Dimensional Analysis for Unit Conversion Using Matlab®

AN INTRODUCTION TO THE INTERNATIONAL SYSTEM OF UNITS (SI) – Conversion Factors for General Use (Bidirectional Conversion App Section)

In the NIST Special Publication 1038{36}, the International System of Units (SI) – Conversion Factors for General Use are defined. Conversion factors are the mathematical multiplier or divisor and associated units that allow any compatible measurements to be converted from one system of units to another system of units (e.g., inches to centimeters or vice versa). As with any measurement, caution needs to be applied so that resolution (number of digits) is not confused with accuracy (number of significant digits). The general rule of thumb (first approximation) is to use no more digits than are absolutely necessary. See the Appendix for more details on significant digits.

The examples below demonstrate calculations as applied to obtain the results shown by the Unit Convertor MATLAB App provided with this book.

Figure 3.1-0 shows the Unit Converter MATLAB App Front Panel with the Space/Time Tab selected. Bidirectional matrices were created and installed within this app to allow the user the ability to easily select via pull-down menus all of the desired conversion pairs required. Each of the Tabs available in the App is explored herein.

FIGURE 3.1-0 Unit Converter Using MATLAB App - Front Panel - Space/Time Tab.

Length Tab

The first Minor Tab under the Space/Time Major Tab is the Length Tab (see Figure 3.1-1). This example demonstrates the conversion of Nautical Miles to Fathoms. In this example, the amplitude of Nautical Miles is set equal to one (1.0). The conversion equation is shown in Example 3.1-1 {37}.

Nautical Miles (nmi) (=1.0) to Fathoms (ftm) Example 3.1-1:

ftm	=	nmi * km/nmi * m/km * ftm/m = nmi * 1.852 * 1000 * 1/1.828804
	=	nmi * 1.01268370E3

Where: ftm	=	the number of fathoms calculated
nmi	=	the number of nautical miles to be converted (1.0)
km/nmi	=	the conversion factor from nautical miles to kilometers (1.852)
m/km	=	the conversion factor from kilometers to meters (1000)
ftm/m	=	the conversion factor from meters to fathoms (1/1.828804)

And:

The resulting solution is:

ftm

1.0 * 1.01268370E3 = 1.01268370E3 Fathoms

(3.1-1)

The Space/Time Length Tab allows the bidirectional selection of the following length dimensions:

Major-Tab	Minor-Tab	Units on Pull-Down
Space/Time
	Length
		nautical mile (nmi)
		mile (mi)
		kilometer (km)
		fathom (ftm)
		yard (yd)
		meter (m)
		foot (ft)
		foot (U.S. Survey)
		inch (in)
		centimeter (cm)
		millimeter (mm)
		pica, printer’s (12p)
		point, printer’s (p)
		mil (0.001 in)
		micrometer (µm)
		microinch (µin)
		nanometer (nm)
		angstrom

Plane Angle Tab

The second Minor Tab under the Space/Time Major Tab is the Plane Angle Tab (see Figure 3.1-2). This example shows the conversion of Radian to degree arc. In this example, the amplitude of Radian is set equal to one (1.0). The conversion equation is shown in Example 3.1-2.

Radian (rad) to degree arc (°) Example 3.1-2:

degree arc = rad * degrees/rad = rad * 57.29578 = 57.29578 degrees

Where: degree arc	=	the number of degrees calculated
rad	=	the starting number of Radian (1.0)
degrees/rad	=	the conversion factor from Radian to degrees (57.29578)

FIGURE 3.1-2 Unit Converter Using MATLAB App - Space/Time Plane Angle Tab.

And:

The resulting solution is:

degree arc = 1.0 * 57.29578 = 57.29578 degrees

(3.1-2)

The Space/Time Plane Angle Tab allows the bidirectional selection of the following angle dimensions:

Major-Tab	Minor-Tab	Units on Pull-Down
Space/Time
	Plane Angle
		Radian
		Degree Arc

Area Tab

The third Minor Tab under the Space/Time Major Tab is the Area Tab (see Figure 3.1-3). This example shows the conversion of Square Feet to Square Kilometers. In this example, the amplitude of Square Feet is set equal to one (1.0). The conversion equation is shown in Example 3.1-3.

Square Feet (ft²) (=1.0) to Square Kilometers (km²) Example 3.1-3:

km²	=	ft² * m²/ ft² * km²/ m² = ft² * 9.290304E-2 * 1/ 1.0E6
	=	ft² * 9.290304E-8

Where: km²	=	the number of Square Kilometers calculated
ft²	=	the number of Square Feet to be converted (1.0)
m²/ft²	=	the conversion factor from Square Feet to Square Meters (9.290304E-2)
km²/m²	=	the conversion factor from Square Meters to Square Kilometers (1/ 1.0E6)

And:

The resulting solution is:

km² = 1.0 * 9.290304E-8 = 9.290304E-8 Square Kilometers

(3.1-3)

The Space/Time Area Tab allows the bidirectional selection of the following area dimensions:

Major-Tab	Minor-Tab	Units on Pull-Down
Space/Time
	Area
		square mi (mi^2)
		square km (km^2)
		hectare (ha)
		acre
		square m (m^2)
		square yd (yd^2)
		square ft (ft^2)
		square in (in^2)
		square cm (cm^2)
		square mm (mm^2)
		circular mil

Volume Tab

The fourth Minor Tab under the Space/Time Major Tab is the Volume Tab (see Figure 3.1-4). This example shows the conversion of Acre-Foot to Liter. In this example, the amplitude of Acre-Foot is set equal to one (1.0). The conversion equation is shown in Example 3.1-4.

Acre-Foot (aft) (=1.0) to Liter (L) Example 3.1-4:

L	=	aft * m³/aft * L/m³ = aft * 1.233489E3 * 1 / 1.0E-3 {38}
	=	aft * 1.23348900E6

Where: L	=	the number of Liter calculated
aft	=	the number of Acre-Foot to be converted (1.0)
m³/aft³	=	the conversion factor from Acre-Foot to Cubic Meters (1.233489E3)
L/m³	=	the conversion factor from Cubic Meters to Liter (1/ 1.0E-3)

And:

The resulting solution is:

L = 1.0 * 1.23348900E6 = 1.23348900E6 Liter

(3.1-4)

The Space/Time Volume Tab allows the bidirectional selection of the following volume dimensions:

Major-Tab	Minor-Tab	Units on Pull-Down
Space/Time
	Volume
		acre-foot (aft)
		barrel-oil (bbl)
		cubic-yard (yd^3)
		cubic-meter (m^3)
		cubic-foot (ft^3)
		board-foot (BF)
		register-ton (RT)
		bushel (bu)
		gallon (gal)
		liter (L)
		quart (qt)
		pint (pt)
		fluid-ounce (fl oz)
		milliliter (mL)
		cubic-inch (in^3)
		cubic-centimeter (cm^3)

Velocity Tab

The fifth Minor Tab under the Space/Time Major Tab is the Velocity Tab (see Figure 3.1-5). This example shows the conversion of Foot per Second to Meter per Second. In this example, the amplitude of Foot per Second (ft/s) is set equal to one (1.0). The conversion equation is shown in Example 3.1-5.

Foot per Second (ft/s) (=1.0) to Meter per Second (m/s) Example 3.1-5:

m/s = ft/s * m/ft = ft/s * 0.3048

Where: m/s	=	the number of Meter per Second calculated
ft/s	=	the number of Foot per Second to be converted (1.0)
m/ft	=	the conversion factor from Foot to Meter (0.3048)

And:

The resulting solution is:

m/s = 1.0 * 0.3048 = 0.3048 Meter per Second

(3.1-5)

The Space/Time Velocity Tab allows the bidirectional selection of the following velocity dimensions:

Major-Tab	Minor-Tab	Units on Pull-Down
Space/Time
	Velocity
		foot per second (ft/s)
		mile per hour (mi/hr)
		knot (nmi/hr)
		meter per second (m/s)
		kilometer per hour (km/hr)

Acceleration Tab

The sixth Minor Tab under the Space/Time Major Tab is the Acceleration Tab (see Figure 3.1-6). This example shows the conversion of Foot per Second Squared to Meter per Second Squared. In this example, the amplitude of Foot per Second Squared (ft/s²) is set equal to one (1.0). The conversion equation is shown in Example 3.1-6.

FIGURE 3.1-6 Unit Converter Using MATLAB App - Space/Time Acceleration Tab.

