Unit Conversion Simplicity

Unit Conversion TablesThis document contains information on using units in Mechanica and on converting values between different systems of units. This document includes the following sections:

Topic

IntroductionBasic EqualitiesSystem of UnitsBasic UnitsExamples of Values for Gravitational Acceleration and Selected Properties of SteelCorrespondence Between Mass and ForceCorrespondence Between Mass and Pounds-massConversion of Basic UnitsCorrespondence Between Degrees Celsius and Degrees Fahrenheit

Note: Throughout this document, scientific notation is written as you would type it in Mechanica. For example,2.07 x 1011 is written as 2.07e11.

IntroductionMechanica does not store information concerning the physical dimensions (units) of the numerical data that you enter. Therefore, whenever you enter numerical data into Mechanica, you must ensure that you are using a consistent set of units.

For example, if you enter distance in terms of inches and force in terms of pounds-force, then you must enter Young's modulus in terms of pounds-force per square inch. In this system of units, Mechanica reports stress in terms of pounds-force per square inch.

If you do not use a consistent set of units when entering data, the values computed by Mechanica will be meaningless. This document provides an overview of the physical dimensions of many of the quantities in Mechanica.

The following abbreviations are used throughout this document:

L = length

M = mass

http://www.eng.cam.ac.uk/DesignOffice/cad/proewild3/usascii/proe/promec/getstart/units/reference/units_conv.htm#837340

















T = time

F = force

E = energy (heat)

P = power

D = temperature (such as F, C, K)

R = angle radian

When choosing a consistent set of units, you must decide which quantities will form the basic physical dimensions and which quantities will be derived from the basic dimensions. Usually, you will choose either mass, length, and time (MLT) or force, length, and time (FLT) as the basic dimensions. The connection between these two systems is given by Newton's second law of motion:

force = mass x acceleration

the dimensions of which are:

F = ML/T2

Some quantities in Thermal are usually expressed in terms of energy and power, the dimensions of which are determined from their definitions:

energy (work, heat) = force x distance

E = FL

power = energy ÷ time

P = E/T

Basic EqualitiesFollowing is a list of many of the quantities in Mechanica and the physical dimensions of each expressed in terms of common physical dimensions and also in terms of MLT and FLT.

Quantity Common MLT FLT

length L L L

time T T T

mass M M FT2/L

force F ML/T2 F

temperature D D D

area L2 L2 L2

volume L3 L3 L3

velocity L/T L/T L/T

acceleration L/T2 L/T2 L/T2

angle, rotation R R R

rotational velocity R/T R/T R/T

rotational acceleration R/T2 R/T2 R/T2

density M/L3 M/L3 FT2/L4

moment, torque FL ML2/T2 FL

distributed force along a curve F/L M/T2 F/L

distributed moment along a curve F ML/T2 F

distributed force over a surface, pressure, stress, Young's modulus F/L2 M/LT2 F/L2

distributed moment over a surface F/L M/T2 F/L

translational stiffness F/L M/T2 F/L

rotational stiffness FL/R ML2/T2R FL/R

coefficient of thermal expansion /D /D /D

moment of inertia of beam cross-sectional area L4 L4 L4

mass moment of inertia ML2 ML2 FLT2

energy, work, heat (E) FL ML2/T2 FL

power, heat transfer rate (P) E/T ML2/T3 FL/T

temperature gradient D/L D/L D/L

heat flux P/L2 M/T3 F/TL

thermal conductivity P/LD ML/T3D F/TD

convection coefficient P/L2D M/T3D F/LTD

specific heat (Cp) E/MD L2/T2D FL/MD

System of Units

To define a system of units, you assign a unit of measure to each of the physical dimensions. This section provides the units of the above quantities in four different systems of units, two different metric systems, MKS and mmNs, and two different English systems, FPS and IPS. The MKS system of units uses MLT as the basic dimensions. The mmNs, FPS, and IPS systems of units use FLT as the basic dimensions.

MKSFollowing are the basic and some of the derived units of the MKS system:

Basic Units Some Derived Units

M: kilogram (kg) F: kg-m/sec2 = Newton (N)

L: meter (m) E: N-m = Joule (J)

T: second (sec) P: J/sec = Watt (W)

D: degree Celsius ( C)

mmNSFollowing are the basic and some of the derived units of the mmNS system:


F: Newton (N) M: (N-sec2/mm) (kg-m/N-sec2) (1000mm/m) = 1000 kg = tonne(t)

L: millimeter (mm) E: (N-mm) (J/N-m) (m/1000mm) = J/1000 = mJ

T: second (sec) P: (mJ/sec) (J/1000mJ) (W-sec/J) = W/1000 = mW


mmKSFollowing are the basic and some of the derived units of the mmKS system:


