l

lab-on-a-chip A microfluidic MEMS device that allows laboratory operations to be conducted at micro- and nano-scales.

laboratory coordinate system An inertial (i.e. non-accelerating) Cartesian-coordinate system, with axes x, y in the horizontal plane and the z axis vertical, which is frequently used to reference experimental observations.

labyrinth seal A low-friction mechanical seal that relies upon an extended path, for example a series of narrow closely-spaced grooves, to minimize fluid leakage. Applications include piston-cylinder arrangements and circular shafts especially to protect bearings.

ladder logic A programming method used in a programmable logic controller, based on the representation of sequential program steps by the opening and closing of relays, the starting and stopping of timers, and the operation of special blocks containing complex functions. A ladder diagram is a diagrammatic representation of a program produced using ladder logic. The name is derived from the similarity between the diagram and a ladder.

lag (Unit s or m or °) The delay when one event happens after another. A signal is described as lagging when it is delayed relative to another signal. See also lead; valve-timing diagram.

lag compensation See lead/lag compensation.

lagging The thermal insulation material, typically in the form of fabric tape, glass fibre, etc., that is wrapped around hot or cold surfaces such as boilers and pipes. Although still installed for some domestic and industrial applications, the use of asbestos is now illegal because of the risk of serious illnesses that can result from the inhalation of asbestos fibres.

Lagrange–Hamiltonian mechanics Newtonian mechanics expressed in terms of energy rather than forces. Particularly useful for determining the trajectories of objects moving in a gravitational field.

Lagrangian description The analysis of fluid flow and finite-deformation plasticity following the motion of individual fluid particles or material elements as they move along pathlines. See also Eulerian description.

lambda sensor (lambda probe, oxygen sensor) An electronic device that measures the fraction of oxygen in a fluid flow. Most commonly used to monitor the oxygen level in the exhaust gases from an internal-combustion engine and control the air/fuel ratio of the mixture entering the engine to control pollutants.

Lambert’s cosine law For a diffuse surface, the intensity i_ϕ of thermal radiation (unit W/m²) (see heat transfer) emitted in a given direction is given by i_ϕ = i_ncosϕ where i_n is the intensity of radiation emitted normal to the surface and ϕ is the angle between the normal and the direction of the radiation.

Lambert surface (Lambertian surface) See diffuse surface.

Lamé constants (Lamé parameters, λ, μ) (Unit Pa) In linear elasticity for a homogeneous isotropic material, the two parameters that relate stress and strain. For normal stresses where σ_i is the normal stress in a given direction, e is the volumetric strain (i.e. dilation), and ε_i is the strain in the same direction as σ_i. For the shear stresses τ_ij = 2με_ij. The first Lamé constant where K is the bulk modulus, E is Young’s modulus, and ν is Poisson’s ratio. The second Lamé constant μ is identical with the modulus of rigidity (shear modulus, G) given by G = E/2(1 + ν). See also generalized Hooke’s law; Hooke’s law.

Lamé equations For linear-elastic behaviour of a thick-walled cylinder subject to internal or external pressure or rotation, the variation of the radial stress σ_r with radius r is given by and the hoop stress σ_θ by The constants A and B are determined from the boundary conditions and the sign convention employed for stresses. For thick-walled spherical vessels, the relations are σ_r = C + D/r³ and σ_θ = C−D/r³ where C and D are constants evaluated from the boundary conditions.

lamina A plane sheet of zero thickness in theory, but in practice applied to thin layers or sheets of materials.

laminar boundary layer A boundary layer for which the Reynolds number is sufficiently low for the flow to remain laminar. For a flat-plate, zero-pressure-gradient boundary layer, the critical Reynolds number Re_x,crit is about 60 000 based upon free-stream velocity and distance from the leading edge, or 162 based upon the momentum thickness. A favourable pressure gradient increases Re_x,crit whereas an adverse pressure gradient causes a decrease, as does free-stream turbulence.

laminar flow Highly ordered and deterministic flow of a viscous fluid at Reynolds numbers below the critical value (which is different for every flow geometry) for instability and transition to turbulence to occur. Such flows may be steady or unsteady, and include both periodic and transient behaviour.

laminarization (reverse transition) A phenomenon whereby turbulent fluctuations in a flow can be suppressed, for example in a boundary layer by a strong favourable pressure gradient, and the flow then has many of the characteristics of a laminar flow.

laminate 1. A body made up of bonded layers of thin sheets. 2. To manufacture a laminate.

laminated spring See leaf spring.

lamination An individual layer within a laminate.

Lami’s theorem If three coplanar, concurrent forces act on a body to keep it in static equilibrium, each force is proportional to the sine of the angle between the other two. This follows from application of the sine rule to the equilibrium triangle of forces.

Lanchester damper A device for damping out linear or torsional vibrations, thus avoiding resonance, in which the damper spring of an undamped vibration absorber is replaced by a dry friction, or viscous friction, element. For the damping of torsional vibrations (as in the balancing of engines), the device is often referred to as a Lanchester balancer.

land 1. See toothed gearing 2. The space on a piston between two ring grooves. 3. In tapered dies, any section parallel to the flow of material.

landing gear Those parts of an aircraft, usually retractable wheels, that allow it to take off and land or to move when on the ground or water. The term undercarriage is more usual for the floats of seaplanes.

lantern ring An annular ring placed between two sets of packings in a packed gland to allow the introduction of lubricant, cooling, or flushing fluid.

lanthanoid See periodic table.

lap joint A riveted, welded, or bonded connection between two plates made by overlapping one plate above the other. Lap joints having plates above and below a butt joint avoid the bending moment associated with a simple lap joint.