Foot per Second Squared (ft/s²) (=1.0) to Meter per Second Squared (m/s²) Example 3.1-6:

m/s² = ft/s² * m/ft = ft/s² * 0.3048

Where: m/s²	=	the number of Meter per Second Squared calculated
ft/s²	=	the number of Foot per Second Squared to be converted (1.0)
m/ft	=	the conversion factor from Foot to Meter (0.3048)

And:

The resulting solution is:

m/s² = 1.0 * 0.3048 = 0.3048 Meter per Second Squared

(3.1-6)

The Space/Time Acceleration Tab allows the bidirectional selection of the following acceleration dimensions:

Major-Tab	Minor-Tab	Units on Pull-Down
Space/Time
	Acceleration
		inch per second squared (in/s^2)
		foot per second squared (ft/s^2)
		meter per second squared (m/s^2)
		standard acceleration of gravity (g)

Flow Rate Tab

The seventh Minor Tab under the Space/Time Major Tab is the Flow Rate Tab (see Figure 3.1-7). This example shows the conversion of Cubic Foot per Second to Cubic Meter per Second. In this example, the amplitude of Cubic Foot per Second (ft³/s) is set equal to one (1.0). The conversion equation is shown in Example 3.1-7.

Cubic Foot per Second (ft³/s) (=1.0) to Cubic Meter per Second (m³/s) Example 3.1-7:

m³/s = ft³/s * m³/ft³ = ft³/s * 2.831685E-2

Where: m³/s	=	the number of Cubic Meter per Second calculated
ft³/s	=	the number of Cubic Foot per Second to be converted (1.0)
m³/ft³	=	the conversion factor from Cubic Foot to Cubic Meter (2.831685E-2)

And:

The resulting solution is:

m³/s = 1.0 * 2.831685E-2 = 2.831685E-2 cubic meter per second

(3.1-7)

The Space/Time Flow Rate Tab allows the bidirectional selection of the following flow rate dimensions:

Major-Tab	Minor-Tab	Units on Pull-Down
Space/Time
	Flow Rate
		cubic foot per second (ft^3/s)
		cubic foot per minute (ft^3/min)
		cubic yard per minute (yd^3/min)
		gallon per minute (gal/min)
		gallon per day (gal/day)
		cubic meter per second (m^3/s)
		liter per second (L/s)
		liter per day (L/day)

Fuel Efficiency Tab

FIGURE 3.1-8 Unit Converter Using MATLAB App - Space/Time Fuel Efficiency Tab.

The eighth Minor Tab under the Space/Time Major Tab is the Fuel Efficiency Tab (see Figure 3.1-8). This example shows the conversion of Mile per Gallon to Kilometer per Liter. In this example, the amplitude of Mile per Gallon (mi/gal) is set equal to one (1.0). The conversion equation is shown in Example 3.1-8.

Mile per Gallon (mi/gal) (=1.0) to Kilometer per Liter (km/L) Example 3.1-8:

km/L	=	mi/gal * km/mi * gal/L = mi/gal * 1.609344 * 1/3.785412
	=	mi/gal * 4.251437E-1

Where: km/L	=	the number of Kilometer per Liter calculated
mi/gal	=	the number of Mile per Gallon to be converted (1.0)
km/mi	=	the conversion factor from Miles to Kilometers (1.609344)
gal/L	=	the conversion factor from Liter to Gallon (1/3.785412)

And:

The resulting solution is:

km/L = 1.0 * 4.251437E-1 = 4.251437E-1 Kilometer per Liter

(3.1-8)

The Space/Time Fuel Efficiency Tab allows the bidirectional selection of the following fuel efficiency dimensions:

Major-Tab	Minor-Tab	Units on Pull-Down
Space/Time
	Fuel Efficiency
		miles per gallon (mi/gal)
		kilometer per liter (km/L)

FIGURE 3.2-0 Unit Converter Using MATLAB App - Front Panel Mechanics1 Tab.

Figure 3.2-0 shows the Unit Converter MATLAB App Front Panel with the Mechanics1 Major Tab selected. Bidirectional matrices were created and installed within this app to allow the user the ability to easily select via pull-down menus all of the desired conversion pairs required. Each of the Mechanics1 Minor Tabs available in the App is explored herein.

Mass/Weight Tab

The first Minor Tab under the Mechanics1 Major Tab is the Mass/Weight Tab (see Figure 3.2-1). This example demonstrates the conversion of ton (long) (2240 lb) to ounce (avoirdupois). In this example, the amplitude of ton (long) is set equal to one (1.0). The conversion equation is shown in Example 3.2-1.

ton (long) (2240 lb) (=1.0) to ounce (avoirdupois) (oz) Example 3.2-1:

oz	=	ton(long) * lb/ton(long) * oz/lb = 1.0 * 2240 * 16
	=	ton (long) * 3.584E4

FIGURE 3.2-1 Unit Converter Using MATLAB App - Mechanics1 Mass/Weight Tab.

Where: oz	=	the number of ounces calculated
ton (long)	=	the number of tons to be converted (1.0)
lb/ton (long)	=	the conversion factor from ton (long) to pounds (2240)
oz/lb	=	the conversion factor from pounds to ounces (16)

And:

The resulting solution is:

oz = ton (long) * 3.584E4 = 3.584E4 ounces

(3.2-1)

The Mechanics1 Mass/Weight Tab allows the bidirectional selection of the following mass/weight dimensions:

Major-Tab	Minor-Tab	Units on Pull-Down
Mechanics1
	Mass/Weight
		ton (long) (2240 lb)
		metric ton (t)
		ton (short) (2000 lb)
		slug
		kilogram (kg)
		pound (avoirdupois)
		ounce (troy)
		ounce (avoirdupois)
		gram (g)
		grain
		milligram (mg)

Moment of Mass Tab

FIGURE 3.2-2 Unit Converter Using MATLAB App - Mechanics1 Moment of Mass Tab.

The second Minor Tab under the Mechanics1 Major Tab is the Moment of Mass Tab (see Figure 3.2-2). This example demonstrates the conversion of pound foot to kilogram meter. In this example, the amplitude of pound foot (lb*ft) is set equal to one (1.0). The conversion equation is shown in Example 3.2-2.

pound foot (lb*ft) (=1.0) to kilogram meter (kg*m) Example 3.2-2:

kg*m	=	lbft kg/lb * m/ft = 1.0 * 0.45359252 * 0.3048
	=	lbft 1.38255E-1

Where: kg*m	=	the number of kilogram meter calculated
lb*ft	=	the number of pound foot to be converted (1.0)
kg/lb	=	the conversion factor from pound to kilogram (0.45359252)
m/ft	=	the conversion factor from foot to meter (0.3048)

And:

The resulting solution is:

kg*m = 1.0 * 1.38255E-1 = 1.38255E-1 kilogram meter

(3.2-2)

The Mechanics1 Moment of Mass Tab allows the bidirectional selection of the following Moment of Mass dimensions:

Major-Tab	Minor-Tab	Units on Pull-Down
Mechanics1
	Moment of Mass
		pound foot
		kilogram meter (kg * m)

Density Tab

The third Minor Tab under the Mechanics1 Major Tab is the Density Tab (see Figure 3.2-3). This example demonstrates the conversion of pound per cubic foot to kilogram per cubic meter. In this example, the amplitude of pound per cubic foot (lb/ft^3) is set equal to one (1.0). The conversion equation is shown in Example 3.2-3.

pound per cubic foot (lb/ft^3) (=1.0) to kilogram per cubic meter (kg/m^3) Example 3.2-3:

	kg/m^3	=	lb/ft^3 * kg/lb * ft^3/m^3 = 1.0 * 0.45359252 * 3.5314662E1
		=	lb/ft^3 * 1.601846E1

Where: kg/m^3	=	the number of kilogram per cubic meter calculated
lb/ft^3	=	the number of pound per cubic foot to be converted (1.0)
kg/lb	=	the conversion factor from pound to kilogram (0.45359252)
ft^3/m^3	=	the conversion factor from cubic meter to cubic foot (3.5314662E1)

And:

The resulting solution is:

kg/m^3 = lb/ft^3 * 1.601846E1= 1.601846E1 kilogram per cubic meter

(3.2-3)

The Mechanics1 Density Tab allows the bidirectional selection of the following Density dimensions:

Major-Tab	Minor-Tab	Units on Pull-Down
Mechanics1
	Density
		ton (2000 lb [short]) per cubic yard
		metric ton per cubic meter (t/m^2)
		pound per cubic foot (lb/ft^3)
		kilogram per cubic meter (kg/m^3)

Concentration Tab

The fourth Minor Tab under the Mechanics1 Major Tab is the Concentration Tab (see Figure 3.2-4). This example demonstrates the conversion of pound per gallon to gram per liter. In this example, the amplitude of pound per gallon (lb/gal) is set equal to one (1.0). The conversion equation is shown in Example 3.2-4.

