned at their ends like a collapsible fan, used for checking clearances, end float, sparking plug gaps, etc.
FEM See finite-element method.
female fitting (female coupling) The outer part of a connection in which one part fits into another. See also male fitting.
female thread See screw.
FEPA The abbreviation for Federation of European Producers of Abrasives. See also abradant.
ferrimagnetism See magnetic materials.
ferrite 1. See steel microstructures. 2. Ceramic compound consisting of a mixed oxide of iron and one or more other metals which has ferrimagnetic properties. See also magnetic materials.
ferroelectricity A property of dielectric materials that exhibit polarization in the absence of an electric field. See also barium titanate ceramics.
ferrography A method of analysis of particles in lubricating oil, used to detect wear in machines, such as gearboxes, and machine components such as bearings.
ferromagnetism See magnetic materials.
ferrule 1. A ring or cap, usually metal (literally iron), attached to a slender shaft, such as the handle of a tool, to strengthen it. 2. A sleeve, usually metal, used to connect two parts, e.g. pipe sections. 3. See olive.
FFLD See fracture forming limit diagram.
FHP See friction power.
fibre 1. A natural or man-made filament of material. Natural fibres include wood and asbestos. Man-made fibres include fibreglass and carbon fibres, but the most common are polymer fibres. See also zylon. 2. A filament, either long (continuous) or short (chopped), used to reinforce matrices in composites.
fibre bridging In fibre-reinforced composites, when intact fibres span across a crack and thereby increase the fracture toughness by pull-out.
fibre content The amount, by volume or mass, of fibres in a composite material. See also volume fraction.
fibre-optic cable (optical fibre cable) A cable consisting of one or more glass fibres through which light is transmitted. Commonly used in long-distance telecommunication and high-speed data connections.
fibre-optic thermometer A temperature sensor in which a luminescing phosphor is attached to the tip of an optical fibre and excited to luminescence by a pulsed light source. The decay rate of luminescence is temperature-dependent.
fibre reinforcement The increase in stiffness and strength of composites by addition of fibres to the matrix.
fibre stress (Unit Pa) 1. In composites under load, the stress σf in the fibres as opposed to that in the matrix, σm. See also composite modulus; rule of mixtures. 2. A term sometimes used in bending theory to relate to the stresses at different distances from the neutral axis.
fibrous fracture A term used to describe the appearance of fracture surfaces in ductile materials that crack by void initiation, growth, and coalescence. Characteristic surface cavities are nucleated on inclusions, such as manganese sulfide in steels, and elongated before fracture is complete. See also cleavage fracture; crystalline fracture; void sheet.
Fick’s law of diffusion The governing equation for mass diffusion due to a concentration gradient. In a binary fluid mixture of species A and B, the mass flux of species A is given by the equation 
where ρ is the mixture density, D is the binary diffusion coefficient, cA is the mass concentration of A, and ∇ represents the gradient operator. The binary diffusion coefficient D can be regarded as being defined by the equation, and the diffusion coefficients of A and B, DAB and DBA, are equal. The corresponding thermal-energy relation is Fourier’s law.
fictitious force See accelerating frame of reference.
fiducial temperature See fixed point.
fiduciary line A fixed reference line marked on an instrument, such as the crosshairs in the eyepiece or graticule of a microscope.
filament 1. A long fibre, particularly of glass or carbon, employed to reinforce composite materials. 2. A fine wire, such as the heating element in an incandescent light bulb.
filament winding The manufacture of vessels made from fibre-reinforced composites, by winding the continuous filament or prepreg over a shaped mandrel, thus avoiding joins. Winding may be performed axially, circumferentially, helically, or longitudinally, or as combinations of these. See also geodesic-isotensoid.
filar micrometer (bifilar micrometer) An instrument for the measurement of objects viewed under a microscope. It consists of two parallel filaments (‘hairs’) within the eyepiece, one fixed and one moved by a screw thread.
file A hand-held cutting tool that cuts on the forward stroke only. Files are classified according to the cut (number and size of ridges) and shape (flat, square, round, half-round, triangular, etc). The harder the material being filed, the finer-toothed the file. See also draw filing.
file hardness A measure similar to the idea of scratch hardness, whereby a material that cannot be cut by a file must be as hard as, or harder than, the file.
filled-system thermometer See fluid-expansion thermometer.
filler Low-cost material such as wood flour, silica flour, or talc, used to bulk out some polymer-moulding compounds.
filler rod See welding.
fillet gauge A device used to check whether the dimensions of a fillet weld are within specified tolerances.
fillet weld A weld of triangular cross section used to join two plates at right angles.
film boiling See boiling.
film coefficient See heat transfer.
film condensation (filmwise condensation) The dominant form of condensation of a vapour on to a surface at a temperature below the saturation vapour temperature and which is wetted and completely covered by the condensate which flows continuously under the action of gravity. See also droplet condensation.
film cooling A method of surface cooling in which a cool fluid is blown through a slot parallel to the surface to be cooled, a series of holes, or one or more slots in the surface, in a direction nearly tangential with the surface. For a gas flow, the cooling effectiveness can be greatly enhanced by using as the coolant a liquid that evaporates (sweat cooling). See also transpiration cooling.
film-cooling effectiveness (adiabatic film-cooling effectiveness, η) If TAS is the temperature of an adiabatic surface for a flow with free-stream temperature T∞, the film-cooling effectiveness is defined as η = (TAS − T∞)/(TF − T∞) where TF is the cooling-fluid temperature.
film pressure (Unit Pa) The pressure in the lubricant film within a bearing.
film temperature (Unit K or °C) The temperature used to evaluate fluid properties in pipe or boundary-layer flow where there are large temperature differences. It is defined as (TREF + TS)/2 where TS is the surface temperature and TREF is the bulk temperature in pipe flow and the free-stream temperature for a boundary layer.
film thickness (Unit μm) The thickness of the thin layer of lubricating oil between two surfaces, such as within a bearing or between two contacting gear teeth.
filmwise condensation See film condensation.
filter 1. (filter screen) A mesh, gauze, paper, or cloth, usually held by a frame, that removes particulates larger in diameter than the mesh or pore size from a fluid stream passing through it. Metal wires, natural and synthetic fibres are all used for filter construction. See also beta ratio. 2. In processing signals, a device that passes a specified range of frequencies and blocks others. Normally used in low-pass, high-pass, or band-pass forms.
filterability The ability of a fluid to pass through a filter without excessive pressure drop.
filter efficiency See beta ratio.
filter pump An aspirator, such as a jet pump, attached to the outlet side of a liquid filter, for example using a side-arm flask, to apply suction and so increase the filtration rate.
filter screen See filter (1).
filter thickener A device that increases the proportion of solids in a liquid–solid mixture such as sewage, sludge, or slurry, by filtering off some of the liquid. Applications include wastewater treatment and fruit-juice concentration.
fin 1. See flash. 2. See cooling fins.
final value The steady-state output of a system after transient effects have decayed.
final-value theorem The result, when a Laplace-transformed (i.e. frequency-domain) variable is multiplied by s, the Laplace-transform variable, and evaluated in the limit as s→0, is the value of the inverse transform (i.e. time-domain solution) as time t→∞. Thus: 
fin cooling See cooling fins.
fin effectiveness (fin efficiency) See cooling fins.
fine particle strengthening See precipitation hardening.
fine thread See screw.
finger gripper A robot gripper using two or more moveable rods, equivalent to human fingers, to pick up components.
finish machining The final stages of manufacture of a component by cutting, where small depths of cut are taken at high speed in order to satisfy dimensional and surface-finish requirements.
finite-difference method A method for the numerical solution of ordinary and partial differential equations in which the solution domain is divided into cells. At the most basic level, a spatial derivative with respect to any quantity is approximated by the difference in that quantity across a cell divided by the cell length, height, or depth. This is termed a first-order difference. Temporal derivatives and higher spatial derivatives are also approximated by differences. Special techniques have been developed to improve numerical accuracy and convergence while avoiding instability, for example using higher-order differences, as well as forward and backward differences and finer cells, in regions where gradients are steep. The method is applied in many problem areas including elasticity, heat transfer, and fluid mechanics. Steady-flow problems are often solved as the final state of a time-evolving problem. See also finite-element method; finite-volume method.
finite-element method (FEM) A numerical method of solving partial differential equations and hence problems in stress analysis, fluid mechanics, heat transfer, etc. In simple terms, the body is divided up into regions (elements) of shapes and sizes appropriate to the problem, and the governing equations of every element written down. Elements are then reconnected at nodes, resulting in a set of simultaneous algebraic equations, solution of which solves the problem. By the process of reconnecting nodes, the field quantity of interest (e.g. displacement field, temperature field) becomes interpolated over the whole body in a piecewise fashion by as many polynomial expressions as there are elements. The ‘best’ values of the nodal field quantities are those that minimize some function such as total energy. In matrix notation, KD = R, where D is a vector of the unknown nodal-field quantities, R is a vector of known loads, temperatures etc., and K is a matrix of known constants. In stress analysis, K is called the stiffness matrix.