Laplace pressure See surface tension.

lapping See honing.

lapse rate (γ) (Units °C/m, Pa/m, kg/m⁴, etc.) The rate of change with altitude z of a thermodynamic property (temperature T, pressure, density, etc.) in the atmosphere. For temperature, γ = −dT/dz. See also adiabatic lapse rate.

Laray viscometer An instrument in which liquid viscosity is determined from the time taken by a weighted rod placed in an orifice, both immersed in the liquid, to fall a fixed distance. Widely used to characterize printing inks.

large calorie See kilocalorie.

large-eddy simulation (LES) A method of calculating turbulent flows in which the large unsteady features of the flow are resolved while the small-scale dissipative eddies are modelled. See also turbulent flow.

large-systems control system See hierarchical control.

Larson–Miller parameter An empirical parameter that relates temperature and stress to time for rupture in tertiary creep. It is used to estimate the time necessary for stress rupture to occur at different temperatures.

laser ablation The process of removing material from a surface by irradiating it with a laser beam. The material is heated by the absorbed laser energy and either evaporates or is converted to a plasma, i.e. a hot ionized gas. Heating of underlying material is minimized by using laser pulses, thus allowing the treatment of a wide range of materials. Applications include machining, hole drilling, surface cleaning, and production of carbon nanotubes. Laser ablation is also used widely in surgery and dentistry. See also ablation cooling.

laser annealing Annealing of metals by a moving CO₂ or Nd:YAG laser beam focused down to a few mm in diameter. A point in the surface of an object is heated above the recrystallization temperature and then cooled to room temperature to remove the effects of work-hardening and restore a soft condition.

laser-Doppler anemometer (laser-Doppler velocimeter, laser anemometer, LDA, LDV) An optical instrument for determining surface velocity or flow velocity in transparent fluids by measuring the transit time of small particles in the flow or surface elements as they cross interference fringes formed at the intersection of two laser beams focussed on to the same point. See also laser 2-focus anemometer; particle-image velocimeter; phase-Doppler anemometer.

laser hardening Hardening of steel by a moving CO₂ or Nd:YAG laser beam focussed down to a few mm in diameter. A point in the surface of an object is rapidly heated into the austenite range and then rapidly cooled to form tempered martensite. See also case hardening; nitriding. Electron-beam hardening can be employed to achieve similar results.

laser micromachining The use of excimer, Nd:YAG, or CO₂ lasers in the fabrication of microchannels, either directly or using a mask.

laser scribing (laser marking) The use of excimer, Nd:YAG, or CO₂ lasers to mark the surfaces of such materials as ceramic, glass, metals, quartz, and silicon. Principal applications are in the production of semi-conductor devices, light-emitting diodes (LEDs), etc.

laser sintering A manufacturing technique by which parts are built layer by layer (each typically 20 μm thick) from plastic or metal (Direct Metal Laser Sintering, DMLS) material in powder form, each layer being sintered by a scanning laser. See also additive-layer manufacturing.

laser 2-focus anemometer An optical instrument for determining flow velocity by measuring the transit time of small particles in the flow as they cross two laser beams focussed to point foci a small, accurately-known distance apart. See also laser-Doppler anemometer.

laser welding See welding.

latent heat (heat of transformation, latent energy) (Unit kJ/kg) The amount of energy absorbed or released in a phase-change process. The magnitude depends upon the process, the temperature, and the pressure at which the phase change occurs. The latent heat of a given phase change is often referred to as the enthalpy or heat of that change.

The latent heat of condensation (h_gf) is the amount of energy released in condensing unit mass of a dry saturated vapour. It is equal to the difference between the specific enthalpies of the saturated liquid h_f and the dry saturated vapour h_g, i.e. h_gf = h_f − h_g. The latent heat of evaporation or vaporization (h_fg) is the amount of energy needed to vaporize unit mass of a saturated liquid (i.e. a liquid at its boiling point). It is equal to the difference between the specific enthalpies of the dry saturated vapour h_g and the saturated liquid h_f, i.e. h_fg = h_g − h_f, and so equal in magnitude but opposite in sign to the latent heat of condensation.

The latent heat of freezing, crystallization or solidification (h_fs) is the amount of energy released in freezing unit mass of a saturated liquid. It is equal to the difference between the specific enthalpies of the saturated liquid h_f and the solid h_s, i.e. h_fs = h_s − h_f.

The latent heat of fusion or melting (h_sf) is the amount of energy needed to melt unit mass of a solid (i.e. a solid at its melting point). It is equal to the difference between the specific enthalpies of the solid h_s and the saturated liquid h_f, i.e. h_sf = h_f − h_s, and so equal in magnitude but opposite in sign to the latent heat of freezing. The latent heat of sublimation (h_sg) is the amount of energy needed to sublimate unit mass of a solid. It is equal to the difference between the specific enthalpies of the solid h_s and the dry saturated vapour h_g, i.e. h_sg = h_g − h_s. See also enthalpy.

latent load (Unit J) The thermal energy required, in an air-conditioning system, to condense water vapour in the air.

lateral extensometer An extensometer that measures displacement perpendicular to the principal loading axis.

lathe A machine tool in which work, gripped in the headstock, is rotated against the cutting tool to produce turned, bored, faced, or threaded components. See also capstan lathe; chuck; feed screw; gap lathe; headstock; lead screw; setover; swing; tailstock; turning; turret lathe.

lattice (lattice structure) See crystal structure.

lattice–Boltzmann method A class of CFD methods in which, instead of solving the Navier–Stokes equations, fluid flow is simulated using discrete particles that undergo consecutive propagation and collision processes over a discrete lattice mesh.

lattice girder An open framework built of two principal members joined by criss-cross reticulated members.