M: kilogram (kg) F: kg-mm/sec2 = mN

L: millimeter (mm) E: mN-mm = J

T: second (sec) P: J/sec = W


FPSFollowing are the basic and some of the derived units of the FPS system:


F: pound-force (lbf) M: lbf-sec2/ft = slug

L: foot (ft) E: ft-lbf

T: second (sec) P: ft-lbf/sec

D: degree Fahrenheit ( F)

IPSFollowing are the basic and some of the derived units of the IPS system:


F: pound-force (lbf) M: lbf-sec2/in

L: inch (in) E: lbf-in

T: second (sec) P: lbf-in/sec


CGSFollowing are the basic and some of the derived units of the CGS system:


M: gram (g) F: g-cm/sec2 = 10-5 N = dyne

L: centimeter (cm) E: g-cm2/sec2 = 10-7 J = erg

T: second (sec) P: g-cm2/sec3 = 10-7 W


Pro/E DefaultFollowing are the basic and some of the derived units of the Pro/E Default system:


M: pounds-mass (lbm) F: in-lbm/sec2

L: inch (in) E: in2-lbm/sec2

T: second (sec) P: in2-lbm/sec3


Basic UnitsUsing the definitions from the previous section, the units of the quantities in these four systems are as follows:

Units

Metric(MKS)

Metric(mmNS)

English(FPS)

English(IPS)

length m mm ft in

time sec sec sec sec

mass kg tonne slug lbf-sec2/in

force N N lbf lbf

temperature C C F F

area m2 mm2 ft2 in2

volume m3 mm3 ft3 (cu-ft) in3 (cu-in)

velocity m/sec mm/sec ft/sec in/sec

acceleration m/sec2 mm/sec2 ft/sec2 in/sec2

angle, rotation rad rad rad rad

rotational velocity rad/sec rad/sec rad/sec rad/sec

rotational acceleration rad/sec2 rad/sec2 rad/sec2 rad/sec2

density kg/m3 tonne/mm3 slug/ft3 lbf-sec2/in4

moment, torque N-m N-mm ft-lbf in-lbf

distributed force along a curve N/m N/mm lbf/ft lbf/in

distributed moment along a curve N N lbf lbf

distributed force over a surface, pressure, stress, Young's modulus N/m2 (Pa) N/mm2 (MPa) lbf/ft2 lbf/in2 (psi)

translational stiffness N/m N/mm lbf/ft lbf/in

rotational stiffness N-m/rad N-mm/rad lbf-ft/rad lbf-in/rad

coefficient of thermal expansion / C / C / F / F

moment of inertia of beam cross-sectional area m4 mm4 ft4 in4

mass moment of inertia kg-m2 tonne-mm2 slug-ft2 lbf-in-sec2

energy, work, heat (E) J mJ ft-lbf in-lbf

power, heat transfer rate (P) W mW ft-lbf/sec in-lbf/sec

temperature gradient C/m C/mm F/ft F/in

heat flux W/m2 mW/mm2 lbf/ft-sec lbf/in-sec

thermal conductivity W/m- C mW/mm- C lbf/sec- F lbf/sec- F

convection film coefficient W/m2- C mW/mm2- C lbf/ft-sec- F lbf/in-sec- F

specific heat (Cp) J/kg- C mJ/tonne- C ft-lbf/slug- F in2/sec2- F

Note: 1W = 1N-m/sec, 1mJ = 1N-mm, 1mW = 1N-mm/sec, N/m2 = Pascal (Pa)

The numerical values of conductivity are the same in the MKS and mmNS systems and in the FPS and IPS systems.

In Structure, units of modal frequency results are always cycles per unit time or Hz. The units of time are affected by the force/length/time units you used to define the model. Structure never reports modal frequency in terms of radians per unit time.

Examples of Values for Gravitational Acceleration and Selected Properties of SteelThe following table shows examples of approximate values for acceleration, density, Young's modulus, thermal coefficient of expansion, and thermal conductivity:

Units

Metric(MKS)

Metric(mmNS)

English(FPS)

English(IPS)

g (gravitational acceleration) 9.81 m/sec2 9810 mm/sec2 32.2 ft/sec2 386 in/sec2

density (steel) 7830.0 kg/m3 7.83e-9 tonne/mm3 15.2 slug/ft3 7.33e-4 lb-sec2/in4

Young's modulus (steel) 2.07e11 N/m2 2.07e5 N/mm2 4.32e9 lb/ft2 3.0e7 lb/in2

coefficient of thermal expansion (steel) 12e-6/ C 12e-6/ C 6.5e-6/ F 6.5e-6/ F

thermal conductivity (steel) 43.37 W/m- C 43.37 mW/mm- C 5.4 lbf/sec- F(25 Btu/hr-ft- F)

5.41bf/sec- F(2.083 Btu/hr-in- F)