finite-life fatigue See fatigue.
finite-strain theory The theories of elasticity and plasticity that employ large-deformation measures of strain, i.e. stretch ratios for rubber elasticity and logarithmic strains for plasticity, rather than incremental strains.
finite-volume method A method for the numerical solution of partial differential equations, widely used in many commercial CFD packages. The solution domain is divided into small but finite volumes surrounding node points on a mesh. The governing equations are formally integrated over each of these volumes. The conservation of any flow variable φ is considered taking into account fluxes of φ due to advection and diffusion across the faces of each volume and the creation of φ within it. The resulting set of algebraic equations is solved iteratively. See also finite-difference method; finite-element method.
finned surfaces See cooling fins.
fin performance See cooling fins.
fins See cooling fins.
fire barrier See thermal barrier (2).
firebox The furnace used to heat a fire-tube boiler, such as used on a steam locomotive.
fire bridge (bridge wall) In a reverberatory furnace, a low barrier that separates the fuel from the ore or metal being smelted.
fireclays See refractory materials.
fire damp An explosive gas, primarily methane, found in coal mines.
fire damper A passive fire-protection device installed in air-conditioning and ventilation systems to prevent the spread of fire and smoke.
fired process equipment Equipment in which the heat for the process concerned is provided by combustion of a fuel.
fire pump A pump used to supply water at high flow rates for fire suppression. Fire pumps are usually powered by Diesel engines or electric motors, and may be vehicle mounted, portable, or permanently installed in a building, on a ship, etc.
fire-tube boiler (fire-tube shell boiler, shell boiler, shell-and-tube boiler, smoke-tube boiler) A boiler in which the hot combustion gases flow through tubes contained within a steel shell and the water to be heated flows around the tubes within the shell. See also dry-back boiler; economic boiler; water-tube boiler; wet-back boiler.
firing 1. The process of combustion occurring in a cylinder of an internal-combustion engine or the combustion chamber of a rocket engine. 2. The process of heating a clay-rich component in a kiln to drive off water and harden the material, including by sintering.
firing order (firing sequence) The sequence in which combustion occurs in the cylinders of a multi-cylinder piston engine. For petrol engines this is achieved by sequencing sparking of the spark plugs. For a Diesel engine it is the sequence of fuel injection. Vibration can be minimized by appropriate choice of firing order.
firing rate (Unit kg/s or L/s) The rate at which fuel is supplied to a burner or combustion chamber. See also turndown ratio.
firing stroke See power stroke.
first-angle projection See projection.
first coefficient of viscosity See dynamic viscosity.
first law of motion See Newton’s laws of motion.
first law of thermodynamics A statement of the principle of conservation of energy. For a closed system, the change in all forms of energy stored in the system ΔE is given by ΔE = Q − W, where Q is the net addition of energy to the system in the form of heat and W is the net reduction of energy from the system in the form of work. For an open system the law is expressed in terms of energy and work flow rates, and account must also be taken of energy associated with mass crossing the control–volume boundary.
first-level controller The low-level controller for one of the sub-systems when a complicated system is split into sub-systems by plant decomposition.
first normal-stress difference (N1) (Unit Pa) The difference, for a viscoelastic fluid, between the normal stresses in the x- and y-directions produced by a shear stress τxy. It is invariably larger than the second normal-stress difference.
first-order difference See finite-difference method.
first-order system A dynamic system fully described by first-order ordinary differential equations.
first-order transition A discontinuous phase transition, such as melting, in which heat (latent heat) is liberated or absorbed. Gibbs free energy is continuous at the transition, but a change in entropy results in the absorption or release of latent heat. See also Gibbs function; glass transition temperature.
first-yield moment (Me) (Unit N.m) The bending moment at which the maximum elastic stress in a component just reaches the yield stress σyield. For a rectangular beam of width 2b and depth 2h, Me = 4bh2σyield/3. See also shape factor.
fir-tree root The serrated wedge-shaped end of a turbine blade used to fix it in a slot of similar design in the shaft.
fishtail burner (flat burner) A burner in which gas is injected through a narrow slot or a line of closely-spaced ports. The flat flame produced may be parallel if the ports are parallel to each other or divergent if they are at angles causing the flame to fan out.
fission See nuclear fission.
fit See limits and fits.
fitted bolt A bolt with a plain unthreaded portion immediately beneath the head. See also machine screw; shoulder bolt.
fittings The small, often standard, parts of a machine or mechanism. See also pipe fittings.
fixed-active tooling A term for powered stationary accessories in a robot system such as a parts feeder or conveyor.
fixed-ended beam See fixity.
fixed error See error (1).
fixed-passive tooling Unpowered stationary accessories, such as jigs and fixtures, in a robot system.
fixed-pitch propeller A propeller for aircraft, marine, or wind-turbine applications for which the pitch has been optimized for optimum efficiency, low vibration, etc. and cannot be adjusted during operation. See also controllable-pitch propeller.
fixed plug In the manufacture of seamless tubing, a conical plug fixed in position within the drawing die which controls the internal diameter of the pipe. See also floating plug.
fixed point (fiducial temperature) A temperature assigned to a reproducible equilibrium state on the International Practical Temperature Scale.
fixed-stop robot A primitive robot where each joint moves between mechanical limit stops without precise control between them. The number of positions at which the robot can stop is mechanically determined and cannot be changed by a program.
fixed wave-energy converter A wave-energy system fixed rigidly either to the shore or the seabed. See also floating wave-energy converter.
fixing moment (Unit N.m) The bending moment required at some location in a beam (usually the end) in order to maintain a specified deflexion and rotation (i.e. deflexion slope).
fixity The different ways in which beams or other structural members are kept in position, idealized as pinned (having rotation and deflexion), simply-supported (rotation but no deflexion) and built-in (encastré, fix ended) (neither rotation nor deflexion).
fixture A device for holding a workpiece in a machine tool for mass production of a component. See also jig.
flame A region of hot gas in which mixing and combustion occurs from a solid, liquid, or gasesous fuel. Most flames are visible with a colour dependent upon temperature and chemical composition. The flames from pure methanol and ethanol are invisible.
flame arrester (flame trap) A device that prevents the spread of fire by forcing it through small holes such as in a wire mesh or perforated sheet. The burning gas is cooled by surface contact to the point where the flame is extinguished. An important application is to fuel-supply lines.
flame-ionization detector See flue-gas analyser.
flame speed (Unit m/s) The speed with which a flame propagates through a gaseous fuel. The speed is higher in a turbulent flame than in a laminar flame.
flame spraying A thermal-spraying process in which a consumable, typically a powder or a wire, is melted and sprayed on to a substrate to form a coating. The consumables are fed into a jet of gaseous fuel such as acetylene or propane, using air, argon, or nitrogen as the carrier fluid. See also arc spraying; plasma spraying.
flame stabilization The creation of a region in a combustion chamber where the local flow speeds are lower than the flame speed, typically a region of recirculating flow. See also swirl burner.
flame trap See flame arrester.
flange 1. Annular rims at the ends of pipes (flanged pipe) or shafts by which they may be coupled together using bolts that pass through holes in the flanges (flange coupling, flange union), or by toggle clamps around the periphery. 2. An extended rim on a wheel that positions it laterally on a track. Commonly used for railway rolling stock. 3. The top and bottom parts of an I-beam. See also web.
flank 1. The side of a screw thread. 2. The side of a cutting tool that may contact the workpiece when the cutting edge is rounded or profiled. 3. See toothed gearing.
flank angle (Unit °) 1. The angle made in an axial plane between the flanks of a screw thread and the perpendicular to the axis of the thread. 2. The angle (part of the tool signature) of the flank of a cutting tool.
flap valve A check valve (non-return valve) installed at a pipe outlet consisting of a circular disk hinged at the top, with a vertical or near-vertical seat to ensure positive closure under gravity. Applications include sewage treatment, water treatment, and water outfalls. The valve body and flap are usually cast iron and the seat bronze, leather, or elastomer.
flare burner A burner consisting essentially of a tall, chimney-like, vertical tube through which flow combustible waste gases, such as the unwanted by-products of refining or other processes, including waste gas from landfill, that mix with air at the tube outlet where they are ignited. The burner may be shrouded by a cylindrical outer tube. The flame at outlet is termed a flare.
flared tube A circular tube that increases in diameter at one or both ends.
flash (fin) In drop-forged and moulded components, excess material that has been squeezed into thin fins at the join of closed dies.
flash boiler A boiler in which water flows through tubes at such a high temperature that superheated steam is produced almost immediately without further heat addition.
flashing (flash boiling) The process of producing flash steam.
flash point (Unit K) The lowest temperature at which a volatile liquid can vaporize to produce an ignitable mixture in air. See also autoignition temperature.
flash steam If water at high pressure is allowed to drop to a low pressure, flash steam is produced if the initial temperature is higher than the saturation temperature corresponding to the low pressure. It is commonly produced in a power plant from hot condensate.