FIGURE 3.2-4 Unit Converter Using MATLAB App - Mechanics1 Concentration Tab.

pound per gallon (lb/gal) (=1.0) to gram per liter (g/L) Example 3.2-4:

g/L	=	lb/gal * kg/lb * g/kg * gal/L
	=	1.0 * 0.45359237 * 1.0E3 * 1/ 3.785412
	=	lb/gal * 1.1982642E2

Where: g/L	=	the number of gram per liter calculated
lb/gal	=	the number of pound per gallon to be converted (1.0)
kg/lb	=	the conversion factor from pound to kilogram (0.45359252)
g/kg	=	the conversion factor from kilogram to gram (1.0E3)
gal/L	=	the conversion factor from liter to gallon (1/ 3.785412)

And:

The resulting solution is:

g/L = lb/gal * 1.1982642E2= 1.1982642E2 gram per liter

(3.2-4)

The Mechanics1 Concentration Tab allows the bidirectional selection of the following Concentration dimensions:

Major-Tab	Minor-Tab	Units on Pull-Down
Mechanics1
	Concentration (mass)
		pound per gallon (lb/gal)
		ounce (avoirdupois) per gallon (oz/gal)
		gram per liter (g/L)

Momentum Tab

The fifth Minor Tab under the Mechanics1 Major Tab is the Momentum Tab (see Figure 3.2-5). This example demonstrates the conversion of pound foot per second to kilogram meter per second. In this example, the amplitude of pound foot per second (lb*ft/s) is set equal to one (1.0). The conversion equation is shown in Example 3.2-5.

pound foot per second (lb*ft/s) (=1.0) to kilogram meter per second (kg*m/s) Example 3.2-5:

	kg*m/s	=	lbft/s kg/lb * m/ft = lbft/s 4.5359252E-1 * 3.048E-1
		=	lbft/s 1.38255E-1

Where: kg*m/s	=	the number of kilogram meter per second calculated
lb*ft/s	=	the number of pound foot per second to be converted (1.0)
kg/lb	=	the conversion factor from pound to kilogram (4.5359252E-1)
m/ft	=	the conversion factor from foot to meter (3.048E-1)

And:

The resulting solution is:

kg*m/s = lb*ft/s * 1.38255E-1 = 1.38255E-1 kilogram meter per second

(3.2-5)

The Mechanics1 Momentum Tab allows the bidirectional selection of the following Momentum dimensions:

Major-Tab	Minor-Tab	Units on Pull-Down
Mechanics1
	Momentum
		pound foot per second (lb*ft/s)
		kilogram meter per second (kg*m/s)

Moment of Inertia Tab

The sixth Minor Tab under the Mechanics1 Major Tab is the Moment of Inertia Tab (see Figure 3.2-6). This example demonstrates the conversion of pound square foot to kilogram square meter. In this example, the amplitude of pound square foot (lb*ft^2) is set equal to one (1.0). The conversion equation is shown in Example 3.2-6.

pound square foot (lb*ft^2) (=1.0) to kilogram square meter (kg*m^2) Example 3.2-6:

kg*m^2	=	lbft^2 kg/lb * m^2/ft^2
	=	lbft^2 4.5359252E-1 * 9.290300E-2
	=	lbft^2 4.2140110E-2

FIGURE 3.2-6 Unit Converter Using MATLAB App - Mechanics1 Moment of Inertia Tab.

Where: kg*m^2	=	the number of kilogram meter squared calculated
lb*ft^2	=	the number of pound foot squared to be converted (1.0)
kg/lb	=	the conversion factor from pound to kilogram (4.5359252E-1)
m^2/ft^2	=	the conversion factor from foot squared to meter squared (9.290300E-2)

And:

The resulting solution is:

kg*m^2 = 1.0 * 4.2140110E-2 = 4.2140110E-2 kilogram meter squared

(3.2-6)

The Mechanics1 Moment of Inertia Tab allows the bidirectional selection of the following Moment of Inertia dimensions:

Major-Tab	Minor-Tab	Units on Pull-Down
Mechanics1
	Moment of Inertia
		pound square foot (lb*ft^2)
		kilogram square meter (kg*m^2)

Force Tab

The seventh Minor Tab under the Mechanics1 Major Tab is the Force Tab (see Figure 3.2-7). This example demonstrates the conversion of pound-force to Newton (N). In this example, the amplitude of pound-force (lbf) is set equal to one (1.0). The conversion equation is shown in Example 3.2-7.

pound-force (lbf) (=1.0) to Newton (N) Example 3.2-7:

N	=	lbf * kg/lb * g_n
	=	lbf * 4.5359237E-1 * 9.80665
	=	lbf * 4.4482216E0

Where: N	=	the number of Newton calculated
lbf	=	the number of pound-force being converted (1.0)
kg/lb	=	the conversion factor from pound to kilogram (4.5359237E-1)
g_n	=	the gravitational acceleration at the surface of the earth (9.80665)

And:

The resulting solution is:

N = 1.0 * 4.4482216E0 Newton

(3.2-7)

The Mechanics1 Force Tab allows the bidirectional selection of the following Force dimensions:

Major-Tab	Minor-Tab	Units on Pull-Down
Mechanics1
	Force
		pound-force
		poundal
		newton (N)

FIGURE 3.3-0 Unit Converter Using MATLAB App - Front Panel Mechanics2 Tab.

Figure 3.3-0 shows the Unit Converter MATLAB App Front Panel with the Mechanics2 Major Tab selected. Bidirectional matrices were created and installed within this app to allow the user the ability to easily select via pull-down menus all of the desired conversion pairs required. Each of the Mechanics2 Minor Tabs available in the App is explored herein.

Moment of Force, Torque Tab

The first Minor Tab under the Mechanics2 Major Tab is the Moment of Force, Torque Tab (see Figure 3.3-1). This example demonstrates the conversion of pound-force foot (lbf*ft) to Newton meter (N*m). In this example, the amplitude of pound-force foot (lbf*ft) is set equal to one (1.0). The conversion equation is shown in Example 3.3-1.

FIGURE 3.3-1 Unit Converter Using MATLAB App - Mechanics2 Moment of Force, Torque Tab.

pound-force (lbf) * foot (ft) (=1.0) to Newton (N) * meter (m) Example 3.3-1:

N*m	=	lbf * kg/lb * g_n *ft
	=	lbf * 4.5359237E-1 * 9.80665 * 0.3048
	=	lbf * ft * 1.355818E0

Where: N * m	=	the number of Newton meter calculated
lbf * ft	=	the number of pound-force foot being converted (1.0)
kg/lb	=	the conversion factor from pound to kilogram (4.5359237E-1)
g_n	=	the gravitational acceleration at the surface of the earth (9.80665)
m/ft	=	the conversion factor from foot to meter (0.3048)

And:

The resulting solution is:

N*m = 1.0 * 1.355818E0 = 1.355818E0 Newton-meter

(3.3-1)

The Mechanics2 Moment of Force, Torque Tab allows the bidirectional selection of the following Moment of Force, Torque dimensions:

Major-Tab	Minor-Tab	Units on Pull-Down
Mechanics2
	Moment of Force, Torque
		pound-force foot
		pound-force inch
		newton meter (N*m)

Pressure, Stress Tab

FIGURE 3.3-2 Unit Converter Using MATLAB App - Mechanics2 Pressure, Stress Tab.