Laval nozzle (de Laval nozzle) See convergent–divergent nozzle.

law of action and reaction See Newton’s laws of motion.

law of corresponding states See principle of corresponding states.

law of gravitation See Newton’s law of gravitation.

law of partial pressures See Dalton’s law.

law of partial volumes See Amagat’s law.

law-of-the-wall variables (inner variables, wall variables, wall coordinates, u⁺, y⁺, T⁺) Non-dimensional variables used in turbulent boundary-layer theory using the friction velocity u_τ together with fluid properties evaluated in the immediate vicinity of the surface (the wall). Wall variables are indicated by the superscript ⁺, e.g. for the mean-flow velocity ū, u⁺ = ū/u_τ, for the distance from the wall y, y⁺ = u_τy/ν_S, where ν_S is the kinematic viscosity of the near-wall fluid, and for the mean temperature where T_S is the surface temperature, ρ_S is the near-wall fluid density, C_P is the specific heat, and is the surface heat flux. The combination μ_S/ρ_Su_τ is termed the viscous length scale, and wall units are lengths made non-dimensional by dividing by it.

The law of the wall is the variation of mean velocity ū with distance from the wall y in the near-wall region of a turbulent boundary layer or pipe flow in law-of-the-wall variables. From dimensional analysis it is found that u⁺ = f(y⁺). In the immediate vicinity of the wall (the viscous sub layer, approximately y⁺ < 5), u⁺ = y⁺. In the turbulent core (approximately y⁺ > 30), the log law applies,

where κ is von Kármán’s constant and B ≈ 5.5. The buffer layer is the transition region 5 < y⁺ < 30. For the entire wall region, Spalding’s formula is widely used. The law of the wake is an approximate empirical function that accounts for the deviation in velocity from the law of the wall in the outer region of a turbulent boundary layer. The outer layer is the region between the law-of-the wall and the free stream where the variation of the mean velocity with distance y from the surface is independent of viscosity but dependent on the fluid density ρ, the wall shear stress τ_W, the boundary-layer thickness δ, and the streamwise pressure gradient dp/dx. It can be shown that the outer-layer velocity profile follows the velocity-defect law

where U_∞ is the free-stream velocity, u_τ is the friction velocity, and the pressure-gradient parameter

The overlap layer is the transition region between the inner layer, where the law-of-the-wall applies, and the outer layer. The log law applies in the overlap layer.

Wall functions are approximate functions, based upon the log law, for the variation of the mean velocity, Reynolds stresses, dissipation, etc. in the near-wall region of a turbulent shear flow. They are used to avoid the expense of high spatial resolution in numerical calculations in near-wall turbulent flows.

laws of thermodynamics See thermodynamics laws.

lay 1. The hand (right or left) of twist in a rope or cable. 2. The main direction of tool marks on a machined surface.

layout blue See engineers’ blue (2).

lay shaft (layshaft) A secondary or intermediate shaft in a gearbox, running parallel to the main shaft and carrying the paired gear wheels that effect the changes in gear ratio. See also countershaft.

lay-up The manufacture of fibre-reinforced composite components using pre-pregs.

lb See pound.

lb_f See pound force.

LCD See liquid crystal.

LDA See laser-Doppler anemometer.

LDR See limiting draw ratio.

L/D ratio The length-to-diameter ratio of an engineering component. See also aspect ratio.

LDV See laser-Doppler anemometer.

lead 1. (Unit s or m or °) When one event happens before another or, for cyclic signals, when the phase of one signal is in advance of another. See also lag; valve-timing diagram. 2. (Unit m) When one entity is spatially ahead of another 3. See screw

lead angle (Unit °) The angle between a tangent to a helix and a plane normal the axis of the helix.

lead compensation See lead/lag compensation.

leaded petrol Petrol to which tetraethyl lead has been added to increase its octane rating and so improve its knock resistance. Now prohibited in most industrialized countries due to the risk of health and environmental damage.

lead/lag compensation (lead/lag control) In a control system, a network (the lead/lag network) introduced in series with the plant having a transfer function given by: where p and z are positive real constants. When z < p, the compensator introduces a phase lead in the output relative to the input. When z > p the opposite is true. A lead compensator lowers the magnitude of the output at low frequencies (ω < 10p) while a lag compensator does so at high frequencies (ω > 0.1p).

leading edge See aerofoil.

lead screw The master screw running along the length of the bed of a lathe from which all screws threads on that machine are cut.

lead zirconate titanate (PZT) A ceramic Pb(Ti,Zr)O₃ in the form of a solid solution of lead titanate (PbTiO₃) and lead zirconate (PbZrO₃) that has a high piezoelectric constant, high dielectric constant, and stable electro-mechanical properties over a wide temperature range. Used for transducers, sensors, ferroelectrics, etc.

leaf spring (laminated spring) A beam-like spring made up of thin independently-acting plates placed over one another and held together in a buckle.