flash-steam power plant A steam-power plant supplied with high-pressure brine from a geothermal source at a temperature above about 180°C. The brine is sprayed into a tank at low pressure where it rapidly vaporizes (flashes) before entering a steam turbine. Condensed steam and waste brine from the flash tank are reinjected into the geothermal reservoir. See also dry-steam power plant.
flash-steam power plant
flat belt A belt of rectangular or trapezoidal cross section used to transmit power between pulleys. See also toothed belt.
flat-blade turbine impeller A mixing device suitable for high-viscosity liquids and slurries and consisting of a number of flat radial blades attached to a central driveshaft. The plane of each blade may be parallel to the shaft axis or at an angle to it, often 45°. The diagram shows an impeller of radius R rotating at angular velocity ω, immersed in a liquid of density ρ and dynamic viscosity μ. See also pitched-blade turbine impeller; Rushton impeller.
flat-blade turbine impeller
flat burner See fishtail burner.
flat crank (flat crankshaft) A crankshaft in which the throws are 180° apart so that in an engine the pistons are horizontally opposed. Commonly used for high-performance V8 petrol engines. See also vee engine.
flat engine See vee engine.
flat-flamed burner See fishtail burner.
flat-foot follower See mushroom follower.
flatness 1. See surface roughness. 2. (flatness factor) See kurtosis.
flat-plate air collector See solar collector.
flat-plate boundary layer (flat-plate flow) A boundary layer that develops in the absence of a streamwise pressure gradient, as it would on a flat surface in a flow of unlimited extent aligned with the surface. See also Blasius problem.
flat-plate solar collector See solar collector.
flat-plate water collector See solar collector.
flat spring A spring in the form of a cantilever.
flaw 1. A defect, imperfection, or blemish in a manufactured component 2. A visible or hidden crack, void, or discontinuity in a solid material. See also fracture mechanics; sonic flaw detection.
flaw detection Identification of the location and size of a flaw by means of dye penetrant, ultrasonic, or other methods. See also sonic flaw detection.
FLD See forming limit diagram.
Flettner rotor A vertical circular cylinder rotating about its own axis that generates a horizontal lift force perpendicular to a flow of fluid transverse to the cylinder as a consequence of the Magnus effect.
Flettner ventilator A ventilator in which an extraction fan is driven by a Savonius wind turbine, commonly employed on caravans, buses, buildings, etc.
flex disc See giubo coupling.
flexibility See compliance.
flexible coupling A coupling that connects two misaligned shafts where the connexion is made using deformable materials such as rubber or steel springs, as opposed to the stiff metal tongues of an Oldham coupling.
flexible manufacturing system (FMS) A manufacturing system that is not dedicated to the production of a single component, as in mass production, but is capable of producing a variety of components through computer control of a series of linked machine tools. FMS is particularly useful for the production of batches in relatively small numbers, say 50 to 500.
flexible shaft A drive shaft that is capable of transmitting rotary motion around corners. See also Bowden cable.
flexible tooling 1. A term for common magazines for holding tools that may be used on a number of adjacent machine tools. 2. Fixtures for a machining centre which are capable of positioning and securing a variety of components. 3. A reusable tool bed in the forming of composites, in which the shape and curvature of the mould may be altered.
flexometer A device for applying a cyclic load to rubber and elastomeric materials and measuring the resulting temperature increase which gives information about heat generation, anisotropy, time of cure, softening, and stiffening due to flexing.
flexural axis The axis about which a beam or plate is bent.
flexural centre See shear centre.
flexural compliance (Unit m/N) The inverse of flexural stiffness.
flexural rigidity (flexural modulus) (Unit Pa.m4) In elastic bending, the product EI where E is Young’s modulus and I is the second moment of area about the neutral axis in the plane of bending.
flexural shear The shear stresses and strains that exist in bent bodies is caused by non-uniform moments. The shear stresses and strains are zero on the top and bottom surfaces in the plane of bending and are a maximum at the neutral axis. For a rectangular beam of depth h and width b, the distribution of shear stress is parabolic with maximum shear stress given by 3V/2bh where V is the shear force. The maximum shear stress is thus 50% greater than the average shear stress. Shear in bending is important in beams of short span.
flexural stiffness (Unit N/m) The ratio of the force on a beam in bending to the resulting deflexion under the load, in particular to the tip deflexion of a loaded cantilever.
flexural strength (modulus of rupture) (Unit Pa) The bending stress at which a beam made of a brittle material fractures. It does not have an absolute value, as it depends on the testpiece and inherent flaws. See also fracture mechanics.
flexure theory See beam theory.
flitched beam See sandwich beam.
flitched girder See sandwich beam.
float 1. An object partially submerged in a liquid as a consequence of a lower average density than the liquid, used e.g. to act as a gauge (a float gauge) that indicates the position of the surface of a liquid in a tank. 2. (float valve) A component that operates a needle valve to control the flow of petrol into a carburettor and maintain a constant level in the float chamber. 3. (floating) The situation whereby an object, such as a balloon, with an average density lower than that of the fluid in which it is fully or partially immersed rises until its weight is balanced by the buoyancy force. See also Archimedes principle.
float chamber (float bowl) A small reservoir in which the float is located and from which petrol is supplied to the throat of a carburettor.
float-glass process (Pilkington process) A method of manufacturing sheet glass by floating molten glass on a bath of molten metal, usually tin. See also Fourcault process.
floating control A control method where the rate of approach to the set point is inversely proportional to the error. Particularly used to describe hydraulic and pneumatic valves that can vary the rate of fluid flow rather than simply switching between open and closed.
floating element A small section of a surface, over which there is a fluid flow, isolated from the surrounding surface by a narrow gap and attached to a sensitive load cell or other electrical balance below the surface which measures the tangential force on the element allowing the local surface shear stress exerted on the surface to be estimated. A similar technique is employed to determine interfacial tractions between die and metal flow in plasticity, and between tool and chip in cutting.
floating-head heat exchanger A shell-and-tube heat exchanger in which the tubesheet that supports the tube bundle is free to move within the shell and so minimize thermal stresses within the tubes.
floating plug In the manufacture of seamless tubing, the wall thickness and diameter of the tube are reduced by drawing through a conical die over either a mandrel or a plug. Plugs floating within the die gap control the inside diameter and remain in position by equilibrium between forces normal to the surface of the cone and the frictional drag along the surface of the cone. See also fixed plug.
floating shoes In a drum-brake arrangement, brake shoes that are machined to match precisely the internal radius of the drum and pivoted in such a way that they are free to contact the drum over their entire length.
floating wave-energy converter An offshore wave-energy converter freely floating on the ocean surface but held in position by mooring lines. See also fixed wave-energy converter.
float switch A switch actuated by the rise and fall of a float on the surface of a liquid.
float valve See float (2).
flood To supply so much fuel to an engine that it cannot form a combustible mixture with the air available.
flood generation See tidal energy.
flow 1. The movement of a fluid, such as through pipes or a machine or around an object or of one fluid within another. See also fluid mechanics. 2. The permanent change of shape imparted to a workpiece by plastic deformation, as in rolling, extrusion, etc. See also plastic flow. 3. The continuous or intermittent movement of solid material, usually in a specified direction, such as coal or powder on a conveyor belt.
flow channel See conduit.
flow chart (flow diagram) A graphical representation, using standard symbols, of the steps in a process. The technique may be applied to a wide range of processes including major engineering projects, manufacturing processes, chemical-production processes, and computer programs.
flow coefficient 1. For a pump, turbine, compressor, or fan, a non-dimensional measure of volumetric flow rate defined by /ωD3 where ω is the angular rotation speed and D is a characteristic diameter. 2. For a Bernoulli obstruction flow meter, a factor introduced into the theoretical equation for the flow rate to account for losses.
flow-control valve A valve that regulates the rate or pressure of fluid flow through a pipe system or out of a pressure vessel.
flow curve 1. The true stress–true strain curve of a plastically-deforming solid. 2. (rheogram) For a non-Newtonian liquid, a graph of shear stress or apparent viscosity vs shear rate.
flow energy (convected energy, flow work, transport energy) (Unit J) The work required to cause mass to flow across the boundary of a control volume. Per unit mass it is given by pʋ where p is the fluid pressure and v is its specific volume. See also specific property.
flow-induced vibration A vibration caused by unsteady, especially periodic, motion of fluid flowing through or around a structure, machine, or device. See also vortex shedding.
flowline The path taken by an element of metal in plastic flow, sometimes called a streamtube.
flow measurement 1. The process of determining the mass or volumetric flow rate for fluid flow in a pipe, duct, or channel using a flow meter (flowmeter). 2. The process of determining velocity using instrumentation such as hot-wire and laser-Doppler anemometers and particle-image velocimeters.
flow mixer See in-line mixer.
flow nozzle See Bernoulli obstruction flow meter.
flow passage See conduit.
flow rate (flowrate) The rate at which fluid, or fluid-borne solid particles, flows through a pipe, duct, flow meter, or machine. It may concern either mass flow rate (unit kg/s) or volumetric flow rate (unit m3/s).