The second Minor Tab under the Mechanics2 Major Tab is the Pressure, Stress Tab (see Figure 3.3-2). This example demonstrates the conversion of pound-force per square inch to kilopascal. In this example, the amplitude of pound-force per square inch (psi) (lbf/in^2) is set equal to one (1.0). The conversion equation is shown in Example 3.3-2.

pound-force per square inch (psi) (=1.0) to kilopascal (kPa) Example 3.3-2:

kPa	=	lbf/in^2* in^2/m^2 * N/lbf * kPa/Pa
	=	lbf/in^2* 1.550031E3 * 4.448222E0 * 1.0E-3
	=	lbf/in^2* 6.894757E0

Where: kPa	=	the number of kilopascal calculated
lbf/in^2 (psi)	=	the number of lbf/in^2 (psi) to be converted (1.0)
in^2/m^2	=	the conversion factor from m^2 to in^2 (1.550031E3)
N/lbf	=	the conversion factor from lbf to N (4.448222E0)
kPa/Pa	=	the conversion factor from Pa to kPa (1.0E-3)

And:

The resulting solution is:

kPa = lbf/in^2* 6.894757E0= 6.894757E0 kilopascal

(3.3-2)

The Mechanics2 Pressure, Stress Tab allows the bidirectional selection of the following Pressure, Stress dimensions:

Major-Tab	Minor-Tab	Units on Pull-Down
Mechanics2
	Pressure, Stress
		megapascal (Mpa)
		standard atmosphere
		bar
		kilopascal (kPa)
		millibar
		pound-force per square inch (psi)
		kilopound-force per square inch
		pound-force per square foot
		inch of mercury (32 degF)
		foot of water (39.2 degF)
		inch of water (39.2 degF)
		millimeter of mercury (32 degF)
		torr (Torr)
		pascal (Pa)

Viscosity (Dynamic) Tab

The third Minor Tab under the Mechanics2 Major Tab is the Viscosity (Dynamic) Tab (see Figure 3.3-3). This example demonstrates the conversion of centipoise to millipascal second. In this example, the amplitude of centipoise (cP) is set equal to one (1.0). The conversion equation is shown in Example 3.3-3.

centipoise (cP) (=1.0) to millipascal second (mPa*s) Example 3.3-3:

mPa*s = cP * mPa*s/cP = 1.0 * 1.0 = cP * 1.0

FIGURE 3.3-3 Unit Converter Using MATLAB App - Mechanics2 Viscosity (Dynamic) Tab.

Where: mPa*s	=	the number of millipascal calculated
cP	=	the number of centipoise to be converted (1.0)
mPa*s/cP	=	the conversion factor from centipoise to millipascal*second (1.0)

And:

The resulting solution is:

mPa*s = cP * mPa*s/cP = 1.0 * 1.0 = 1.0 millipascal second

(3.3-3)

The Mechanics2 Viscosity (Dynamic) Tab allows the bidirectional selection of the following Viscosity (Dynamic) dimensions:

Major-Tab	Minor-Tab	Units on Pull-Down
Mechanics2
	Viscosity (Dynamic)
		centipoise
		millipascal second (mPa*s)

Viscosity (Kinematic) Tab

The fourth Minor Tab under the Mechanics2 Major Tab is the Viscosity (Kinematic) Tab (see Figure 3.3-4). This example demonstrates the conversion of centistokes to square millimeter per second. In this example, the amplitude of centistokes (cSt) is set equal to one (1.0). The conversion equation is shown in Example 3.3-4.

centistokes (cSt) (=1.0) to square millimeter per second (mm^2/s) Example 3.3-4:

mm^2/s = cSt * (mm^2/s)/cSt = 1.0 * 1.0 = cSt * 1.0

FIGURE 3.3-4 Unit Converter Using MATLAB App - Mechanics2 Viscosity (Kinematic) Tab.

Where: mm^2/s	=	the number of millimeter squared per second calculated
cSt	=	the number of centistoke to be converted (1.0)
(mm^2/s)/cSt	=	the conversion factor from centistoke to mm^2 per second (1.0)

And:

The resulting solution is:

mm^2/s = cSt * (mm^2/s)/cSt = 1.0 * 1.0 = 1.0 millimeter squared per second

(3.3-4)

The Mechanics2 Viscosity (Kinematic) Tab allows the bidirectional selection of the following Viscosity (Kinematic) dimensions:

Major-Tab	Minor-Tab	Units on Pull-Down
Mechanics2
	Viscosity (Kinematic)
		centistokes
		square millimeter per second (mm^2/s)

Energy, Work, Heat Tab

The fifth Minor Tab under the Mechanics2 Major Tab is the Energy, Work, Heat Tab (see Figure 3.3-5). This example demonstrates the conversion of kilowatthour to joule. In this example, the amplitude of kilowatthour (kW * h) is set equal to one (1.0). The conversion equation is shown in Example 3.3-5.

kilowatthour (kW * h) (=1.0) to joule (J) Example 3.3-5:

J	=	kW * h * W/kW * min/h * s/min
	=	kW * h * 1.0E3 * 6.0E1 * 6.0E1
	=	kW * h * 3.6E6

Where: J	=	the number of joule calculated
kW * h	=	the number of kilowatthour to be converted (1.0)
W/kW	=	the conversion factor from kilowatt to watt (1.0E3)
min/h	=	the conversion factor from hour to minute (6.0E1)
s/min	=	the conversion factor from minute to second (6.0E1)

FIGURE 3.3-5 Unit Converter Using MATLAB App - Mechanics2 Energy, Work, Heat Tab.

And:

The resulting solution is:

J = 1.0 * 3.6E6 = 3.6E6 joule per kilowatthour

(3.3-5)

The Mechanics2 Energy, Work, Heat Tab allows the bidirectional selection of the following Energy, Work, Heat dimensions:

Major-Tab	Minor-Tab	Units on Pull-Down
Mechanics2
	Energy, Work, Heat
		kilowatthour
		megajoule (MJ)
		calorie (physics)
		kilojoule (kJ)
		calorie (nutrition) (kCal)
		joule (J)
		Btu
		therm (U.S.)
		horsepower hour
		foot pound-force

Power Tab

The sixth Minor Tab under the Mechanics2 Major Tab is the Power Tab (see Figure 3.3-6). This example demonstrates the conversion of Btu per second to Btu per hour. In this example, the amplitude of Btu per second (Btu/s) is set equal to one (1.0). The conversion equation is shown in Example 3.3-6.

Btu per second (Btu/s) (=1.0) to Btu per hour (Btu/h) 3.3-6:

Btu/h	=	Btu/s * s/min * min/h
	=	Btu/s * 6.0E1 * 6.0E1
	=	Btu/s * 3.6E3

Where: Btu/h	=	the number of Btu/h calculated
Btu/s	=	the number of Btu/s to be converted (1.0)
min/h	=	the conversion factor from hour to minute (6.0E1)
s/min	=	the conversion factor from minute to second (6.0E1)

And:

The resulting solution is:

Btu/h = 1.0 * 3.6E3 = 3.6E3 Btu per hour

(3.3-6)

The Mechanics2 Power Tab allows the bidirectional selection of the following Power dimensions:

Major-Tab	Minor-Tab	Units on Pull-Down
Mechanics2
	Power
		ton, refrigeration (12 000 Btu/h)
		kilowatt (kW)
		Btu per second
		Btu per hour
		watt (W)
		horsepower (550 ft-lbF/s)
		horsepower, electric
		foot pound-force per second (ft-lbF/s)

Figure 3.4-0 shows the Unit Converter MATLAB App Front Panel with the Heat1 Major Tab selected. Bidirectional matrices were created and installed within this app to allow the user the ability to easily select via pull-down menus all of the desired conversion pairs required. Each of the Heat1 Minor Tabs available in the App is explored herein.

Temperature Tab

The first Minor Tab under the Heat1 Major Tab is the Temperature Tab (see Figure 3.4-1). This example demonstrates the conversion of Fahrenheit to Celsius. In this example, the amplitude of Fahrenheit (°F) is set equal to fifty (50). The conversion equation is shown in Example 3.4-1.

Temperature (°F) (= 50.0) to Temperature (°C) Example 3.4-1:

°C = (°F-32)/1.8 = (50.0-32.0)/1.8 = 18.0/1.8 = 10

Where: °C	=	the Celsius temperature calculated
°F	=	the Fahrenheit temperature being converted (50.0)
(°F-32)/1.8	=	the conversion formula from Fahrenheit to Celsius

And:

The resulting solution is:

°F (50.0) = °C (10.0)

(3.4-1)

The Heat1 Temperature Tab allows the bidirectional selection of the following Temperature dimensions:

Major-Tab	Minor-Tab	Units on Pull-Down
Heat1
	Temperature
		Fahrenheit
		Celsius
		Kelvin

Linear Expansion coefficient Tab

The second Minor Tab under the Heat1 Major Tab is the Linear Expansion coefficient Tab (see Figure 3.4-2). This example demonstrates the conversion of reciprocal Fahrenheit (°F) to reciprocal Celsius (°C). In this example, the amplitude of Fahrenheit (°F) is set equal to eighteen (18). The conversion equation is shown in Example 3.4-2.