leakage flow 1. The flow of working fluid that occurs in a turbomachine between the tips of the rotor blades and the casing. 2. The flow of any fluid past a seal. 3. The escape of fluid through cracks in a pressure vessel.

leakage losses (Unit kW) The power losses in a turbomachine associated with the leakage flow that does not do its full complement of work on the rotor.

leakage rate (Unit kg/s or m³/s) The rate at which fluid leaks past a seal or through cracks in a pressure vessel.

leak-before-burst A fracture-mechanics-based design methodology for pressure vessels, whereby propagation of a crack will result in the pressure being relieved by leakage rather than the vessel bursting.

lean mixture See stoichiometric mixture.

learning control A control method where the controller continuously uses identification to determine the plant parameters and thus modifies the operation of the controller.

least-energy principle (least-work theory) See work–kinetic-energy theorem.

leaving loss (Unit kW) The kinetic energy of the working fluid at outlet from the last stage of an axial-flow turbine.

LED See light-emitting diode.

Ledoux bell meter A flow meter in which an inverted weighted bell sealed with mercury moves up and down as the flow rate changes.

Leduc’s law See Amagat’s law.

Lee’s disc apparatus An apparatus for determining the thermal conductivity of a poor conductor in the form of a thin disc sandwiched between two thick metal discs (typically of brass or copper).

LEFM See fracture mechanics.

left-handed thread See screw.

lehr A special type of oven or kiln used in glass manufacture for annealing by slow cooling to remove internal stresses.

Leidenfrost effect The phenomenon that occurs when a liquid droplet is in near contact with a horizontal surface at a significantly higher temperature than the liquid’s boiling point. A vapour layer is created beneath the bubble causing it to float and evaporate relatively slowly.

Leidenfrost point See boiling.

leptokurtic See kurtosis.

LES See large-eddy simulation.

Le Système international d’unités See International System of Units.

lever A stiff rod or beam pivoted about a fulcrum with a load at some point along the lever being moved by a force (effort) at a third point. There are three classes of lever defined according to the relative positions of the effort, fulcrum, and load. For class 1, the effort and the load are on opposite sides of the fulcrum (as in a pair of pliers); for class 2, effort and load are on the same side of the fulcrum with the effort further away (as in a wheelbarrow); class 3 is like class 2, but with the load further away (as with tweezers). Classes 1 and 2 provide a mechanical advantage, but class 3 does not.

leverage See mechanical advantage.

Levi-Civita operator See permutation operator.

levitation See maglev.

Levy–Mises equations (Levy–Mises flow rules) The relationships, in rigid-plasticity theory, between normal and shear plastic strain increments (dε_x and dγ_yz respectively) and the instantaneous deviatoric stresses. There are three equations of the type

and three of the type where σ and τ are normal and shear stresses respectively and dλ is an instantaneous non-negative constant of proportionality that may vary as the strain changes. See also flow rules; Prandtl–Reuss equations.

lewis (lewisson) A mechanical device used by stonemasons to assist in lifting large blocks of stone. It consists typically of two connected curved steel legs. For the internal design, the outwardly curved legs are inserted into a prepared hole (or seating) in the stone which increases in width with increasing depth. For the external lewis, the legs are hinged at the top forming a tong-like, bow-shaped tool.

Lewis equation See toothed gearing.

Lewis form factor See toothed gearing.

Lewis number (Le) A non-dimensional parameter that arises in problems involving combined convective heat and mass transfer, defined by Le = ρC_PD_A/k where ρ is the fluid density, C_P is its specific heat, k is its thermal conductivity, and D_A is the diffusion coefficient for species A. The inverse k/ρC_PD_A is sometimes used as the definition.

lexan See polycarbonate.

life-cycle analysis (full life-cycle analysis) An analysis, in terms of money, mass or embodied energy, of all aspects involved in a process and its consequences, including environmental impact, manufacture, mining or recycling and processing of raw materials, energy consumption, and decommissioning, including disposal as scrap.

life factor See toothed gearing.

lift (lift force) (Unit N) The aerodynamic or hydrodynamic force exerted on a body as it moves relative to a fluid, acting in a direction perpendicular to that of the relative motion. The term applies if the force is vertically upward, whereas a downward force is termed download. Whether the force is upward or downward depends upon the shape and orientation of the body. See also aerofoil; drag; wing loading.

lift check valve A valve similar in configuration to a globe valve but with an automatically-operated cone-shaped plug. The cone is lifted off its seat by flow in the forward direction and returns to its seat if the flow reverses.

lift coefficient (C_L) A non-dimensional quantity defined by where L is the lift force exerted on a body by a fluid flow with dynamic pressure q and A is an appropriate area. In the case of an aerofoil A is taken as the wing planform area, but for other bodies it is usually the projected area in the flow direction.

lifting surface Any surface, such as an aerofoil, a propeller, or a turbomachine blade, that produces a lift force when moving relative to a fluid.

lift pump See suction pump.

lift valve A valve, such as a poppet valve, that is opened by being mechanically lifted.

light-emitting diode (LED) A diode formed from a single piece of semiconductor doped to be n-type on one side and p-type on the other. Under the application of a voltage that is positive on the p-side and negative on the n-side, holes in the former and electrons in the latter move towards the junction, where they combine and annihilate with the release of energy in the form of electromagnetic radiation. LEDs can be small—typically less than 1 mm²—and may be designed to produce radiation with wavelength from across the spectrum from infrared to ultraviolet. They produce energy-efficient lights for a wide range of uses, including commercial and domestic properties, vehicles and aircraft, traffic signals, and advertising displays.