flow rules The relations, in plasticity theory, between increments of true strain and the current true stresses. There is a different flow rule associated with every yield criterion. For the isotropic von Mises yield criterion, 
with corresponding expressions for dε2 and dε3 by altering the suffices, where 
is the effective stress and d
is the effective strain increment, σ1, σ2, and σ3 are the principal stresses, and dε1, dε2, and dε3 are the principal strain increments. In general,
where f is the yield criterion and G is a scalar that may depend on stress, strain, and history. In total-strain (Hencky) plasticity theory, incremental strains dε1 etc. are replaced by total strains ε1 etc. See also Levy–Mises equations; Prandtl–Reuss equations.
flow stress (Unit Pa) The true stress during plastic deformation.
flow transmitter A system that incorporates a flow meter to measure flow rates for fluid flow through a pipe and provide the output in the form of an electrical signal.
flow variable Any physical parameter that either varies in a fluid flow or influences it, such as velocity, vorticity, shear stress, turbulence intensity, pressure, density, temperature, and enthalpy.
flow visualization Any technique that allows the features occurring in a flow to become visible. In fluid flow, the introduction of smoke into a gas flow, dye or particles into a liquid flow is employed. There are also optical techniques such as shadowgraphy, Schlieren and interferometry that allow density variations in a flow to be made visible. In plastic flow, patterns of grids or circles are marked either on the interior surfaces of split testpieces before deformation, or on the exterior surfaces of sheets, and their distortion determined after flow by direct measurement or using image recognition software. Speckle interferometry is also employed with sheets.
flow work See flow energy.
fluctuating stresses (Unit Pa) The shear stresses that arise in unsteady fluid flow, especially turbulent flow, as a consequence of momentum transfer due to correlated velocity fluctuations in orthogonal directions. There are also normal stresses due to fluctuations in a given direction. See also fatigue.
flue A passage through which mainly gaseous products of combustion, also including any excess oxygen and particulates, from a furnace, oven, or fireplace (flue gas), flow to a chimney or pollution-treatment system. A fan (flue exhauster) may be used to enhance the gas flow.
flue-gas analyser An instrument used to monitor the composition of the flue gas from a furnace to check whether emissions, including unburned hydrocarbons (UHC), carbon monoxide (CO), oxides of nitrogen (NOx), sulfur dioxide (SO2), and hydrogen sulfide (H2S), are within allowable limits, and to analyse furnace efficiency. The analysis methods used include: a flame-ionization detector (UHC); a non-dispersive infrared detector (carbon dioxide and CO); a chemiluminescent analyser (NOx). See also exhaust-gas analyser.
flue-gas expander (hot-gas expander) A gas turbine used to recover energy from hot, often high-pressure, exhaust or flue gas.
flue-gas stack See smoke stack.
flueric element A term sometimes used for a dynamic fluidic device.
fluid A continuous material that cannot support a shear stress when at rest but undergoes unlimited deformation without fracture. Some fluids exhibit a yield stress and so have the characteristics of a solid material at shear stresses below that level. Gases, vapours, liquids, and slurries are all fluids. The physical property that distinguishes any real fluid from a solid is viscosity, the distinction, in materials science, being drawn conventionally at a value of 1014 Pa.s. See also Bingham plastic; dynamic viscosity; ideal fluid; non-Newtonian fluid.
fluid amplifier See fluidics.
fluid capacitor (fluidic capacitor) A device in which pressure energy can be stored in a compressed fluid. Similar to an accumulator, but usually on a smaller scale.
fluid-controlled valve A valve actuated by pneumatic or hydraulic pressure.
fluid coupling (fluid clutch, fluid drive, fluid flywheel, hydraulic clutch, hydraulic coupling, hydraulic drive, turbo coupling) A type of clutch used in motor- and marine-vehicle drive trains consisting of an impeller driven by the engine and a vaned output rotor coupled to the gearbox, the impeller/rotor pair being in close proximity and enclosed by a casing filled with oil. Torque is transmitted by circulation of the oil between the impeller/rotor pair.
fluid dynamics See fluid mechanics.
fluid end The parts of a pump in direct contact with high-pressure fluid, including cylinders, liners, pistons, and valves. An example is the mud pumps used in the drilling of oil and gas wells.
fluid-expansion thermometer (filled- system thermometer) An instrument for temperature measurement comprising a fluid-filled bulb connected by a capillary tube to a device that changes shape due to expansion of the fluid caused by a temperature increase, such as a Bourdon tube, diaphragm, or bellows. The fluid may be a liquid, a liquid plus its vapour, or a gas.
fluid-film lubrication See hydrodynamic lubrication.
fluid flywheel See fluid coupling.
fluidics (fluidic logic) The use of flow phenomena, such as jet impingement, separation, reattachment, entrainment, the Coanda effect, and vortex motion, to perform analogue or digital operations, such as amplification, rectification, and resistance. Fluidic devices are devices, widely used in nuclear applications, with no moving parts that use small pressure differences or a small proportion of the total flow (control flow) to control the overall flow, for example by switching a bistable flow from one side to another (wall-attachment amplifiers) or by causing a flow to swirl (vortex amplifiers or vortex diodes). A fluidic amplifier amplifies the difference in pressure across its control ports and increases the flow rate. In a wall-attachment amplifier symmetrical flow through a divergent channel is caused to attach to one of the walls by a control flow applied on one side. A device consisting of a fluidic amplifier with negative feedback that produces an output frequency proportional to flow rate can be used as a fluidic flow meter (fluidic oscillator meter). In a fluidic diode there is either much higher resistance to flow in one direction than the other or high resistance is created by the control flow, e.g. by causing the flow to swirl as in a vortex diode which consists of a flat circular chamber with the supply flow entering radially at the periphery and the control flow entering tangentially. In the case of a fluidic cascade diode (fluid-flow rectifier, fluidic rectifier), flow in the high-resistance direction is progressively caused to swirl by a series of stators of increasing angle of attack. Pressure ratios approaching 200 are possible. The term fluidic rectifier is also used to mean a fluidic device that reduces the fluctuation levels in a periodic flow. Any fluidic device designed such that an increase in back pressure caused by partial or total blockage of an outlet can be used as a proximity sensor (fluidic sensor). The term fluid network is a combination of fluidic devices represented by capacitance, resistance, and inductance elements.
fluidity (ϕ) (Unit 1/Pa.s) The reciprocal of dynamic viscosity. A measure of the tendency of a fluid to flow.
fluidization The process created by a fluid flowing upwards through a column of solid particulate material at a sufficiently high rate that the drag force on some or all of the particles is sufficient to overcome their weight. If the resulting fluidized bed consists of particles of different densities, the lighter particles will rise to the surface and the heaviest sink to the bottom. The fluid velocity when the bed just becomes fluidized is called the minimum fluidization velocity. See also aggregative fluidization; particulate fluidization.
fluidized-bed combustion A combustion technology in which solid fuel particles form a fluidized bed through which air is blown. Limestone (primarily calcium carbonate, CaCO3) or dolomite (calcium magnesium carbonate, CaMg(CO3)2) is added to the fuel to absorb sulfur oxides. At atmospheric pressure the fuel burns at temperatures too low (below about 900°C) for oxides of nitrogen to be formed. Such systems may be used to heat steam boilers. See also pressurized fluidized-bed combustion.
fluid-logic system A system of connected elements that utilize orifices, diaphragms, valves, etc. to control the flow in a pneumatic or hydraulic circuit.
fluid mechanics The study of fluids in motion (fluid dynamics) or fluid statics where there is no relative motion between fluid particles. Fluid statics concerns primarily the variation of pressure with altitude or depth; it includes aerostatics and hydrostatics. Fluid dynamics includes the topics of aerodynamics, gas dynamics, hydraulics, hydrodynamics and many aspects of acoustics, chemical engineering, flight, lubrication, meteorology, non-Newtonian fluid flow, oceanography, power-plant technology, propulsion, and turbomachinery. It involves the application of the laws of mass, momentum, and energy conservation. In continuum mechanics generally, both Eulerian and Lagrangian formulations are possible, but for fluid flow the Eulerian approach is almost always employed. In general there is a balance between shear stresses, pressure gradients, and inertia represented for a Newtonian fluid by the Navier–Stokes equations, a set of non-linear partial differential equations. The general situation includes fluid properties that depend upon pressure and temperature, imposed unsteadiness or turbulent flow that arises from instabilities. Exact analytical solutions are limited to simple flows such as fully-developed, steady, laminar pipe flow of a constant-property fluid (Poiseuille flow). More generally, even for relatively simple steady, laminar flow, numerical methods must be resorted to. For example, the situation of a developing laminar boundary layer in the absence of a free-stream pressure gradient (Blasius problem) requires numerical solution. Full numerical solution of turbulent-flow problems (DNS) is beyond the scope of any existing computer except for quite low Reynolds numbers, and it is necessary to resort to sophisticated turbulence modelling, in which many terms in the transport equations for turbulent kinetic energy, dissipation, etc. are modelled empirically. Many practical problems are dealt with by making simplifications that allow either analytical or numerical solution. Examples include one-dimensional analysis of compressible gas flow, including shock waves, and laminar boundary-layer theory including pressure-gradient effects. Extensive use is made of dimensional analysis to identify the non-dimensional parameters and variables that characterize a flow and enable analytical or numerical calculations and experimental data to be presented in the most compact form possible. The Reynolds, Mach, and Froude numbers arise most frequently together with the Stanton, Nusselt, and Prandtl numbers for problems involving convective heat transfer. The complexity of fluid-flow analysis is significantly greater for non-Newtonian fluids.
