Consistency of units

Objective

To obtain the measurements in the above different system of units. Also, mention the conversion factors.

Given task:

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. For example, automotive industries use kg,mm,ms as their standard unit system. Construction industries are likely to use tonne,m,s as their unit system. Similarly, PCB simulation in electronic industry uses gm, micrometer,ms as their system of units.

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.

Here\'s an example: Young\'s Modulus of steel is 210GPa which is input as 210e+9 in LS-DYNA as per SI unit system. However, if you use kg/mm/ms unit system, the input quantity will be 210000. Thus the conversion factor is 10^-6.

But, how?

That\'s for you to find out in this assignment.

Value of the following measurements are given as follows:

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

Now, here are a few 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:

As per requirement i am going to explain in detail calculation for conversion from SI unit to gm/mm/ms unit.For others unit systems ,I had plotted a table below with the unit systems as rows and measured quantities as columns.

SI units for gm mm ms

MASS 1 Kg = 1000 gm

LENGTH 1 m = 1000 mm

TIME 1 s = 1000 ms

FORCE 1N = (1Kg * m)/s^2

= (1000 gm * 1000 mm) / (1000 ms *1000 ms)

= (1 gm * mm ) / ms^2

STRESS 1Pa = N / m^2 = {(1 gm * mm ) / ms^2} / (1000 ms *1000 ms)

= 10^-6 gm /mm*ms^2

ENERGY 1Nm = { (1Kg * m)/s^2 } X (1000 mm)

= 10^3 gm*mm^2/ms^2

DENSITY 1Kg/m3 = 1000 gm /{ 10^3 ms}^3 { w.k.t , [(x^3)^3] =( x^9)}

= 10^3 gm/ 10^9 ms^3

= 10^-9 gm/ms^3

YOUNG\'S Modulus 210GPa

210GPa = 210 X [10^9 X (N / m^2)] { 1 GPa = 10^9 X (N / m^2)}

= 210 X [10^9 X (10^-6 gm /mm*ms^2)]

= 210 X 10^3 gm/mm*ms^2

= 210000 gm/mm*ms^2

Velocity 56.33KMPH

1KMPH = 10^6mm / (3600 *1000 ms) { 1KM = 10^6mm}

= 10/36 = 0.277 mm/ms { 1hr = 3600 *1000 ms}

56.33KMPH = 56.33 x 0.277

56.33KMPH = 15.64 mm/ms

GRAVITY 9.8m/s2

1 m/s2 = 1000 mm/(1000 ms X 1000 ms)

= 10^-3 mm/ms^2

9.8m/s2 = 9.8 X 10^-3 mm/ms^2

Measured quantities
		MASS	LENGTH	TIME	FORCE	STRESS	ENERGY	DENSITY	YOUNG\'S MODULUS	VELOCITY	GRAVITY
U	Kg cm ms	1 Kg	100 m	1000 ms	10^-4 Kg*cm/ms^2	10^-8Kg*cm/ms^2	10^-2 Kg*cm^2/ms^2	10^-6 Kg/cm^3	210 Kg/cm*ms^2	156.4*10^-2 cm/ms	9.8*10^-4 cm/ms^2
n	Kg cm s	1 Kg	100 cm	1 s	10^2 Kg*cm/s^2	10^-2 Kg/cm*s^2	10^4 Kg*cm^2/s^2	10^-6Kg/cm^3	210*10^7 Kg/cm*s^2	15647.22 cm/s	980 cm/s^2
i	gm mm ms	1000 gm	1000 mm	1000 ms	1 gm*mm/ms^2	10^-6 gm/mm*ms^2	10^3 gm*mm^2/ms^2	10^-6 gm/mm^3	210000 gm/ms*ms^2	15.64 mm/ms	9.8*10^-3 mm/ms^2
t	kg m s	1 Kg	1 m	1 s	Kg*m/s^2	Kg/m*s^2	Kg*m^2/s^2	1 Kg/m^3	210*10^9 Kg/m*s^2	15.64m/s	9.8m/s^2
	g cm s	1000 g	100 cm	1 s	10^5 g*cm/s^2	10 g/cm*s^2	10^7 g*cm^2/s^2	10^-3 g/cm	210*10^10 g/cm*s^2	1564.7 cm/s	980 cm/s^2
S	g cm us	1000 g	100 cm	1000000 us	10^-7 gm*cm/us^2	10^-11 gm/cm*us^2	10^-5 gm*cm^2/us^2	10 gm/cm	210*10^-2 gm/cm*us^2	1564.7*10^-6 cm/us	9.8*10^-10 cm/us^2
y	g mm s	1000 g	1000 mm	1 s	10^6 gm*mm/s^2	1 gm/mm*s^2	10^9 gm*mm^2/s^2	10^-6 g/mm^3	210*10^9 gm/mm*s^2	15647.2 mm/s	9.8*10^3 m/s^2
s	ton mm s	0.001 ton	1000mm	1 s	1 ton*mm/s^2	10^-6 ton/mm*s^2	10^3 ton*mm^2/s^2	10^-12 ton/mm^3	210*10^3 ton/mm*s^2	15647 mm/ms	9.8*10^3 mm/s^2
t	slug ft s	0.068 slug	3.28 ft	1 s	0.223 slug*ft/s^2	0.020 slug/ft*s^2	0.731 slug/ft*s^2	1.92*10^-3 slug/ft^3	4.2*10^9 slug/ft*s^2	51.33 ft/s	32.144 ft/s^2
e	kg mm s	1 Kg	1000 mm	1 s	1000 Kg*mm/s^2	10^-3 Kg/mm*s^2	10^6 Kg/mm^3	10^-9 Kg/mm^3	210*10^6Kg/mm*s^2	15647.22 mm/s	9.8*10^3 m/s^2
m	g cm ms	1000g	100 cm	1000 ms	0.1 g*cm/ms^2	10^-5 gm/cm*ms^2	10 g*cm^2/ms^2	10^-6 gm/cm^3	210*10^4 gm/cm*ms^2	1564*10^-3 cm/s^2	9.8*10^-4 cm/s^2
	kg mm ms	1 Kg	1000 mm	1000 ms	10^-3 Kg*mm/ms^2	10^-9 Kg/mm*ms^2	1 Kg*mm/ms^2	10^-9 Kg/mm^3	210 Kg/mm*ms^2	15647*10^-3 mm/ms	9.8*10^-3 mm/ms^2

Conclusion :

For this assignment i had learned about unit system and its conversion of its ,in detail.