limit control (limit switch) A switch used, in devices where motion over a fixed range of displacement or angle is required, to stop the driving motor at a predetermined location.

limit cycling Oscillation of the output of a system through a fixed range between limits.

limited-degree-of-freedom robot A robot with insufficient joints to allow independent control of the six degrees of freedom (translations along x, y, z and rotations about x, y, z) of the end effector.

limited-life fatigue See fatigue.

limited-rotation hydraulic motor A hydraulic motor or actuator that provides rotary motion over a finite angle.

limited-slip differential A differential that permits one wheel to slip relative to the other by only a limited amount, after which it becomes locked.

limit gauge A ‘go/no-go’ gauge to check that a component is within specified dimensions.

limiting draw ratio (LDR) 1. In deep drawing of cups, the greatest ratio of circular blank diameter to diameter of the drawn cup before fracture of the cup wall occurs. Allowing for friction and work-hardening, LDR ≈ 2. 2. Polymer sheet drawing is limited by the formation and propagation of stable necks and the LDR for such a process is given by the ratio of the initial thickness of the sheet to the thickness of the stable neck.

limiting friction (Unit N) The friction between two bodies in contact when sliding is imminent.

limiting moment See plastic hinge.

limiting range of stress See fatigue.

limit load See collapse load.

limit of proportionality (proportional limit) (Unit Pa) The maximum stress up to which a solid material obeys Hooke’s law.

limit of size See tolerances.

limits and fits Special tolerance combinations which, for certain applications, have been established for successful functioning of particular types of fit: running fits for shafts in bearings and pistons in cylinders; sliding fits for parts assembled by hand pressure or with the help of a light hammer; keying or driving fits, where parts are assembled with a medium hammer; and press or force fits, for parts such as wheels and hubs which, once assembled, are unlikely to be dismantled. Running and sliding fits are clearance fits; press fits, where the shaft is bigger than the hole, are interference fits; keying fits are transition fits in between the two.

These limits and fits are part of the wider system issued in ISO 286 intended to cover most engineering purposes from the finest to the coarsest. Among the many possible combinations of tolerances, those that have been found conveniently practical, in terms of ease of manufacture and use of material, are termed preferred fits. Although written in terms of holes and shafts, the system may be applied to mating parts having other geometries, such as a flat surface where the ‘hole’ is a slot and the ‘shaft’ a key. The system is concerned simultaneously with (a) the quality or grade of tolerance (the +/− bandwidth on the limits of size); and (b) the type of fit (the location of the bandwidth with respect to the nominal size). Except for very large sizes (where temperature effects become important), hole-basis fits are usually specified, i.e. fits in which the design size for a given hole is the basic size, and variations in the grade of fit for any particular hole are obtained by varying the clearance and tolerance on the shaft. This comes about since it is easier to manufacture and measure the male member of a fit, and only one reamer is required for the hole. See also tolerances.

limit state (Unit N) The loading on a structure or a component when plastic collapse is imminent.

limit switch See limit control.

linear acceleration (Unit m/s²) Acceleration in linear motion. See also angular acceleration.

linear actuator An actuator providing translational motion.

linear control system A control system described by linear differential equations and the resulting transfer functions.

linear elasticity In a material, component or structure, when the applied loads and the resulting deflexions are directly proportional. See also elastic; Hooke’s law; limit of proportionality.

linear expansivity See thermal expansion.

linear feedback control A linear control system employing closed-loop control.

linear generator A device in which alternating current electricity is generated where the motion between magnetic field and coil is linear rather than the more conventional rotational. See also maglev.

linear hydraulic motor See hydraulic cylinder.

linear momentum (Unit kg.m/s) The momentum of a body or fluid in linear motion. See also angular momentum; momentum.

linear-momentum conservation equation See momentum.

linear motion (rectilinear motion) Motion in a straight line.

linear–quadratic-Gaussian control (LQG control) An optimal control method for controlling an uncertain linear system subjected to noise added to its inputs and outputs and with incomplete knowledge of the states.

linear roller bearing See bearing.

linear spring See spring.

linear system A system in which the output is directly proportional to the input. It is characteristic of such a system that if an input x₁ produces an output y₁ and an input x₂ produces an output y₂, an input (x₁ + x₂) will produce an output (y₁ + y₂).

linear variable differential transformer (LVDT) An inductive sensor which uses a transformer with variable coupling between a single primary coil and a pair of secondary coils to give an output voltage proportional to the translational displacement of the iron core. The core is fitted with a projecting non-magnetic shaft so that the LVDT can be coupled to the displacement to be measured. See also rotary variable differential transformer.

linear variable differential transformer (LVDT)

linear velocity (Unit m/s) The velocity of a body or fluid in linear motion. See also angular velocity.

line load The idealization, in 2-dimensional analysis, that a load applied to a surface acts over zero contact area. See also contact mechanics; point load.

line of action See toothed gearing.

line of condition In a vapour-power cycle, such as the Rankine cycle, the path of the irreversible expansion on a temperature–entropy diagram.

line of contact See toothed gearing.

line oiler See air-line lubricator.

liner See cylinder liner.