FIGURE 3.4-2 Unit Converter Using MATLAB App - Heat1 Linear Expansion coefficient Tab.

Temperature (°F) (=18.0) to Temperature (°C) Example 3.4-2:

	delta (1/°C)	=	delta (1/°F)*1.8 = delta (1.8/18) = 0.1
	delta (°C)	=	1/0.1 = 10

Where: delta °C = the differential Celsius temperature calculated delta °F = the differential Fahrenheit temperature being converted (18.0)

And:

The resulting solution is:

delta °F (18.0) = delta °C (10.0)

(3.4-2)

The Heat1 Linear Expansion coefficient Tab allows the bidirectional selection of the following Linear Expansion coefficient dimensions:

Major-Tab	Minor-Tab	Units on Pull-Down
Heat1
	Linear expansion coefficient
		delta T Fahrenheit (delta °F)
		delta T kelvin (delta K)
		delta T Celsius (delta °C)

Thermal Conductivity Tab

FIGURE 3.4-3 Unit Converter Using MATLAB App - Heat1 Thermal Conductivity Tab.

The third Minor Tab under the Heat1 Major Tab is the Thermal Conductivity Tab (see Figure 3.4-3). This example demonstrates the conversion of Btu inch per hour square foot degree Fahrenheit to watt per meter kelvin. In this example, the amplitude of Btu inch per hour square foot degree Fahrenheit (Btu * in/(h*ft^2*F)) is set equal to one (1.0). The conversion equation is shown in Example 3.4-3.

Btu * in/(h*ft^2*F) (=1.0) to W/(m*K) Example 3.4-3:

W/(m*K)	=	Btu * in/(hft^2F) * h/min * min/s * m/in * ft^2/m^2 * F/K
	=	1.0 * 1.055056E3 * 1/60 * 1/60 * 2.54E-2 * 1/9.290304E-2 * 1.8
	=	Btu * in/(hft^2F) * 1.4422791E-1

Where: W/(m*K)	=	the SI Thermal Conductivity calculated
Btu as joules	=	W s 1.055056E3
Btu * in/(hft^2F)	=	Thermal Conductivity being converted (1.0)
h/min	=	number of hours per minute (1/60)
min/s	=	number of minutes per second (1/60)
m/in	=	number of meter per inch (2.54E-2)
ft^2/m^2	=	number of square meter per square foot (1/9.290304E-2)
F/K	=	number of degree Fahrenheit per degree kelvin (1.8)

And:

The resulting solution is:

W/(m*K) = 1.0 * 1.4422791E-1 = 1.4422791E-1 watt per meter kelvin

(3.4-3)

The Heat1 Thermal Conductivity Tab allows the bidirectional selection of the following Thermal Conductivity dimensions:

Major-Tab	Minor-Tab	Units on Pull-Down
Heat1
	Thermal Conductivity
		Btu inch per hour square foot degree Fahrenheit
		watt per meter kelvin [W/(m*K)]

Coefficient of Heat Transfer Tab

The fourth Minor Tab under the Heat1 Major Tab is the Coefficient of Heat Transfer Tab (see Figure 3.4-4). This example demonstrates the conversion of Btu inch per hour square foot degree Fahrenheit (Btu * in/(h*ft^2*F)) to watt per square meter kelvin (W/(m^2*K)). In this example, the amplitude of Btu inch per hour square foot degree Fahrenheit (Btu * in/(h*ft^2*F)) is set equal to one (1.0). The conversion equation is shown in Example 3.4-4.

Btu * in/(h*ft^2*F) (=1.0) to W/(m^2*K) Example 3.4-4:

W/(m^2*K)	=	Btu * 1/(hft^2F) * h/min * min/s * ft^2/m^2 * F/K
	=	1.0 * 1.055056E3 * 1/60 * 1/60 * 1/9.290304E-2 * 1.8
	=	Btu * 1/(hft^2F) * 5.678264E0

FIGURE 3.4-4 Unit Converter Using MATLAB App - Heat1 Coefficient of Heat Transfer Tab.

Where: W/(m^2*K)	=	the SI Coefficient of Heat Transfer calculated
Btu as joules	=	W s 1.055056E3
Btu * 1/(hft^2F)	=	Coefficient of Heat Transfer being converted (1.0)
h/min	=	number of hours per minute (1/60)
min/s	=	number of minutes per second (1/60)
ft^2/m^2	=	number of square meter per square foot (1/9.290304E-2)
F/K	=	number of degree Fahrenheit per degree kelvin (1.8)

And:

The resulting solution is:

W/(m^2*K) = Btu * 1/(h*ft^2*F) * 5.678264E0 = 1.0 * 5.678264E0 = 5.678264E0 watts per square meter

(3.4-4)

The Heat1 Coefficient of Heat Transfer Tab allows the bidirectional selection of the following Coefficient of Heat Transfer dimensions:

Major-Tab	Minor-Tab	Units on Pull-Down
Heat1
	Coefficient of Heat Transfer
		Btu per hour square foot degree Fahrenheit
		watts per square meter kelvin [W/(m^2*K)]

Heat Capacity Tab

The fifth Minor Tab under the Heat1 Major Tab is the Heat Capacity Tab (see Figure 3.4-5). This example demonstrates the conversion of Btu per degree Fahrenheit (Btu/ °F) to kilojoule per kelvin (kJ/K). In this example, the amplitude of Btu per degree Fahrenheit (Btu/F)) is set equal to one (1.0). The conversion equation is shown in Example 3.4-5.

Btu/ °F (=1.0) to kJ/K Example 3.4-5:

kJ/K	=	Btu/ °F * kJ/J * °F/K
	=	Btu/ °F * 1.055056E3 * 1.0E-3 * 1.8
	=	Btu/ °F * 1.899101E0

Where: kJ/K	=	the SI Coefficient of Heat Capacity calculated
Btu as joules	=	W s 1.055056E3
Btu/ °F	=	Coefficient of Heat Capacity being converted (1.0)
°F/K	=	number of degree Fahrenheit per degree kelvin (1.8)
kJ/J	=	1.0E-3

And:

The resulting solution is:

kJ/K = 1.0 * 1.899101E0 = 1.899101E0 kilojoules per kelvin

(3.4-5)

The Heat1 Heat Capacity Tab allows the bidirectional selection of the following Heat Capacity dimensions:

Major-Tab	Minor-Tab	Units on Pull-Down
Heat1
	Heat Capacity
		Btu per degree Fahrenheit
		kilojoule per kelvin (kJ/K)

Figure 3.5-0 shows the Unit Converter MATLAB App Front Panel with the Heat2 Tab selected. Bidirectional matrices were created and installed within this app to allow the user the ability to easily select via pull-down menus all of the desired conversion pairs required. Each of the Tabs available in the App is explored herein.

Specific Heat Capacity Tab

The first Minor Tab under the Heat2 Major Tab is the Specific heat capacity Tab (see Figure 3.5-1). This example shows the conversion of Btu per pound degree Fahrenheit (Btu/(lb * °F) to Kilojoule per kilogram kelvin [kJ/(kg * K)]. In this example, the amplitude of Btu per pound degree Fahrenheit is set equal to one (1.0). The conversion equation is shown in Example 3.5-1.

FIGURE 3.5-1 Unit Converter Using MATLAB App - Heat2 Specific Heat Capacity Tab.

Btu/(lb* °F) (=1.0) to kJ/(kg * K) Example 3.5-1:

kJ/(kg * K)	=	Btu/(lb * °F) * J/Btu * kJ/J * lb/kg * F/K
	=	Btu/(lb* °F) * 1.055056E3 * 1/1000 * 1/4.535924E-1 *1/5.55556E-1
	=	BTU/(lb * F) * 4.1868E0

Where: kJ/(kg * K)	=	the number of kilojoule per kilogram kelvin calculated
Btu/(lb*F)	=	the number of Btu per pound degree Fahrenheit to be converted (1.0)
J/BTU	=	the conversion factor from Btu to joule (1.055056E3)
kJ/J	=	the conversion factor from joule to kilojoule (1/1000)
lb/kg	=	the conversion factor from kilogram to pound (1/4.535924E-1)
F/K	=	the conversion factor from kelvin degree interval to Fahrenheit degree interval (1/5.55556E-1)

And:

The resulting solution is:

kJ/(kg * K) = 1.0 * 4.1868E+0 = 4.1868E+0 kilojoule per kilogram kelvin

(3.5-1)

The Heat2 Specific heat capacity Tab allows the bidirectional selection of the following Specific heat capacity dimensions:

Major-Tab	Minor-Tab	Units on Pull-Down
Heat2
	Specific Heat Capacity
		Btu per pound degree Fahrenheit
		kilojoule per kilogram kelvin (KJ/(kg * K))

Entropy Tab

The second Minor Tab under the Heat2 Major Tab is the Entropy Tab (see Figure 3.5-2). This example shows the conversion of Btu per degree Rankine (Btu/R) to kilojoule per kelvin (kJ/K). In this example, the amplitude of Btu per degree Rankine is set equal to one (1.0). The conversion equation is shown in Example 3.5-2.