fluid meter See flow meter.
fluid network See fluidics.
fluid ounce (fl oz) A non-SI unit of volume. The conversion of the imperial fluid ounce to SI is 1 fl oz (UK) = 28.413 075 00 × 10−6 m3. The conversion of the customary US fluid ounce to SI is 1 fl oz (US) = 29.573 529 58 × 10−6 m3.
fluid particle (material particle) A mass of fluid that can be treated as having infinitesimally small volume, but which contains a sufficient number of molecules for the continuum hypothesis to apply.
fluid pressure See pressure.
fluid spring A spring that uses the compressibility of a gas to provide compliance, typically in a piston–cylinder arrangement.
fluid statics See fluid mechanics.
fluid stress (Unit Pa) The stresses that arise in fluid flow are pressure (a normal stress) and shear. See also stress (2).
flush 1. Said of independent adjacent surfaces that are at the same level. 2. See purge.
flute A helical groove such as on the inside of a rifle barrel or the outside of a twist drill.
flutter A form of flow-induced vibration in which energy from a flow causes a contiguous elastic structure to vibrate at one of its natural frequencies, resulting in vibration amplitudes that increase the aerodynamic forces causing vibration, until a point is reached where either the structure fails or there is sufficient damping to limit the amplitude. Flutter can affect aircraft wings, chimneys, bridges, valves, etc. See also chatter.
flutter valve See reed valve.
flux 1. See brazing; soldering; welding. 2. In fluid mechanics and heat transfer, the quantity of a substance or property transported per unit area. See also Darcy flux; heat flux; mass flux; momentum; radiant flux.
flux density See radiant flux density.
fly ash Fine, glass-like, particulate matter in the flue gas resulting from the combustion of ground or powdered coal and other solid fuels.
flycutter 1. A milling cutter having only one tooth employed to finish-cut soft materials, fine surfaces being produced as swarf does not get trapped under the tool. 2. A revolving arm, attached to the end of which is a cutting tool, employed to cut holes of large diameter in sheet material. See also trepanning tool.
flypress A press actuated by a vertical square screw thread, to the bottom of which is attached a punch for stamping out shapes in thin sheets of metal, and at the top of which are attached two heavy balls at the ends of an arm to give a large moment of inertia and hence large energy-storage capacity. It is also used for press fits.
flywheel A device used to store energy and to smooth out motion that is either (a) intermittently driven (e.g. a single cylinder engine) or (b) has energy removed periodically (e.g. a crank press). It is typically a heavy rotating wheel having a large moment of inertia.
FMS See flexible manufacturing system.
foam 1. (froth) A concentrated dispersion of gas bubbles in a detergent or other surfactant solution. Applications include mineral separation from extracted ore (froth flotation), drilling fluids in oil production, and agents to fight oil fires. 2. Cellular polymer or rubber material containing many bubbles, that may be isolated (closed-cell foam) or interconnected (open-cell foam). So-called flexible foams are deformable, while ‘rigid foams’ are stiff. See also polyurethane; sponge.
focusing collector See parabolic-bowl concentrator; parabolic mirror; solar concentrator.
foil Thin sheets of metal of thickness typically 5 to 50 μm (often expressed as wire-gauge numbers), such as aluminium, copper, brass, bronze, silver, gold, stainless steel, and nickel (sometimes metal-coated polymer), produced by rolling and employed to make shims and spacers. Other uses include thermal insulation, packaging, shielding against electromagnetic radiation, and electrical components. Some foils (e.g. aluminium kitchen foil) are bright on one side and matt on the other, resulting from cold-rolling two sheets simultaneously, only the surfaces in contact with the rolls being burnished.
following error (follower error) The error in a control system when attempting to follow a varying set point.
foot A non-SI, imperial unit of length, now defined as 304.8 mm.
foot valve A form of check valve, often incorporating a strainer, installed at the bottom of a pump suction line to prevent backflow and aid priming.
force (F) (Unit N) A force is a push (compressive force) or pull (tensile force) applied to a body or system of bodies. It is a vector quantity requiring magnitude, direction and point of application for its complete specification. Statics is the study of forces in equilibrium applied to a body or system which may cause changes in its shape or size during a transient to a new state of equilibrium. An unknown force may be measured in terms of the final extension it produces in an elastic body, such as a spring (at which extension the load in the spring is in equilibrium with the applied force) compared with that produced by a known force. An unbalanced force applied to a body will move it or tend to move it; if applied to a body already moving, the force will change its motion. See also applied mechanics; Newton’s laws of motion.
force-balance meter See direct in-line variable-area flow meter.
force coefficient (CF) The ratio, for a wind turbine, of the actual thrust FA acting on the vanes to the thrust that would be exerted on a disc of the same diameter D as the blading by the dynamic pressure of the wind q, i.e. CF = 4FA/qπD2.
force control In mechanical property testing, where the load applied to the specimen is regulated rather than the displacement, as in hydraulic testing machines. See also displacement control.
force-controlled motion The control of a robot so as to apply a controlled force through the end effector rather than a controlled displacement.
forced-air heating A system in which air heated in a furnace is circulated by a fan through ductwork which distributes it to a building.
forced-circulation boiler A water-tube boiler in which the water is circulated by a pump rather than by natural circulation due to density differences.
forced-circulation evaporator A system in which a liquid is pumped through a heat exchanger, where it is heated but does not boil, and then through a flash vessel, where evaporation occurs. It is used for the evaporation of liquids with a high solids content, high viscosity, tendency to foul, and for crystalizers, or as a finishing evaporator for the concentration of a liquid.
forced convection See heat transfer.
forced-convection boiling (forced-flow boiling) See boiling.
forced draught See draught.
forced-draught cooling tower A mechanical-draught cooling tower with a fan at the intake to force air through the tower. See also induced-draught cooling tower; natural-draught cooling tower.
forced induction The process of forcing air at a pressure above ambient into the cylinders of an internal-combustion engine using a turbocharger or supercharger. See also natural aspiration.
forced lubrication The supply of oil under pressure from a pump to lubricate bearings in engines and other machinery.
forced vibration (forced oscillation, forced response, harmonic response) To maintain steady oscillating motion of a system in the presence of damping, it must be ‘forced’, i.e. a periodic disturbing influence must be applied. Where the system is linear, the response will be of the same frequency as the input but the phase and amplitude will vary according to the frequency. See also free oscillation.
forced vortex See Rankine vortex.
force feedback Feedback in which the signal is the force applied by the plant. Used, for example, in force-controlled motion.
force fit See limits and fits.
force polygon See funicular polygon.
force pump A reciprocating pump used to pump liquids. Depending upon the valve arrangements, it may be single- or double-acting.
force ratio See mechanical advantage.
force transducer (force gauge) Any device for measuring an applied force. Modern transducers are usually based upon a load cell. See also dynamometer (2).
Forchheimer flow See Darcy’s law.
forge The workplace, including fire, furnace, and equipment, in which forging is carried out.
forge welding See welding.
forging 1. A method of component manufacture by hammering metal by hand or by machine (drop forge, press). 2. A part made by the process of forging.
form cutter See toothed gearing.
form generation See toothed gearing.
forming The process of shaping materials (particularly metals) into separate items such as beverage cans, or the manufacture of feedstock (such as rolled sheet) for further processing. See also cold working; hot working; warm working.
forming limit diagram (FLD) In sheet-metal forming, a diagram of major and minor in-plane strains during biaxial loading on which is plotted the locus of experimental strains at which localized necking occurs. Strains are determined from pre-marked circles on the surface of the sheet. Used for tool and die design. See also fracture forming limit diagram.
Fortin barometer A laboratory-standard mercury-in-glass barometer. Ambient pressure is estimated from the height of mercury in a vertical, precision-bore glass tube sealed at the top. The space above the mercury is evacuated. The lower end of the tube sits in a mercury reservoir held in a flexible pouch, traditionally of wash-leather, beneath which is a screw jack that adjusts the level of the mercury in the reservoir to a fixed point. The height of the mercury in the tube is read from a scale using a vernier.
forward extrusion See direct extrusion.
forward kinematics The process of determining the position and orientation of a robot end effector from the positions and angles of the joints. It is the opposite of the more useful process of inverse kinematics which determines the joint angles and positions required to achieve a specified end-effector position and orientation.
forward path The path through a control system from the set point input to the plant output, omitting any feedback paths.
forward transfer function See open-loop transfer function.
fossil fuels Naturally occurring fuels containing a high percentage of carbon (hydrocarbons), formed by the anaerobic decomposition of organisms at great depth below the Earth’s surface, including natural gas (primarily methane), oil, and coal. These fuels (particularly oil) are refined to produce petroleum, kerosene, etc.