line sink An idealized line, in plane potential-flow theory, into which there is a radial inflow of fluid with velocity inversely proportional to the radial distance. There is a singularity at the line itself. A line source is the counterpart when there is flow out of the line. See also point sink.

link 1. Any connecting member in a mechanism that is pivoted at both ends. 2. The part of a robot arm running between two joints.

linkage Any combination of links, sliders, pivots, and rotating members forming a mechanism that produces a desired motion.

link length See joint.

liquefaction The conversion of a gas into a liquid using liquefier. This can be achieved by cooling the gas below its critical temperature and compressing it, or by expansion, for example using the Joule–Thompson effect.

liquefaction point See condensation (1).

liquefied natural gas (LNG) Natural gas at a temperature of about −162°C, well below its critical temperature of −83°C and so in a liquid state.

liquefied petroleum gas (LPG) A liquefied gaseous fuel, normally propane or butane, but sometimes a mix based on 60% propane and 40% butane.

liquid An essentially incompressible wet fluid that forms a free surface in a container. See also gas.

liquid-cooled engine A piston engine in which a liquid, usually water with additives such as antifreeze, is circulated through passages in the engine block and a radiator.

liquid cooling The use of circulated liquid, usually water, to cool engines or other machines.

liquid crystal One of a group of organic or inorganic compounds that has a mesomorphic (intermediate) state between solid and liquid. The arrangement of its molecules exhibits a crystal-like structure, which can be one of several types, even when the compound has liquid-like properties. Some liquid crystals occur naturally, for example in cell membranes, viruses, and clays. Those in liquid crystal displays (LCDs) are organic compounds with aligned rod-like molecules that transmit and change polarized light. Molecular orientation can be varied by application of an electric field. This property is used to control light passing through a display panel by sandwiching a liquid crystal film between cross-polarized films.

liquid-in-glass thermometer A bulb thermometer in which the bulb and stem are glass.

liquid-in-metal thermometer A fluid-expansion thermometer in which the expanding fluid is a liquid contained in a metal tube such as a Bourdon tube.

liquid piston compressor A positive-displacement rotary compressor in which a rotor with forward-curved blades rotates within an elliptical casing with the rotor partly filled by a liquid.

liquid-sealed meter See Crossley meter.

liquid-sorbent dehumidifier A dehumidifier in which the air to be dried is passed through sprays of a liquid absorbent, such as lithium chloride or glycol solution.

liquid spring A piston-cylinder device dependent upon the compressibility of a liquid, typically silicone-based, to cushion shock loads. Used in heavy-duty applications such as heavy military vehicles and the landing gear of aircraft and the space shuttle. See also gas spring.

liquidus line In materials science, the line on a temperature-composition phase diagram for a binary alloy system that separates liquid and liquid+solid regions. It shows temperatures above which only the liquid phase exists under equilibrium conditions. See also phase diagram; solidus line.

liquid-vapour dome The two-phase region in a p–v–T diagram enclosed by the saturated-liquid and saturated-vapour lines, in which the liquid phase and the vapour phase co-exist in equilibrium.

Lissajous patterns (Lissajous figures) The locus of the resultant displacement of a point moving under the influence of two independent harmonic motions. In the case of two orthogonal simple harmonic motions having the same frequency, the Lissajous figures are a series of ellipses corresponding to possible differences in phase between the two motions.

lithography The transfer of a pattern to a photosensitive material, typically a photoresist, by selective exposure through a mask to radiation. It is the most important process for fabricating MEMS and other microscale structures. See also photolithography.

litre (liter, L) A non-SI unit of volume defined as 10⁻³ m³ and approximately equal to the volume of 1 kg of water at 4°C, which is how it was formerly defined.

little end See connecting rod.

live axle An unsprung axle to which wheels are rigidly fixed.

live load (Unit N) The load on a structure caused by vehicles, etc. passing over it, as opposed to the dead weight of the structure itself.

live steam Steam under pressure as supplied direct from a boiler.

living hinge (integral hinge) A thin flexible connection made of the same material as the two rigid parts it connects. Typically manufactured by injection moulding. The most common choice of material is either polypropylene or polyethylene, both of which have excellent fatigue resistance. Applications include the caps of plastic bottles, food containers, aircraft storage doors, and home cabinetry.

Ljungström pre-heater A regenerative air pre-heater for a boiler furnace in which a rotating cylindrical matrix passes alternately through the air and the flue gas. See also rotary regenerator.

Ljungström turbine An outward-flow steam turbine consisting of concentric rows of blades attached to the opposing faces of two rotor discs that rotate in opposite directions.

LMTD See log-mean temperature difference.

LNG See liquefied natural gas.

load 1. (Unit N) The force applied to a component or structure. 2. (Unit kW) The power drawn from a prime mover.

load-carrying capacity (Unit N) 1. The maximum weight that can safely be carried by a vehicle or structure. 2. In robotics, the maximum weight that can be carried by the end effector without causing out-of-specification operation, for example, excessive steady-state error.

load cell A device for measuring forces by means of strain gauges, piezoelectric detectors, etc., as opposed to the use of hydraulic pressure or mechanical means. Such devices are sometimes only uniaxial, or simultaneously measure loads along other orthogonal axes. See also dynamometer (2).

load control The action of a testing machine when the load applied to the testpiece can be altered in a controlled fashion, the corresponding displacement of the specimen being dependent on the stress–strain characteristics of the specimen. See also displacement control.