Btu/R (=1.0) to kJ/K Example 3.5-2:

kJ/(K)	=	Btu/R * J/Btu * kJ/J * R/K
	=	Btu/R * 1.055056E3 * 1/1000 * 1/5.55556E-1
	=	Btu/R * 1.899101E0

Where: kJ/K	=	the number of kilojoule per kelvin calculated
Btu/R	=	the number of Btu per degree Rankine to be converted (1.0)
J/Btu	=	the conversion factor from Btu to joule (1.055056E3)
kJ/J	=	the conversion factor from joule to kilojoule (1/1000)
R/K	=	the conversion factor from kelvin degree interval to Rankine degree interval (1/5.55556E-1)

And:

The resulting solution is:

kJ/K = 1.0 * 1.899101E0 = 1.899101E0 kilojoule per kelvin

(3.5-2)

The Heat2 Entropy Tab allows the bidirectional selection of the following entropy dimensions:

Major-Tab	Minor-Tab	Units on Pull-Down
Heat2
	Entropy
		Btu per degree Rankine (BTU/R)
		kilojoule per kelvin (kJ/K)

Specific Entropy

The third Minor Tab under the Heat2 Major Tab is the Specific entropy Tab (see Figure 3.5-3). This example shows the conversion of Btu per pound degree Rankine [Btu/(lb*R)] to kilojoule per kilogram kelvin [kJ/(kg*K)]. In this example, the amplitude of Btu per pound degree Rankine [Btu/(lb*R)] is set equal to one (1.0). The conversion equation is shown in Example 3.5-3.

FIGURE 3.5-3 Unit Converter Using MATLAB App - Heat2 Specific Entropy Tab.

Btu/(lb*R) (=1.0) to kJ/(kg*K) Example 3.5-3:

kJ/(kg*K)	=	Btu/(lbR)J/BtukJ/Jlb/kg*R/K
	=	Btu/(lbR)1.055056E31/1000 1/4.535924E-1*1/5.55556E-1
	=	Btu/(lbR)4.1868E0

Where: kJ/(kg*K)	=	the number of kilojoule per kilogram kelvin calculated
Btu/(lb*R)	=	the number of Btu per pound degree Fahrenheit to be converted (1.0)
J/Btu	=	the conversion factor from Btu to joule (1.055056E3)
kJ/J	=	the conversion factor from joule to kilojoule (1/1000)
lb/kg	=	the conversion factor from kilogram to pound (1/4.535924E-1)
R/K	=	the conversion factor from kelvin degree interval to Fahrenheit degree interval (1/5.55556E-1)

And:

The resulting solution is:

kJ/(kg*K) = 1.0*4.1868E+0 = 4.1868E+0 kilojoule per kilogram kelvin

(3.5-3)

The Heat2 Specific Entropy Tab allows the bidirectional selection of the following Specific Entropy dimensions:

Major-Tab	Minor-Tab	Units on Pull-Down
Heat2
	Specific Entropy
		Btu per pound degree Rankine [Btu/(lb * R)]
		kilojoule per kilogram kelvin ([kJ/(kg*K)])

Specific Internal Energy Tab

The fourth Minor Tab under the Heat2 Major Tab is the Specific Internal Energy Tab (see Figure 3.5-4). This example shows the conversion of Btu per pound (Btu/lb) to kilojoule per kilogram (kJ/kg). In this example, the amplitude of Btu per pound is set equal to one (1.0). The conversion equation is shown in Example 3.5-4.

Btu per pound to kilojoule per kilogram (kJ/kg) Example 3.5-4:

kJ/kg	=	Btu/lb* J/Btu * kJ/J * lb/kg
	=	Btu/lb * 1.055056E3 * 1/1000 * 1/4.535924E-1
	=	Btu/lb * 2.326E0

Where: kJ/kg	=	the number of kilojoule per kilogram calculated
Btu/lb	=	the number of Btu per pound to be converted (1.0)
J/Btu	=	the conversion factor from Btu to joule (1.055056E3)
kJ/J	=	the conversion factor from joule to kilojoule (1/1000)
lb/kg	=	the conversion factor from kilogram to pound (1/4.535924E-1)

FIGURE 3.5-4 Unit Converter Using MATLAB App - Heat2 Specific Internal Energy Tab.

And:

The resulting solution is:

kJ/kg = 1.0 * 2.326E0 = 2.326E0 kilojoule per kilogram

(3.5-4)

The Heat2 Specific Internal Energy Tab allows the bidirectional selection of the following specific internal energy dimensions:

Major-Tab	Minor-Tab	Units on Pull-Down
Heat2
	Specific Internal Energy
		Btu per pound (Btu/lb)
		kilojoule per kilogram (kJ/kg)

Figure 3.6-0 shows the Unit Converter MATLAB App Front Panel with the Electricity and Magnetism (ElecMag) Tab selected. Bidirectional matrices were created and installed within this app to allow the user the ability to easily select via pull-down menus all of the desired conversion pairs required. Each of the Tabs available in the App is explored herein.

Magnetic Field Strength Tab

The first Minor Tab under the Elec/Mag Major Tab is the Magnetic Field Strength Tab (see Figure 3.6-1). This example demonstrates the conversion of oersted to ampere/meter (A/m). In this example, the amplitude of oersted is set equal to one (1.0). The conversion equation is shown in Example 3.6-1 {37}.

FIGURE 3.6-1 Unit Converter Using MATLAB App - Elec/Mag Magnetic Field Strength Tab.

oersted (=1.0) to ampere/meter (A/m) Example 3.6-1:

A/m = oersted * (A/m)/oersted = 1.0 * 1000/4p = 1.0 * 79.57747

Where: A/m	=	the number of amperes per meter calculated
oersted	=	the number of oersted to be converted (1.0)
(A/m)/oersted	=	the conversion factor from oersted to ampere/meter (79.57747)

And:

The resulting solution is:

A/m = 1.0* 7.957747E+1 = 7.957747E+1 ampere per meter

(3.6-1)

The Elec/Mag Magnetic Field Strength Tab allows the bidirectional selection of the following Magnetic Field Strength dimensions:

Major-Tab	Minor-Tab	Units on Pull-Down
Elec/Mag
	Magnetic Field Strength
		oersted
		ampere per meter (A/m)

Magnetic Flux Tab

The second Minor Tab under the Elec/Mag Major Tab is the Magnetic Flux Tab (see Figure 3.6-2). This example shows the conversion of maxwell to nanoweber. In this example, the amplitude of maxwell is set equal to one (1.0). The conversion equation is shown in Example 3.6-2.

maxwell (Mx) (=1.0) to nanoweber (nWb) Example 3.6-2:

nWb	=	maxwell * Wb/Mx * nWb/Wb
	=	maxwell * 10^-8 * 10⁹
	=	maxwell * 10
	=	1.0E+1 nWb

Where: nWb	=	the number of nanoweber calculated
Mx	=	the starting number of maxwell (1.0)
Wb/Mx	=	the conversion factor from maxwell to weber (10^-8)
nWb/Wb	=	the conversion factor from weber to nanoweber (10⁹)

FIGURE 3.6-2 Unit Converter Using MATLAB App - Elec/Mag Magnetic Flux Tab.

And:

The resulting solution is:

nWb = 1.0 * 10 = 10 nanoweber

(3.6-2)

The Elec/Mag Magnetic Flux Tab allows the bidirectional selection of the following magnetic flux dimensions:

Major-Tab	Minor-Tab	Units on Pull-Down
Elec/Mag
	Magnetic Flux
		maxwell (Mx)
		nanoweber (nWb)

Magnetic Flux Density Tab

The third Minor Tab under the Elec/Mag Major Tab is the Magnetic Flux Density Tab (see Figure 3.6-3). This example shows the conversion of gauss to millitesla. In this example, the amplitude of gauss is set equal to one (1.0). The conversion equation is shown in Example 3.6-3.