Correspondence Between Mass and ForceThe following list describes the correspondence between mass and force at sea level for four common unit systems:

1 kg weighs 9.81 Newtons

1 tonne weighs 9810 Newtons

1 slug weighs 32.2 lbs

1 (lb-sec2/in) weighs 386 lbs

Correspondence Between Mass and Pounds-massIn some English systems of units, mass is sometimes given in pounds-mass (lbm). The relationship between pounds-mass and mass in the FPS and IPS systems of units is determined by the fact that one pound-mass weighs one pound-force in the gravitational field of the earth at sea level:

lbf = lbm x g

where g = 32.2 ft/sec2 = 386 in/sec2

Therefore:

lbm = 1/386 lbf-sec2/in

lbm = 1/32.2 lbf-sec2/ft = 1/32.2 slug

Conversion of Basic Units

The following tables show conversion factors for various quantities:

Length Conversion Factors

m

mm

ft

in

1 m = 1 1000 3.281 39.37

1 mm = 1.0e-3 1 3.281e-3 3.937e-2

1 ft = 0.3048 304.8 1 12

1 in = 2.54e-2 25.4 8.333e-2 1

Mass Conversion Factors

kg

tonne(N-sec2/mm)

slug(lb-sec2/ft)

lb-sec2/in

1 kg = 1 1.0e-3 6.852e-2 5.71e-3

1 tonne = 1000 1 68.52 5.71

1 slug = 14.59 14.59e-3 1 8.333e-2

1 lb-sec2/in = 175.1 0.1751 12 1

Moments of Inertia

kg m2

tonne mm2

slug ft2

lbf-sec2-in

1 kg m2 = 1 1000 .738 8.85

1 tonne mm2 = 1e-3 1 7.375e-4 8.85e-3

1 slug ft 2 = 1.356 1.356e3 1 12

1 lbf-sec2-in = 0.113 113 1/12 1

Force Conversion Factors

N

Kg-force

lb

1 N = 1 0.101972 0.2248

1 lb = 4.448 0.453594 1

Moment Conversion Factors

N-m

N-mm

lb-ft

lb-in

1 N-m = 1 1000 0.7376 8.851

1 N-mm = 1.0e-3 1 7.376e-4 8.851e-3

1 lb-ft = 1.356 1356 1 12

1 lb-in = 0.113 113 8.33e-2 1

Density Conversion Factors

kg/m3

tonne/mm3

slug/ft3

lb-sec2/in4

1 kg/m3 = 1 1e-12 1.94e-3 9.36e-8

1 tonne/mm3 = 1e12 1 1.94e9 9.36e4

1 slug/ft3 = 515 5.15e-10 1 4.82e-5

1 lb-sec2/in4 = 1.07e7 1.07e-5 20700 1

Stress Conversion Factors

N/m2

N/mm2

lb/ft2

lb/in2

1 N/m2 = 1 1e-6 2.09e-2 1.45e-4

1 N/mm2 = 1e6 1 20900 145

1 lb/ft2 = 47.9 47.9e-5 1 6.94e-3

1 lb/in2 = 6890 6.89e-3 144 1

Translational Stiffness Conversion Factors N/m N/mm lb/ft lb/in

1 N/m = 1 1.0e-3 6.8525e-2 5.7104e-3

1 N/mm = 1000 1 68.525 5.710

1 lb/ft = 14.593 1.4593e-2 1 8.33e-2

1 lb/in = 175.118 1.7512e-5 12 1

Rotational Stiffness Conversion Factors

N-m/rad

N-mm/rad

lb-ft/rad

lb-in/rad

1 N-m/rad = 1 1000 0.7376 8.851

1 N-mm/rad = 1.0e-3 1 7.376e-4 8.851e-3

1 lb-ft/rad = 1.356 1356 1 12

1 lb-in/rad = 0.113 113 8.33e-2 1

Thermal Conductivity Conversion Factors

W/m- C

mW/mm- C

Btu/hr-ft- F

Btu/hr-in- F

lbf/sec- F

1 W/m- C = 1 1 0.5777 4.817e-2 0.1249

1 mW/mm- C = 1 1 0.5777 4.817e-2 0.1249

1 Btu/hr-ft- F = 1.731 1.731 1 8.333e-2 0.2162

1 Btu/hr-in- F = 20.76 20.76 12 1 2.594

1 lbf/sec- F = 8.007 8.007 4.626 0.3854 1

Correspondence Between Degrees Celsius and Degrees FahrenheitThe following two formulas describe the correspondence between the Celsius and Fahrenheit degree scales:

C = ( F 32)/1.8

F = 1.8 C + 32

Thus, a temperature difference of 1 C is equal to a difference of 1.8 F.

Documents

Unit Conversion Simplicity