load‐deformation diagram A plot of load vs deformation based upon the data given by a testing machine from which stress and strain, and hence mechanical properties, may be calculated.

load distribution factor See toothed gearing.

load factor 1. The ratio of the design working load on a component or structure to the load at which failure would occur. See also factor of safety. 2. See capacity factor.

load inertia (Unit kg.m²) The moment of inertia of the load applied to a motor.

loading diagram A schematic of the loads and their points of application to which a component or structure is subjected, often accompanied by the corresponding shear force and bending-moment diagrams.

load intensity (q, w) (Unit N/m) The value of a distributed load acting on a structure or component. See also distributed load; point load.

load rating See bearing.

load shedding 1. If the force (load) in a member of a structure falls to zero due to failure of the member, the original load and energy in that member are released and transferred into adjacent members. These members may become overloaded, leading to a cascade of failures. 2. The process of disconnecting parts of the load on a power station when the demand exceeds the capacity.

lobe 1. The part projecting from a circular profile in a cam, gear or other basically circular component. 2. A type of rotor or impeller used in some flow meters, pumps, etc.

lobed impeller meter A flow meter in which two lobed impellers rotate in opposite directions within an ovoid housing. A wide range of materials is used for the impellers, including thermoplastics and stainless steel.

lobe pump Similar to a gear pump, but the lobes are prevented from being in contact by external gearing. Commonly used in food handling since they do not damage the material.

local acceleration (Unit m/s²) In unsteady fluid flow, the time derivative of the vector velocity V at a point, ∂V/∂t. See also total acceleration.

local buckling Buckling of a thin-walled component which is contained within a small region of the surface.

localized necking In sheet-metal forming, a neck that is localized into a thin trough, the orientation of which depends on the applied strain or stress ratio.

local structural discontinuity See stress concentration.

location fit See limits and fits.

locking differential The differential of a motor vehicle in which the half-shafts may be locked together if required, thus eliminating differential action, so that both wheels rotate at the same speed.

locknut 1. A thin auxiliary nut tightened against another nut to prevent loosening. 2. A single nut with special features that prevent loosening.

lock washer See tab washer.

locomotive A vehicle on rails, powered by electric, diesel, or diesel-electric motors, used to haul passenger carriages or goods wagons. Vintage steam locomotives are powered by coal-fired boilers.

locomotive boiler A multi-fire-tube boiler with integral firebox.

logarithmic creep See creep.

logarithmic decrement (δ) The natural logarithm of the ratio of the amplitudes of any two successive peaks, x_n and x_n+1, in the output of an underdamped oscillatory system, given by . It allows the determination of the damping ratio of the system.

logarithmic spiral See spiral.

logarithmic strain See true strain.

log law See law-of-the-wall variables.

log-mean temperature difference (LMTD, temperature difference, ΔT_M) (Unit °C) If the heat-transfer rate for a simple one-tube pass, one shell-pass heat exchanger, with either parallel flow or counterflow, is expressed as = UAΔT_M, where U is the overall heat-transfer coefficient and A is the heat-exchanger total surface area, it is found that

where ΔT₁ and ΔT₂ are the temperature differences between the hot and cold streams at inlet and outlet, respectively. For a more complex arrangement, a correction factor F is introduced such that for the actual heat exchanger ΔT_M = F ΔT_M,CR where ΔT_M,CR is for a simple counterflow heat exchanger.

longitudinal-drum boiler The original type of water-tube boiler operating on the thermo-siphon principle. Cooled feedwater, fed into the drum which is placed longitudinally above the heat source, flows down a header and into the inclined heated tubes that lead back to the drum. See also cross-drum boiler.

longitudinal wave A wave in which the displacement of the propagating medium is normal to the local wavefront. Examples are plane acoustic waves in fluids and compressional waves in isotropic solids.

long-stroke engine See undersquare engine.

long-term repeatability A measure of the ability of a robot to return to the same programmed position over a long period of time.

long ton (imperial ton, ton) A non-SI unit of mass equal to 2 240 pounds. Conversion to SI is 1 long ton = 1 016.046 908 8 kg. See also short ton; metric ton.

Lontra blade compressor^® See blade compressor.

loop gain See closed-loop gain; open-loop gain.

loop strength (loop tenacity) A mechanical-property test for fibres, in which two interlinked loops are pulled until crushing or cutting occurs under the loading pins.

loss (Unit kW) For a machine or system, power that does not perform useful work. The principal losses are due to mechanical or viscous friction windage loss, and leakage loss, for example leakage of working fluid from one stage to the next in a turbine or through seals. See also brake power; friction power; shaft power.

loss modulus (Unit Pa) 1. (E^″, G^″) A measure of the energy dissipated in a viscoelastic solid, determined by applying an oscillatory stress to the material and recording the strain. E^″ corresponds to a tensile stress and G^″ to a shear stress. 2. See non-Newtonian fluid.

loss tangent See non-Newtonian fluid.

lost motion (Unit s or m) The delay in time or in displacement between the driving and driven parts in a mechanism. See backlash.

lost-wax casting See investment casting.

lost-wax technique See investment casting.