FIGURE 3.6-3 Unit Converter Using MATLAB App - Elec/Mag Magnetic Flux Density Tab.

gauss (G) to millitesla (mT) Example 3.6-3:

mT = G * T/ G * mT/T = G * 10^-4 ^* 10³ = gauss * 1.0E-1

Where: mT	=	the number of millitesla calculated
G	=	the number of gauss to be converted (1.0)
T/G	=	the conversion factor from gauss to tesla (10^-4)
mT/T	=	the conversion factor from tesla to millitesla (10³)

And:

The resulting solution is:

mT = 1.0 * 1.0E-1 = 1.0E-1 millitesla

(3.6-3)

The Elec/Mag Magnetic Flux Density Tab allows the bidirectional selection of the following Magnetic Flux Density dimensions:

Major-Tab	Minor-Tab	Units on Pull-Down
Elec/Mag
	Magnetic Flux Density
		gauss (G)
		millitesla (mT)

Electric Charge Tab

FIGURE 3.6-4 Unit Converter Using MATLAB App - Elec/Mag Electric Charge Tab.

The fourth Minor Tab under the Elec/Mag Major Tab is the Electric Charge Tab (see Figure 3.6-4). This example shows the conversion of ampere hour to coulomb. In this example, the amplitude of ampere hour is set equal to one (1.0). The conversion equation is shown in Example 3.6-4.

ampere hour (A*h) (=1.0) to coulomb (C) Example 3.6-4:

C	=	Ah (C/s)(1/A) * min/h * s/min
	=	Ah 1 * 60 * 60
	=	Ah 3600 = Ah 3.6E+3

Where: C	=	the number of coulomb calculated
A*h	=	the number of ampere hour to be converted (1.0)
(C/s)(1/A)	=	the conversion factor from ampere to coulomb per second (1)
min/h	=	the conversion factor from hours to minutes (60)
s/min	=	the conversion factor from minutes to seconds (60)

And:

The resulting solution is:

C = 1.0 * 3.6E+3 = 3.6E+3 coulomb

(3.6-4)

The Elec/Mag Electric Charge Tab allows the bidirectional selection of the following Electric Charge dimensions:

Major-Tab	Minor-Tab	Units on Pull-Down
Elec/Mag
	Electric Charge
		ampere hour (A*h)
		coulomb (C)

Resistivity Tab

The fifth Minor Tab under the Elec/Mag Major Tab is the Resistivity Tab (see Figure 3.6-5). This example shows the conversion of ohm circular mil per foot to Nanoohm meter (nOhm * m). In this example, the amplitude of ohm circular mil per foot is set equal to one (1.0). The conversion equation is shown in Example 3.6-5.

ohm circular mil per foot (Ω*cmil/ft) (=1.0) to nanoohm meter (nΩ * m) Example 3.6-5:

nΩ* m	=	Ωcmil/ft nΩ/Ω * m²/cmil * ft/m
	=	Ωcmil/ft 1.0E+9 * 5.067075E-10 * 1/0.3048
	=	Ωcmil/ft 1.662426E+0

Where: nΩ * m	=	the number of nanoohm meter calculated
Ω*cmil/ft	=	the number of ohm circular mil per foot to be converted (1.0)
nΩ/Ω	=	the conversion factor from ohm to nanoohm (1.0E+9)
m²/cmil	=	the conversion factor from circular mil to meter squared (5.067075E-10)
ft/m	=	the conversion factor from meter to foot (1/0.3048)

And:

The resulting solution is:

nΩ * m = 1.0 * 1.662426E+0 = 1.662426E+0 nanoohm meter

(3.6-5)

The Elec/Mag Resistivity Tab allows the bidirectional selection of the following Resistivity dimensions:

Major-Tab	Minor-Tab	Units on Pull-Down
Elec/Mag
	Resistivity
		ohm circular mil per foot
		nanoohm meter (nΩ * m)

Conductivity Tab

The sixth Minor Tab under the Elec/Mag Major Tab is the Conductivity Tab (see Figure 3.6-6). This example shows the conversion of mho per centimeter (mho/cm) to siemens/meter (S/m). In this example, the amplitude of mho per centimeter (mho/cm) is set equal to one (1.0). The conversion equation is shown in Example 3.6-6.

mho per centimeter (mho/cm) (=1.0) to siemens per meter (S/m) Example 3.6-6:

S/m	=	mho/cm * cm/m * S/mho
	=	mho/cm * 100 * 1.0
	=	mho/cm * 100 = mho/cm * 1.0E+2

Where: S/m	=	the number of siemens per meter calculated
mho/cm	=	the number of mho per centimeter to be converted (1.0)
cm/m	=	the conversion factor from meter to centimeter = 100
S/mho	=	the conversion factor from mho to siemens (1.0)

And:

The resulting solution is:

S/m = 1.0 * 100 = 100 siemens per meter

(3.6-6)

The Elec/Mag Conductivity Tab allows the bidirectional selection of the following conductivity dimensions:

Major-Tab	Minor-Tab	Units on Pull-Down
Elec/Mag
	Conductivity
		mho per centimeter (mho/cm)
		siemens per meter (S/m)

3.7 QUANTITIES OF LIGHT AND RELATED ELECTROMAGNETIC RADIATION (LIGHT/EM RADIATION)

Figure 3.7-0 shows the Unit Converter MATLAB App Front Panel with the Light and Related Electromagnetic Radiation (Light/EM Radiation) Tab selected. Bidirectional matrices were created and installed within this app to allow the user the ability to easily select via pull-down menus all of the desired conversion pairs required. Each of the Tabs available in the App is explored herein.

FIGURE 3.7-0 Unit Converter Using MATLAB App - Front Panel Light/EM Radiation Tab.

Wavelength Tab

FIGURE 3.7-1 Unit Converter Using MATLAB App - Light/EM Radiation Wavelength Tab.

The first Minor Tab under the Light/EM Radiation Major Tab is the Wavelength Tab (see Figure 3.7-1). This example shows the conversion of angstrom (Å) to nanometer (nm). In this example, the amplitude of angstrom (Å) is set equal to one (1.0). The conversion equation is shown in Example 3.7-1.

angstrom (Å) (=1.0) to nanometer (nm) Example 3.7-1:

nm = Å * m/Å * nm/m = Å * 1.0E-10 * 1.0E9 = Å * 1.0E-1

Where: nm	=	the number of nanometer calculated
Å	=	the number of angstrom to be converted (1.0)
m/Å	=	the conversion factor from angstrom to meter (1.0e-10)
nm/m	=	the conversion factor from meter to nanometer (1.0E9)

And:

The resulting solution is:

nm = 1.0 * 1.0E-1 = 1.0E-1 nanometer

(3.7-1)

The Light/EM Radiation Wavelength Tab allows the bidirectional selection of the following wavelength dimensions:

Major-Tab	Minor-Tab	Units on Pull-Down
Light/EM Radiation
	Wavelength
		angstrom (Å)
		nanometer (nm)

Luminance Tab

FIGURE 3.7-2 Unit Converter Using MATLAB App - Light/EM Radiation Luminance Tab.

The second Minor Tab under the Light/EM Radiation Major Tab is the Luminance Tab (see Figure 3.7-2). This example shows the conversion of candela per square inch (cd/in²) to candela per square meter (cd/m²). In this example, the amplitude of candela per square inch (cd/in²) is set equal to one (1.0). The conversion equation is shown in Example 3.7-2.

candela per square inch (cd/in²) (-1.0) to candela per square meter (cd/m²) Example 3.7-2:

cd/m²	=	cd/in² * in²/ m²
	=	cd/in² * 1/6.4516E-4
	=	cd/in² * 1.550003E+3

Where: cd/m²	=	the number of candela per square meter calculated
cd/in²	=	the number of candela per square inch to be converted (1.0)
in²/ m²	=	the conversion factor from square meter to square inch (1.550003E+3)

And:

The resulting solution is:

cd/m² = 1.0 * 1.550003E+3 = 1.550003E+3 candela per square meter

(3.7-2)

The Light/EM Radiation Luminance Tab allows the bidirectional selection of the following luminance dimensions:

Major-Tab	Minor-Tab	Units on Pull-Down
Light/EM Radiation
	Luminance
		lambert (L)
		candela per square inch (cd/in²)
		footlambert
		candela per square meter (cd/m²)

Luminous Excitance Tab

FIGURE 3.7-3 Unit Converter Using MATLAB App - Light/EM Radiation Luminous Excitance Tab.