Föttinger coupling The original name for a turbo-coupling. See also fluid coupling.
fouling factor (fouling resistance, R) (Unit m2.K/kW) An empirical factor used to account for the additional thermal resistance to heat transfer caused by deposits on, or corrosion of, a heat-transfer surface.
foundry A place where metals are melted and cast into moulds to manufacture intricately-shaped components.
four-ball tester An instrument, in which one ball is rotated under load against three stationary balls, to assess the performance of lubricants as indicated by the extent of wear scars on the balls.
four-bar linkage (four-bar chain) Four links pinned together to form a trapezium, the motion of all corners of which follows from the motion of adjoining elements. In many applications, one element is fixed, an adjoining link is a crank, and the other arms form part of a mechanism that performs repetitive motion. See also kinematic chain; kinematic pair.
Fourcault process A method for manufacturing flat glass by drawing a sheet vertically upwards from a pit of molten glass. Now largely superseded by the float-glass process.
four-cylinder engine A piston engine with four cylinders, in an in-line, vee, or boxer configuration.
475°C embrittlement A change that occurs in ferritic stainless steels when they are held in the temperature range 450–550°C, resulting in a severe loss of toughness and an increase in hardness. Such embrittlement is avoided by rapid cooling after annealing.
Fourier analyser A spectrum analyser that determines the frequency spectrum by applying a fast Fourier transform to the input signal. Modern analysers are software- rather than hardware-based.
Fourier number (Fourier modulus, F, Fo) See heat transfer.
Fourier’s law of heat conduction (Fourier’s heat equation) See heat transfer.
Fourier transform A mathematical process for the decomposition of a time-domain function or signal into its component frequencies so that the amplitude and phase of each frequency is determined. The process can thus be used to produce the frequency spectrum of a signal with applications such as in a spectrum analyser. See also fast Fourier transform.
four-jaw chuck A chuck, the four jaws of which may be moved independently so as to grip non-circular workpieces.
four-stroke engine An internal-combustion engine operating on a practical four-stroke cycle. For a given cylinder, as shown in the first diagram, each cycle consists of (i) intake of a fuel/air mixture, (ii) compression, ignition and combustion, (iii) expansion, and (iv) exhaust. The dashed lines in the second diagram show the variation of cylinder pressure (p) with cylinder volume (𝓥). For a real spark-ignition engine, the cycle is approximated by the Otto cycle shown by the unbroken lines. See also two-stroke engine.
four-stroke engine
http://www.animatedengines.com/otto.html
• Animation and explanation of the principles of a four-stroke engine
four-way valve A two-position flow-control valve, the body of which has four ports A, B, C, and D. In one position, A and B, C and D are connected. In the other A and D, B and C are connected. There is also a fully-closed position.
four-wheel drive A motor vehicle in which power is transmitted to all four wheels, including those steering, usually from a single engine.
fracking See hydraulic fracturing.
fractional pitch See screw.
fractography The study of the surfaces of broken components in order to establish the type and cause of fracture. See crystalline fracture; fibrous fracture.
fracture (rupture) The separation of materials, components, or structures into two or more parts by the propagation of one or more cracks. Cracking may be globally elastic (brittle) or accompanied by varying degrees of plasticity (ductile).
fracture-appearance transition temperature See ductile–brittle transition temperature.
fracture deformation map See deformation-mechanism map.
fracture forming limit diagram (FFLD) A forming limit diagram on which the locus of fracture, as well as necking, strains is plotted.
fracture mechanics The stress analysis of bodies containing cracks. The use of stress-concentration factors and other correction factors of traditional strength of materials is inadequate when flaws are present initially (or develop during loading), since fracture depends not only on stress but also the size of the crack. Traditional strength of materials stress calculations cannot predict either the safe working stress in the presence of a known flaw, or the critical size of flaw just tolerable with a given working stress.
At the instant of fracture, stresses throughout the body may be smaller than the yield stress σy and therefore within the elastic range, so that after fracture the broken parts may be refitted to regain the original size and shape of the cracked body (brittle fracture). Alternatively, at fracture the working stresses may exceed the yield stress resulting in regions of plasticity where the body is permanently distorted to varying degrees. In such elastoplastic (ductile, post-yield) fracture, it is impossible to refit the broken parts to regain the original size and shape of the fractured component. Fracture toughness is the property of a material that determines its resistance to cracking. The basic definition of this rate-, temperature- and environment-dependent mechanical property is the work required to propagate a crack by unit area and given various symbols (R, GC, JC), the subscript C meaning ‘critical’. Initiation work is performed in the fracture process zone at the tip of the crack that, on propagation, forms thin boundary layers contiguous with the crack faces. Values range from 10’s of J/m2 for brittle materials, to kJ/m2 for ductile materials. An alternative measure of toughness is the critical crack opening displacement (CTOD) with symbol δC. Yet another is the critical stress-intensity factor KC having the peculiar unit N/m3/2, i.e. 
. These different ways of defining the same physical property mean that they must be related, and R = mσyδC, where σy is the yield stress and m = 1 for plane stress and 3 for plane strain; 
where E is Young’s modulus (from which the peculiar unit follows). Note that KC is also sometimes confusingly called the fracture toughness.
Depending upon conditions, brittle and ductile cracks may variously propagate in tension, in-plane shear and out-of-plane (through-thickness and twisting) shear, such modes of fracture being called by the Roman numerals I, II and III. The fracture toughnesses may differ in magnitude in the different modes and are designated by RI, RII, and RIII (similar subscripts are employed with GC, JC, KC, and δC).
modes of fracture
Toughness also depends upon constraint, so that cracks propagating in plane stress (with through-thickness deformation) experience greater resistance than those in plane strain where through-thickness deformation is inhibited and hydrostatic stresses are consequently higher. Values for the lower plane strain fracture toughness are used for conservative design. To ensure plane strain deformation, a specimen has to have certain minimum dimensions, in particular that its thickness B ≥ 2.5(KIC/σy)2 where σy is the yield strength. Because the plane strain KIC value is not known until after a test is conducted, yet B must be selected beforehand, a preliminary thickness is selected and a tentative toughness value (KQ) is determined, from which it may be established whether B needs to be thicker.
There are two approaches to the determination of elastic fracture stresses, the one based upon consideration of the complicated stress fields around the tips of cracks and giving rise to KC; the other based upon energy methods. Both have their parallels in the Theory of Elasticity on the one hand, and Castigliano’s theorems on the other. All linear elastic fracture mechanics (LEFM) formulae have the general form 
where σf is the fracture stress, Y(a/W) is a non-dimensional correction factor to take into account the geometry of different cracked bodies, the way of loading and so on, a is the crack length, and W is a representative dimension of the body.
In elastoplastic fracture mechanics, use is made of the equivalence between non-linear elasticity and total strain (Hencky) plasticity theory to obtain σf from the critical value of the J-integral, JC. While correct for crack initiation, it is not correct for elastoplastic crack propagation during decreasing load, as only part of the work done is recoverable. The use of JR crack resistance curves in ductile fracture mechanics is likely to overestimate the real resistance to propagation and is therefore non-conservative.
High-cycle fatigue crack propagation may be described in terms of fracture mechanics by the Paris equation and its variants: 
where da/dN is the crack growth per cycle, and C and n are material constants. ΔK is the range of stress intensity factor given by 
with σmax the biggest stress in a cycle and σmin the smallest. Integration of the Paris equation gives the number of cycles required for a crack to grow from an initial length to a longer length, in particular to the length that results in final failure.
The scale effect in fracture mechanics means that σf in large structures can be lower than σf in similar small structures, possibly lower than the yield strength of the material, and possibly even smaller than the strength of materials design stress based on the yield stress divided by a factor of safety. Hence there is a danger of brittle fracture of large structures made from materials that behave in a ductile fashion in the laboratory. It also explains the transitions with change in depth of cut between different types of chip in cutting and machining.
Employment of fracture mechanics requires knowledge of crack size (a in the formulae above). In the absence of obvious cracks in brittle materials, a is identified with microstructural features. With ductile materials, cracks are initiated during loading through the formation of voids at inclusions and hard second-phase particles which grow and coalesce. The rate of void growth depends upon hydrostatic stress and plastic strain for which there are various mathematical expressions. In welds, slag inclusions act as starter cracks. See also cohesive zone; critical crack tip opening displacement; damage mechanics; design methodologies; fatigue; Johnson–Cook fracture equation; Kachanov’s theorem; leak-before-burst; R6 failure assessment diagram; threshold stress-intensity factor.
fracture-mechanism map See deformation-mechanism map.
fracture mechanisms The microstructural mechanisms that cause fracture, such as void initiation, growth and coalescence, cleavage.
fracture strength (fracture stress) (Unit Pa) The stress at which a material breaks. It is not absolute for a given material, as it depends on the laws of fracture mechanics and is size-dependent. See also modulus of rupture.
fracture test 1. The recording of load-deflexion (or stress–strain) in a specimen loaded monotonically until it breaks in tension, compression, shear, or torsion. 2. In fatigue, determination of the number of cycles to fracture for a specimen under different patterns of repeated loading. 3. Experiments to determine fracture toughness.
fracture toughness See fracture mechanics; specific work of fracture.
fracture transition plastic temperature See ductile–brittle transition temperature.
frame of reference Any set of axes to which points in space, moments in time, etc. may be referred, typified by the Cartesian, polar, cylindrical, and spherical-polar coordinate systems. Frames of reference may move but are usually fixed. See also inertial coordinate system; accelerating frame of reference.
framework See structural analysis; strut; tie.