Love wave See surface wave.

low-cycle fatigue See fatigue.

low-E coating (low-emittance coating) A thin metallic or metal-oxide coating on a glass sheet to absorb and reflect infrared radiation. The coating is applied either by a pyrolytic chemical vapour-deposition process (hard coat), or by sputtering (soft coat).

low-enthalpy resource See geothermal energy.

lower-bound theorem A statically-admissible stress distribution for a loaded body or structure is one that satisfies equilibrium, the boundary conditions, and is within the yield locus, but does not satisfy displacement compatibility. The stiffness of the body according to such a stress field is greater than the exact stiffness. The theorem states that loads producing such stress distributions are equal to, or lower than, the true load that will produce plastic flow. Thus an underestimate of working loads in plasticity (a lower bound) is obtained by employing such a field. The highest upper bound of a series of such stress fields will be closest to the true load. The lower-bound theorem was formerly known as the principle of maximum plastic resistance. See also upper-bound theorem.

lower calorific value See Boys gas calorimeter; calorific value of a fuel.

lower consolute temperature See consolute temperature.

lower pair A mechanism where the elements have surface (not line or point) contact and where one slides over the other during relative motion. See also higher pair; kinematic pair.

lower yield point See Lüders band.

low explosive See high explosive.

low-head hydroelectric plant See high-head hydroelectric plant.

low heat value See calorific value of a fuel.

low-pass filter See band-pass filter.

low-pressure burner A Venturi device in which gaseous fuel injected at the throat draws in air from the surroundings, the two mix and burn downstream of the divergent section.

low-pressure cylinder The large cylinder, in a compound steam engine or steam-turbine system, that receives steam exhausted from the high- or intermediate-pressure cylinder.

low-pressure steam Steam at a pressure close to atmospheric.

low-pressure turbine (LP turbine) In a compound steam-turbine system or a two- or three-spool gas-turbine engine, the turbine following the high- or intermediate-pressure turbine from which the working fluid is exhausted.

low-solidity wind turbine A wind turbine with a small number (usually no more than three) of narrow blades. See also solidity.

low-temperature solar collector A solar collector operating at temperatures a few degrees (maximum 20°C) above ambient. Swimming-pool heating is a typical application.

low vacuum See vacuum.

LPG See liquefied petroleum gas.

LQG control See linear–quadratic-Gaussian control.

lubricant Any substance such as oil, grease, or gas under pressure that, when supplied to bearing surfaces in relative motion, reduces friction.

lubricating system The system of pipes that takes liquid lubricant from a central reservoir to bearing surfaces within a machine or system.

lubrication The process of providing lubricant to bearing surfaces.

lubrication stability The dependence on the Sommerfeld number, S, of the thickness of the film of lubricant in a bearing. If S exceeds a critical value, the film is thick and stable. Below the critical value the film becomes too thin, is unstable and there is a possibility of metal-to-metal contact.

lubrication theory A theory of viscous fluid flow between two surfaces in close proximity, one moving tangentially relative to the other. The principal application is to bearings.

lubricity (oiliness) A qualitative measure of the effectiveness of a lubricant, high lubricity being desirable to minimize wear.

lucite See polymethyl methacrylate.

Lüders band (stretcher strain) A localized band of plastic deformation in a metal due to tensile stress. Lüders bands are associated with a yield-point phenomenon in a tensile test (see figure). After initial elastic strain, plastic deformation occurs in a discrete band at the upper yield point due to the sudden release of dislocations from atmospheres of solute atoms. The load falls to the lower yield point and with increasing applied strain Lüders bands propagate along the length of the specimen until occupying the entire length. After yield elongation the flow stress increases with strain as usual. The phenomenon is common in low-carbon steels, in which atmospheres of interstitial carbon atoms lock dislocations after ageing, and several other alloys, and is evident as vein-like marks in pressed sheets. It can be avoided in steel by reducing the concentration of carbon solute or cold rolling prior to pressing.

yield-point phenomenon

Ludwieg–Tillmann drag law A widely used empirical formula for the skin-friction coefficient c_f of a turbulent boundary layer in terms of the shape factor H and the momentum-thickness Reynolds number Re_θ. It is given by .

Ludwig–Sorét effect See Sorét effect.

Ludwik relation See Ramberg–Osgood equation.

Luenberger observer In a control system, a function that uses signals from the feedback sensor output, the plant input, and a knowledge of the mathematical model of the sensor and plant to provide a more accurate feedback signal than that obtained directly from the sensor.

luffing Lifting or lowering the jib of a crane. See also slewing.

lug See ear.

lumped-capacity method (lumped-system analysis) A method of analysing transient-conduction problems in which it is assumed that a solid body has uniform temperature with convective heat transfer at the surface to or from surroundings at temperature T_∞. If the surface heat-transfer coefficient is h, the surface area is A, the mass of the body is m, and its specific heat is C_P, it can be shown that the variation of temperature T with time t is given by where a = hA/mC_P and T₀ is the temperature when t = 0. The inverse of α has the dimensions of time and is termed the thermal time constant (τ).

lumped-parameter system A system represented by a number of discrete components such as masses, dampers, and springs, rather than by a continuum. Unlike a continuum model, it has a finite number of states.

LVDT See linear variable differential transformer.

Lyapunov stability criterion A sufficient criterion for the stability of a system based on the properties of the Lyapunov function for the system. Satisfying the criterion guarantees that the energy in the system cannot increase without limit and thus the output is bounded.

lyophilization See freeze drying.

Lysholm compressor A twin-screw supercharger with improved sealing between the two rotors when compared with a Roots blower. One rotor has thin blades with a thick ridge, while the other has thick teardrop-shaped lobes and a sharp edge.