The third Minor Tab under the Light/EM Radiation Major Tab is the Luminous Excitance Tab (see Figure 3.7-3). This example shows the conversion of lumen per square foot (lm/ft²) to phot (ph = lumen per square centimeter). In this example, the amplitude of lumen per square foot (lm/ft²) is set equal to one (1.0). The conversion equation is shown in Example 3.7-3.

lumen per square foot (lm/ft²) to phot (ph) Example 3.7-3:

ph	=	lm/ft² * ft²/m² * m²/cm²
	=	lm/ft² * 1/0.09290304 * 1/10⁴
	=	lm/ft² * 0.00107639 = lm/ft² * 1.07639E-3

Where: ph	=	the number of phot calculated
lm/ft2	=	the number of lumen per square foot to be converted (1.0)
in²/m²	=	the conversion factor from square meter to square foot (1/0.09290304)
m²/cm²	=	the conversion factor from square centimeter to square meter (1/10⁴)

And:

The resulting solution is:

ph = 1.0 * 1.07639E-3 = 1.07639E-3 phot

(3.7-3)

The Light/EM Radiation Luminous Excitance Tab allows the bidirectional selection of the following Luminous Excitance dimensions:

Major-Tab	Minor-Tab	Units on Pull-Down
Light/EM Radiation
	Luminous Excitance
		lumen per square foot (lm/ft²)
		phot (ph)
		lux (lx)

Illuminance Tab

FIGURE 3.7-4 Unit Converter Using MATLAB App - Light/EM Radiation Illuminance Tab.

The fourth Minor Tab under the Light/EM Radiation Major Tab is the Illuminance Tab (see Figure 3.7-4). This example shows the conversion of footcandle (fc = lumen per square foot) to lux (lx = lumen per square meter). In this example, the amplitude of footcandle (fc) is set equal to one (1.0). The conversion equation is shown in Example 3.7-4.

footcandle (fc) to lux (lx) Example 3.7-4:

lx	=	fc * ft²/m²
	=	fc * 1/0.09290304
	=	fc * 10.76391
	=	fc * 1.076391E+1

Where: lx	=	the number of lux calculated
fc	=	the number of footcandle to be converted (1.0)
ft²/m²	=	the conversion factor from square meter to square foot (1.07639E+1)

And:

The resulting solution is:

lx = 1.0 * 1.07639E+1 = 1.07639E+1 lux

(3.7-4)

The Light/EM Radiation Illuminance Tab allows the bidirectional selection of the following illuminance dimensions:

Major-Tab	Minor-Tab	Units on Pull-Down
Light/EM Radiation
	Illuminance
		footcandle
		lux (lx)

FIGURE 3.8-0 Unit Converter Using MATLAB App - Front Panel Radiology Tab.

Figure 3.8-0 shows the Unit Converter MATLAB App Front Panel with the Radiology Tab selected. Bidirectional matrices were created and installed within this app to allow the user the ability to easily select via pull-down menus all of the desired conversion pairs required. Each of the Tabs available in the App is explored herein.

Activity (of a radionuclide) Tab

FIGURE 3.8-1 Unit Converter Using MATLAB App - Radiology Activity (of a radionuclide) Tab.

The first Minor Tab under the Radiology Major Tab is the Activity (of a radionuclide) Tab (see Figure 3.8-1). This example shows the conversion of Curie (ci) = 3.7×10¹⁰ decays per second) to megabequerel (MBq; 1 Bq = 1 decay per second). In this example, the amplitude of Curie (ci) is set equal to one (1.0). The conversion equation is shown in Example 3.8-1.

Curie (ci) to megabequerel (MBq) Example 3.8-1:

MBq	=	ci * Bq/ci * MBq/Bq
	=	ci * = ci * 3.7E+10 * 1.0E-6
	=	ci * 3.7E+4

Where: MBq	=	the number of megabequerel calculated
ci	=	the number of Curie to be converted (1.0)
Bq/ci	=	the conversion factor from Curie to bequerel (3.7E+10)
MBq/Bq	=	the conversion factor from bequerel to megabequerel (1.0E-6)

And:

The resulting solution is:

MBq = 1.0 * 3.7E+4 = 3.7E+4 megabequerel

(3.8-1)

The Radiology Activity (of a radionuclide) Tab allows the bidirectional selection of the following Activity (of a radionuclide) dimensions:

Major-Tab	Minor-Tab	Units on Pull-Down
Radiology
	Activity (of a radionuclide)
		Curie
		megabequerel (MBq)

Absorbed Dose Tab

FIGURE 3.8-2 Unit Converter Using MATLAB App - Radiology Absorbed Dose Tab.

The second Minor Tab under the Radiology Major Tab is the Absorbed Dose Tab (see Figure 3.8-2). This example shows the conversion of Rad to centigray (cGy). In this example, the amplitude of Rad is set equal to one (1.0). The conversion equation is shown in Example 3.8-2.

Rad to centigray (cGy) Example 3.8-2:

cGy	=	rad * Gy/rad * cGy/Gy
	=	rad * 0.01 * 1.0E+2
	=	rad * 1.0E0

Where: cGy	=	the number of centigray calculated
Rad	=	the number of Rad to be converted (1.0)
Gy/Rad	=	the conversion factor from Rad to gray (0.01)
cGy/Gy	=	the conversion factor from gray to centigray (1.0E+2)

And:

The resulting solution is:

cGy = 1.0 * 1.0E+0 = 1.0E0 centigray

(3.8-2)

The Radiology Absorbed Dose Tab allows the bidirectional selection of the following absorbed dose dimensions:

Major-Tab	Minor-Tab	Units on Pull-Down
Radiology
	Absorbed Dose
		Rad (rad)
		gray (Gy)
		centigray (cGy)

Dose Equivalent

FIGURE 3.8-3 Unit Converter Using MATLAB App - Radiology Dose Equivalent Tab.

The third Minor Tab under the Radiology Major Tab is the Dose Equivalent Tab (see Figure 3.8-3). This example shows the conversion of Rem (rem) to sievert (Sv). In this example, the amplitude of Rem (rem) is set equal to one (1.0). The conversion equation is shown in Example 3.8-3.

Rem (rem) to sievert (Sv) Example 3.8-3:

Sv = rem * Sv/rem = rem* 0.01 = rem * 1.0E-2

Where: Sv	=	the number of sievert calculated
rem	=	the number of Rem to be converted (1.0)
Sv/rem	=	the conversion factor from Rem to sievert (0.01)

And:

The resulting solution is:

S = 1.0 * 1.0E-2 = 1.0E-2 sievert

(3.8-3)

The Radiology Dose Equivalent Tab allows the bidirectional selection of the following dose equivalent dimensions:

Major-Tab	Minor-Tab	Units on Pull-Down
Radiology
	Dose Equivalent
		Rem (rem)
		sievert (Sv)

Exposure (x and gamma rays) Tab

FIGURE 3.8-4 Unit Converter Using MATLAB App - Radiology Exposure (x and gamma rays) Tab.

The fourth Minor Tab under the Radiology Major Tab is the Exposure (x and gamma rays) Tab (see Figure 3.8-4). This example shows the conversion of roentgen (R = lumen per square foot) to coulomb per kilogram (C/kg = lumen per square meter). In this example, the amplitude of roentgen (R) is set equal to one (1.0). The conversion equation is shown in Example 3.8-4.

roentgen (R) to coulomb per kilogram (C/kg) Example 3.8-4:

C/kg = R * (C/kg)/R = R * 0.000258 = R * 2.58E-4

Where: C/kg	=	the number of coulomb per kilogram calculated
R	=	the number of roentgen to be converted (1.0)
(C/kg)/R	=	the conversion factor from roentgen to coulomb per kilogram (0.000258)

And:

The resulting solution is:

C/kg = 1.0 * 2.58E-4 = 2.58E-4 coulomb per kilogram

(3.8-4)

The Radiology Exposure (x and gamma rays) Tab allows the bidirectional selection of the following exposure (x and gamma rays) dimensions:

Major-Tab	Minor-Tab	Units on Pull-Down
Radiology
	Exposure (x and gamma rays)
		roentgen (R)
		coulomb per kilogram (C/kg)

kg*m^2	=	lbft^2 kg/lb * m^2/ft^2
	=	lbft^2 4.5359252E-1 * 9.290300E-2
	=	lbft^2 4.2140110E-2