Francis turbine A high-efficiency (c.90%) mixed-flow hydraulic reaction turbine with a spiral inlet scroll (or volute) followed by radial inlet guide vanes and a runner through which the flow turns into the axial direction where it flows to the draft tube and the tailrace.
frangible A qualitative term for ease of fracture.
free-air delivery (FAD) (Unit m3/s) The volumetric flow rate of air delivered by an air compressor converted to the ambient pressure and temperature, pA and TA, using the ideal gas law, i.e. 
where pACT and TACT are the actual pressure and temperature of the air at the compressor outlet. The air mass flow rate is given by ρACT = ρAFAD where ρACT is the actual air density at outlet and ρA is the ambient air density.
free-body diagram (FBD) When using force-equilibrium calculations in statics and dynamics, the physical limits of the system under consideration, and the nature of all forces and moments which act upon it, must be identified clearly. Any part of a body may be isolated by means of an imaginary system boundary to give a ‘free body’, the equilibrium of which is determined solely from the forces and moments acting upon it as shown by the free-body diagram. Application of Newton’s third law is particularly important in the correct assignment of internal forces for inclusion on any part-system FBD.
free convection (natural convection) See heat transfer.
free electron See interatomic bonding.
free energy See Gibbs function.
free enthalpy See Gibbs function.
free expansion (unresisted expansion) An irreversible process in which a gas expands into an evacuated insulated chamber.
free fall Strictly, the vertically downward motion of an object falling under the influence of gravity, but more frequently used to describe an object falling through the atmosphere. See also terminal velocity.
free field In acoustics, an environment free of boundaries so that outgoing acoustic waves are not scattered or reflected. See also anechoic chamber.
free flight A term for unpowered flight, such as gliding.
free gyroscope A gyroscope used in aircraft to give an artificial reference horizon during ascent or descent from level flight.
free jet A jet of fluid developing in effectively infinite surroundings.
free-jet amplifier A fluidic amplifier in which a jet, often rectangular in cross section, is deflected into downstream collection passages by control nozzles on either side of the jet nozzle.
free joint The joint on a robot arm and wrist that causes the greatest end-effector movement when a specified force is applied to the end effector, i.e. that has the lowest stiffness with regard to the force.
free-molecular flow Gas flow in which the mean-free path between molecular collisions is much larger than a characteristic dimension of a body or flow channel. For such flows the Knudsen number is much greater than unity.
free oscillation See free vibration.
free outflow The discharge from beneath an underflow gate when the liquid surface immediately downstream is open to the atmosphere. See also drowned outflow.
free-piston engine A reciprocating internal-combustion engine in which the pistons move back and forth but are not connected to a crankshaft. Dual piston engines can have separate or common combustion chambers, the pistons being linked for synchronization in the latter case. Such engines are used primarily as gas compressors or gas generators (free-piston gas generator, gasifier) to supply hot exhaust gas to drive a gas-turbine.
free-piston gauge See deadweight tester.
free power turbine See free turbine.
free-shear flow A shear flow not in direct contact with a solid boundary.
free shear layer The shear flow that develops between two contacting, parallel streams of miscible fluids having different velocities.
free stream In fluid dynamics, the region beyond the outside edge of a boundary layer, jet, wake, or other shear layer.
free-stream turbulence Turbulent fluctuations in the free stream of a boundary layer.
free-stream velocity (Unit m/s) The flow velocity in the free stream of a shear layer.
free surface 1. The interface between a liquid and a gas, particularly a flowing liquid. 2. The surface between a supersonic flow, such as a jet, and stagnant surroundings at constant pressure.
free turbine (free power turbine) The turbine in a turboshaft engine that powers the driveshaft, separate from that which powers the compressor. Both extract energy from the same gas stream. See also shaft turbine.
free vibration (free oscillation) A body, restrained at least at one point, when displaced from its stable position of rest and released will perform free vibrations when acted upon by a restoring force such as that provided by a spring. Under the influence of damping, free vibrations eventually die out. See also forced vibration.
free vortex See Rankine vortex.
freeze drying (lyophilization; vacuum freeze drying) A dehydrating process in which a substance, such as a food product, is deep frozen (typically at −65°C) and then subjected to reduced pressure (below 100 mbar), causing any ice to sublime. The resulting water vapour is then removed.
french coupling See Guillemin coupling.
french curves Templates composed of many different curves used in manual draughting to draw smooth lines of varying radii. The shapes are segments of the Euler spiral in which curvature changes linearly with arc length.
Frenkel defect See point defect.
frequency (temporal frequency, f) (Unit Hz) The number of cycles per second in an oscillation or the repetition rate for a cyclic process.
frequency domain The mathematical representation of a signal or system in terms of the behaviour as a function of frequency, usually obtained through taking Laplace transforms of the time-domain equations. Also used to refer to the representation of a signal through the Fourier transform.
frequency-domain analysis The analysis of a control system using the Laplace transform of its behaviour, e.g. using the transfer function. Also used to refer to analysis using the results obtained from the application of a Fourier transform.
frequency locus The behaviour of the transfer function as a function of frequency. It can be used to determine the describing function for a non-linear system.
frequency response The magnitude (in dB) or phase of the output of a system for a specified input as a function of frequency. It may also be specified as the range of frequencies that are passed by a system within a specified magnitude range. For example, a control system may be specified as having a frequency response of 0 Hz (DC) to 10 Hz with a specified maximum error. It can be represented as a graph (frequency-response curve).
frequency-response function The magnitude and phase of the transfer function of a system as a function of frequency obtained by replacing s with iω where s is the Laplace-transform variable, 
, and ω is the angular frequency. The frequency-response function is used to produce the Bode plots for a system.
frequency-response trajectory The locus plotted on the complex plane of the frequency-response function as the frequency is changed.
frequency spectrum See power spectral density.
frequency transformation A method for the design of filters based on transforming the behaviour of a low-pass filter into either a high-pass or band-pass characteristic.
frettage The expansion by internal pressure of a thick-walled vessel, such as a large-calibre gun barrel, so that the bore material deforms plastically. On unloading, the inside surfaces are both harder and in a state of residual compression, and therefore may be subjected to higher loads. The same effect produced by shrink-fitting two thick-walled tubes is termed autofrettage.
fretting The extraneous small-amplitude (<100 μm) oscillatory loading associated with cyclic relative tangential displacement between surfaces notionally in stationary contact.
fretting failure The progressive wear and eventual failure of bodies such as nut-and-bolt assemblies, bearings, and press-fitted joints subjected to fretting.
FRIC See front-to-rear interconnected suspension.
friction The resistance that a body encounters when sliding over another body, or experiences when a viscous fluid flows over its surface. See also Amontons friction; coefficient of friction; drag; dynamic friction; friction factor; rolling friction; skin-friction coefficient; starting friction; sticking friction; stiction.
frictional flow The flow of a viscous fluid.
friction angle See angle of friction.
friction bearing See bearing.
friction clutch A clutch, the engagement of which relies on friction between its plates.
friction coefficient See coefficient of friction; skin-friction coefficient.
friction damping (Coulomb damping) The damping that results from bodies sliding over one another.
friction drag See drag.
friction drive The coupling of shafts by wheels and discs in contact, operation of which relies on friction that is great enough to prevent slipping.
friction factor See Darcy friction factor; Fanning friction factor.
friction gear See friction clutch; friction drive.
friction loss (Unit J) The conversion of mechanical energy to heat due to friction within a machine, mechanism, linkage, etc. See also loss.
friction materials Materials having a high coefficient of friction which, when coupled with a long life, may be employed as brake linings or the facing of the plates of a clutch.
friction power (FHP, friction horsepower) (Unit W) The power expended in overcoming frictional losses within an engine, and in pivots, bearings, gears, etc. Friction torque (unit N.m) is friction power/engine speed. See also brake power; loss; shaft power.
friction-stir welding See welding.
friction-tube viscometer See capillary viscometer (2).
friction vacuum gauge (molecular gauge, viscosity gauge) A device used to measure very low gas pressures.
friction variable See wall variable.
friction velocity (uτ, u*) (Unit m/s) For viscous fluid flow over a solid surface, a scaling velocity particularly used in the analysis of turbulent flows defined by 
where τS is the wall shear stress and ρS is the fluid density at the surface. See also wall variable.
friction welding See welding.
frigorie (fg) An obsolete unit of heat used in refrigeration and cryogenics; approximately equal to one calorie.
front-to-rear interconnected suspension (FRIC) A suspension system for an automotive vehicle in which a hydraulic system links the front and rear suspensions to improve aerodynamic stability and drivability.
frost-point hygrometer A type of hygrometer in which a metal mirror is cooled, typically by a Peltier device, until a temperature termed the frost point is reached, at which a film of white frost is observed to appear on it.
