Week - 1 - Consistency of Units

AIM:

Convert the given values in the required conversion factor units with detailed calculation.

OBJECTIVES:

Different industries use different system of units as per their convenience. The units for the basic measurement quantities, mass distance and time - dictate how the other derived quantities will be expressed.

LS-DYNA doesn't have a default system of units. User needs to input material properties and physical dimensions according to a consistent system of units as per their choice. This warrants that to use LS-DYNA in different circumstances, users has to be conversant with converting quantities from one system of units to another.

GIVEN DATA:

MASS - 1kg
LENGTH - 1m
TIME - 1s
FORCE - 1N
STRESS -1Pa
ENERGY - 1Nm
DENSITY - 1Kg/m3
YOUNG'S Modulus - 210GPa
Velocity - 56.33KMPH
GRAVITY - 9.8m/s2

System of Units:

Kg cm ms

Kg cm s

gm mm ms

kg m s

g cm s

g cm us

g mm s

ton mm s

slug ft s

kg mm s

g cm ms

kg mm ms

PROCEDURE:

1. Conversion of SI unit to kg cm ms

• Mass = 1 kg

=1 kg

• Length = 1m

=100 cm

• Time = 1 sec

=1000 ms

• Force = 1 N

F = mass* acceleration

= 1 kg * 1m/s^2

= (1 kg*100cm)/(1000ms)²

= 1E-04 (kg*cm)/ms²

Conversion factor = 10^-4

• Stress = 1 Pa

1 Pa = 1N/m^2

As from the above derived 1N = 1E-04 (kg*cm)/ms²

= {10^-4 (kg cm/ms²)} / (100 cm²)

= 1E-8 kg/cm^2 * ms^2

Conversion factor = 10^-8

• Energy = 1 Nm

=1N *1 m

={10^-4 kg cm/ms²} * 100 cm

=10 kg cm²/ms²

=1E-02 kg cm/ms^2

Conversion factor = 10^-2

• Density = 1Kg/m^3

=1 kg / (100 cm)³

=1 kg/1000000 cm³

=1E-06 kg/cm^3

Conversion factor = 10^-6

• Young’s Modulus = 210 GPa

1 Pa = 10^-3 kg/cm*ms²

1 GPa = 10⁹ * 10^-3 kg/cm*ms²

^{= 10^6 kg/cm*ms2}

210 GPa = 210 * 10⁶ kg/cm*ms²

= 210*E+06 kg/cm * ms^2

Conversion factor = 10⁶

• Velocity = 56.33 Kmph

Km/h

1Km = 10000 cm = 10⁴ cm

1 hr = 60min*60sec*1000

= 3600000

= 36*10⁵ ms

1 kmph

= (10⁴ )/(36*10⁵)

= 0.00277 cm/ms

56.33 kmph =

= 56.33 * 0.00277 cm/ms

= 0.1560 cm/ms

Conversion factor =

• Gravity = 9.8 m/s²

1 m/s2 = 100 cm/(1000ms)²

= 10 ^-4 cm/ms2

9.8 m/s2 = 9.8*10^-4 cm/ms2

= 9.8 E-04 cm/ms^2

Conversion Factor = 10^-4

^{(Note : Repeat the calculations for the other unit systems)}

CONVERTION TABLE:

	mass	Length	Time	Force	Stress	Energy	density	young's modulus	velocity	gravity
kg cm ms	1kg	1E+02cm	1E+03ms	1E-04 kg cm/ms^2	1E-8 kg/cm^2 * ms^2	1E-02 kg cm/ms^2	1E-06 kg/cm^3	210*E+06 kg/cm * ms^2	0.1564 cm/ms	9.8 E-04 cm/ms^2
Kg cm s	1kg	1E+02 cm	1s	1E+02 kg cm/s^2	1E-02 kg/cm s^2	1E+04 kg cm/s^2	1E-06 kg/cm^3	210*E+07 kg/cm * s^2	156.47 cm/s	9.8 E+02 cm/s^2
gm mm ms	1000 gm	1E+03 mm	1E+03 ms	1 gm*mm/ ms^2	1E-06 gm/ mm*ms^2	1E+03 gm*mm^2/ ms^2	1E-06 gm/mm^3	210E+03 gm/ mm*ms^2	15.647 mm/ms	9.8 E-03 mm/ms2
kg m s	1 kg	1 m	1s	1kg*m/s^2	1kg/m×s^2	1kg*m^2/s^2	1kg/m^3	210E+09 kg/m*s^2	15.64 m/s	9.8 m/ s^2
g cm s	1000 g	1E+02 cm	1s	1E+5 g cm/s2	10 g/cm*s^2	1E+07 g cm/s^2	1E-03 g/cm^3	210E+10 g/ cm*s^2	156.03 cm/s	9.8 E+02 cm/s2
g cm us	1000 g	1E+02 cm	1E+06 us	1E-01 g*cm/us2	1E-03 g/cm*us^2	10 g cm^2 /us2	1E-03 g/cm^3	210E+06 g/cm*us2	1.56E-04 cm/us	9.8 E-10 cm/us2
g mm s	1000 g	1E+03 mm	1s	1E+06 g mm/s2	1 g/mm s^2	1E+09 g mm2/s2	1E-06 g/mm3	210E+09 g/mm s2	15603 mm/s	9.8E+03 mm/s2
ton mm s	0.001 ton	1E+03 mm	1s	1E-06 ton mm/ms2	1E-12 ton/mm ms2	1E-03 ton mm2/ms2	1E-12 ton/mm3	210E-03 ton/mm ms2	15.60 mm/ms	9.8E-03 mm/ms2
slug ft s	0.068 slug	3.28 ft	1s	0.22 slug ft/s2	0.0205 slug/ft s2	0.7216 slug ft2/s2	0.0019 slug/ft3	4.305E+09 slug/ft s2	51.316 ft/s	32.14 ft/s2
kg mm s	1 kg	1E+03 mm	1s	1E+03 kg mm/s2	1E-03 kg/mm s2	1E+06 kg mm2/s2	1E-09 kg/mm3	210E+06 kg/mm s2	15603 mm/s	9.8E+03 mm/s2
g cm ms	1000 g	1E+02 cm	1E+03ms	1E-01 g cm/ms2	1E-03 g/cm ms2	10 g cm2/ms2	1E-03 g/cm3	210E+06 g/cm ms2	1.5603 cm/ms	9.8E-04 cm/ms2
kg mm ms	1 kg	1E+03 mm	1E+03ms	1E-03 kg mm /ms2	1E-09 kg/mm ms2	1 kg mm2/ms2	1E-09 kg/mm3	210 kg/mm ms2	15.60 mm/ms	9.8E-03 mm/ms2

RESULT:

The above given unit systems are coverted and tabulated.