Froude dynamometer See hydraulic dynamometer.
Froude number (Fr) A non-dimensional parameter that arises in the study of open-channel liquid flow and is defined by 
where V is the liquid speed and H is its depth, and g is the acceleration due to gravity. It is an indicator of the relative importance of inertia and gravity forces. The definition can be generalized to characterize flow at the interface between two immiscible fluids of density difference Δρ using a densimetric Foude number FrD, defined by
where 
is the average density of the two fluids. See also Richardson number; subcritical flow; supercritical flow.
frozen The state of a substance that is normally liquid at STP when caused to become solid, usually by cooling. See also molten.
frozen expansion The expansion of a gas at sufficiently high (hypersonic) Mach numbers that the gas becomes so rarefied that molecular collisions no longer occur, and limiting conditions are reached.
frozen-stress technique A method of analysing 3-dimensional stress distributions using 2-dimensional photoelasticity, in which the model is annealed while under load. This preserves the birefringency after unloading and the model can be sliced into sections, each of which is analysed as a plane problem. To avoid the need for polishing the cut surfaces, the sections are examined in a fluid having a refractive index the same as that of the model material.
frustum A solid object that is regular in cross section (not necessarily uniform) and has two plane parallel ends. Examples are a truncated cone or pyramid.
FTP See ductile–brittle transition temperature.
fuel 1. A substance from which energy can be extracted: by combustion to give thermal energy in the case of a liquid, gaseous, or solid fossil fuel or biofuel; by nuclear fission to give thermal energy from a radioactive substance. 2. A substance from which electrical energy can be produced by chemical reaction in a battery or fuel cell.
fuel assembly (fuel bundle, fuel element) A structured group of fuel rods in a nuclear power reactor, or one or more fuel rods in a research reactor.
fuel bed A layer of fuel in a solid-fuel combustion system.
fuel cell A device that converts a fuel and oxidant, such as hydrogen and oxygen, into electricity directly (i.e. without combustion).
fuel consumption (Unit kg/hr) The mass rate at which an engine, furnace or other power-producing device must be supplied with fuel to operate. See also specific fuel consumption.
fuel element See fuel assembly.
fuel injection The supply of pressurized liquid fuel to an engine or furnace by a mechanical pump.
fuel oil Any liquid hydrocarbon (single or blended) that is burned in a furnace, boiler or engine. Most are distilled from petroleum, and they range from low-viscosity products with a low boiling point (around 175°C), such as kerosene, to viscous, heavy fuel oils which boil at about 600°C. See also fossil fuels.
fuel rail A supply tube through which high-pressure fuel flows from the injector pump directly to the individual injectors of an internal-combustion engine.
fuel rod A long, slender metal tube containing pellets of fissionable material which provide fuel for a nuclear reactor. See also fuel assembly.
fuel system (fuel-supply system) The entire fuel-delivery system for an engine or furnace, which may include: the reservoir in which fuel in liquid or gas form is stored (fuel tank); the fuel pump(s) that delivers liquid fuel through a line from a fuel tank; the pipe or tube through which a gas or liquid fuel is delivered (fuel line); a main supply pipe that distributes fuel through smaller branch pipes (fuel manifold) e.g. to each combustion chamber of a gas turbine; the nozzle arrangement that converts liquid fuel to a spray (fuel injector) e.g. as it is injected into the combustion chamber of an engine; a fuel filter installed in a fuel line to remove particulates; valves, control units, and heaters. See also injection pump; petrol injection.
fulcrum The point at which a lever is supported and turns. See also pivot.
full admission The admission of working fluid into a turbomachine over its full circumference. See also partial admission.
full life-cycle analysis See life-cycle analysis.
fully-developed pipe flow (fully-developed duct flow) Flow in a long pipe or duct of constant cross section that has reached a location beyond which there are no changes in the distribution of any flow quantity. For turbulent flow, this applies to the time-averaged flow. See also developing flow; Poiseuille flow.
fully-plastic moment See plastic hinge.
fully-rough flow The regime, for turbulent boundary-layer and pipe flow over a rough surface, where the skin-friction coefficient or friction factor is independent of Reynolds number. For pipe flow, this is when the sand-grain-roughness height k exceeds about 70ν/uτ, ν being the kinematic viscosity of the fluid and uτ the friction velocity. See also hydraulically-smooth surface; transitional roughness.
functional decomposition The design of a control system by splitting the system into components with specific actions, for example the regulator, adaptive control element, and optimal control element.
functional design A design technique that concentrates on achieving the overall objectives required of the system being designed, without detailed reference to individual components. This is achieved by the assembly of individual sub-systems having specified input–output characteristics which only interact through their inputs and outputs.
functional dimension A dimension on an engineering drawing that directly affects the function of a part or an assembly.
fundamental derivative (Γ) In gas dynamics, a non-dimensional measure of the dependence of sound speed c on density ρ, defined by
where the subscript S denotes an isentropic process.
fundamental dimension See dimension (1).
fundamental frequency (Unit Hz) The first harmonic of a periodic signal.
fundamental interval The interval between two fixed points on a temperature scale that is divided into units of temperature; 100° for the Celsius scale and 180° for the Fahrenheit scale.
fundamental mode The mode of free oscillation of an oscillatory system with the lowest natural frequency, i.e. at the fundamental frequency.
fundamental physical constant (universal constant) A physical quantity which is universal in nature with a value which is constant with time. Such a quantity cannot be derived from more fundamental principles. The number of fundamental physical constants is about 70. Those of most relevance to mechanical engineering are the Avogadro number, the Boltzmann constant, the Newtonian constant of gravitation, the Planck constant, the speed of light in vacuum, the Stefan–Boltzmann constant, and the universal gas constant. Minor adjustments to the values of these constants were introduced in May 2019. See also atom; International System of Units.
funicular polygon A graphical construction from which the line of action of a set of co-planar forces may be obtained. In the diagram, a body has forces P1, P2, etc. applied to it. The sides 1, 2, etc. of the force polygon are parallel and proportional to the forces P1, P2, etc. The closing side 5 of the polygon gives the magnitude and direction of the resultant force P5. The funicular polygon gives the line of action of P5. It is constructed by joining an arbitrary point O to the corners of the force polygon, giving lines 1–2, 2–3 etc. and drawing, from an arbitrary point L, LA1 parallel to 5–1 cutting P1 at A1. A1A2 is drawn parallel to 1–2, cutting P2 at A2, and so on until A4A5 cuts LA1 at A5 that is a point on the line of action of P5. If the force polygon is closed the system is not necessarily in equilibrium but may reduce to a couple, revealed by the funicular polygon becoming two parallel forces acting in opposite directions.
funicular polygon
funnel 1. The chimney or smokestack on a vehicle powered by fossil fuel, such as a ship or steam locomotive, used to emit exhaust gases and steam into the atmosphere. 2. A pipe with a wide, often conical, entry used to guide liquid or fine-grained-solid material into a container.
furling speed See cut-out speed.
furnace 1. A type of combustion chamber in which solid, liquid, or gaseous fuels are burned to supply hot gases to a boiler or other process plant. Examples include the firebox, boiler furnace (steam-generating furnace), hot-air furnace, oil-fired furnace, updraught furnace, and water-cooled furnace. 2. A chamber, sometimes having a controlled atmosphere or under vacuum (vacuum furnace), for heating and melting materials. Examples include the blast furnace, direct- and indirect-arc furnaces, the induction furnace (high-frequency furnace), muffle furnace, reverberatory furnace, and solar furnace.
fused A term for materials joined together by melting and then allowed to cool, for example glass and metals.
fused deposition modeling (FDM) An additive manufacturing process involving the ejection of a thermoplastic material from a temperature-controlled nozzle to form a part layer by layer.
fusibility 1. The ease with which materials can be fused together. 2. The ease with which a substance can be melted, i.e. the amount of heat required and the temperature to which it must be raised.
fusible plug (safety plug) A safety device used on a pressure vessel, such as an LPG container, based on a metal plug which melts at a predetermined temperature to prevent the buildup of excessively high pressure and allow a controlled release. In the case of a boiler, the plug is designed to melt should the water level drop and the temperature rise to a dangerous level. Steam escapes into the firebox, gives a warning, and damps the fire.
fusion 1. See latent heat. 2. See nuclear fusion.
fusion welding See welding.
fuzzy logic An extension of Boolean (i.e. two-valued, true/false) logic to depict situations where variables representing answers to questions may be partially true, i.e. somewhere between completely true and completely false. A set of rules somewhat similar to the human decision-making process can then be applied to the variables to give fuzzy control of the system. Fuzzy control is frequently applied to large, complex systems, and to those where the control process replaces human decision-making. A fuzzy controller is a control system employing fuzzy logic to determine the input to the plant.