Week - 1 - Consistency of units

OBJECTIVE: The objective of this challenge is to convert given quanities in different systems of units. LS-DYNA does not have its default unit system so we havae to be consistant with the units while working on it. Hence it is very imposrtant to understand the unit conversion from one unit system to another.

Given Quantities:

1) MASS 1kg
2) LENGTH 1m
3) TIME 1s
4) FORCE 1N
5) STRESS 1Pa
6) ENERGY 1Nm
7) DENSITY 1Kg/m3
8) YOUNG'S Modulus 210GPa
9) Velocity 56.33KMPH
10)GRAVITY 9.8m/s2

System Of units:

1) Kg cm ms
2) Kg cm s
3) gm mm ms
4) kg m s
5) g cm s
6) g cm us
7) g mm s
8) ton mm s
9) slug ft s
10) kg mm s
11) g cm ms
12)kg mm ms

Coversion Factors:

1) Mass

1 Kg = 1000 g.

2) Length

1 m=100 cm.=1000 mm.

3) Time

1 Sec. = 1000 mili.sec.

4) Force

we know that, F = mass* acceleration

Threfore

1N = 1kg `m/s^2`

= 1000 g `(1000mm)/s^2`

= 1000 g `(1000 mm)/(10^6 ms)`

1N = 1g `(mm)/(ms^2)`

5) Stress

We know that SI unit of stress is Pa or `N/m^2`

1Pa = 1`N/m^2`

1Pa = 1g*`(mm)/(ms^2)` * `1/(10^6 mm^2)`

1Pa = `10^-6` (g/ mm * ms^2)`

6) Energy

We know that SI unit of energy is Nm

1Nm = 1 `(g*mm)/(ms^2)` *(1000 mm)

1Nm = `10^3` `(g*mm^2)/(ms^2)`

7) Density

We know that SI unit of desnity is Kg/m^3

1 kg/m^3 = `(1000 g)/(10^9 mm^3)`

1 kg/m^3 = `10^-6 g/(mm^3)`

8) Youngs Modulus

We know that we generally specifiy 'Y' in GPa

210GPa = 210 `10^9``10^-6` (g/ mm * ms^2)`

210GPa= 210*`10^3` `(g)/(mm*ms^2)`

9) Velocity

We specify velocity in 'm/s'

56.33 KMPH = 56.33 `( 10^6 mm)/(3600*1000 msec)`

56.33 KMPH = 15.64 `(mm)/(ms)`

10) Gravity

we know that value pf 'g' =9.81 m/s^2

9.81 m/s^2 = 9.81 `(1000 mm)/( 10^6 ms^2)`

9.81 m/s^2 = 9.81 `10^3 (mm)/(ms^2)`

Here we come across one of the unit system with which we are not familier that much i.e slug ft s , slug is a measure of mass ( 1kg=0.068 slug, 1m=3.28ft)

Units/ Quantites	Mass (1Kg)	Length ( 1m)	time (1 sec)	Force (1N)	Stress ( 1Pa)	Energy ( 1J)	Density ( 1Kg/m^3)	Youngs Modulus (210Gpa)	Velocity(56.33KMPH)	gravity (9.81 m/sec^2)
Kg m sec	1 Kg	1 m	1 sec	1 Kg m/sec^2	1 Kg/ (m sec^2)	1J=1Nm = 1Kg m^2/ sec^2	1 Kg/m^3	210*10^9 kg/( m sec^2)	15.64 m/sec	9.81 m/sec^2
Kg cm s	1 Kg	100 cm	1 sec	10^2 Kg cm/sec^2	10^-2 Kg/(cm sec^2)	10^4 kg cm^2/sec^2	10^-6 Kg/cm^3	210*10^7 Kg/(cm sec^2)	1564 cm/sec	981 cm/sec^2
Kg cm ms	1 Kg	100 cm	1000 msec	10^-4 Kg cm/ms^2	10^-8 Kg/( cm ms^2)	10^-2 kg cm^2/sec^2	10^-6 Kg/cm^3	2100 kg /(cm ms^2)	1.564 cm/ms	9.81*10^-4 cm/ms^2
g mm ms	10^3g	1000 mm	1000 msec	1 g mm/ms^2	10^-6 g/(mm ms^2)	10^3 g mm^2/ms^2	10^-6 Kg/cm^3	210*10^3 g/(mm ms^2)	15.64 mm/ms	9.81*10^-3 mm/ms^2
g cm s	10^3g	100 cm	1 sec	10^5 g cm/sec^2	10 g/(cm sec^2)	10^7 g cm^2/sec^2	10^-3 g/cm^3	210*10^10 g/(cm sec^2)	1564 cm/sec	981 cm/us^2
g cm us	10^3g	100 cm	10^6 sec	10^-7 g cm/us^2	10^-11 g/(cm us^2)	10^-5 g cm^2/us^2	10^-3 g/cm^3	210*10^-2 g/(cm us^2)	15.64*10^-4 cm/us	9.81*10^-10 cm/us^2
g mm s	10^-3g	1000 mm	1 sec	10^6 g mm/sec^2	1 g/( mm sec^2)	10^9 g mm^2/sec^2	10^-6 Kg/cm^3	210*10^9 g/(mm sec^2)	15.64*10^3 mm/sec	9.81*10^3 mm/sec^2
ton mm s	10^-3 ton	1000 mm	1 sec	1 ton mm/sec^2	10^-6 ton/(mm sec^2)	10^3 ton.mm^2/sec^2	10^-12 ton/mm^3	210*10^3 ton/(mm sec^2)	15.64*10^3 mm/sec	9.81*10^3 mm/sec^2
slug ft s	0.068 slug	3.28 ft	1 sec	0.224 slug ft/sec^2	0.020 slug/(ft sec^2)	0.736 slug ft^2/sec^2	1.9*10^-3 slug/ft^3	4.38*10^9 slug/(ft sec^2)	51.32 ft/sec	32.14 ft/sec^2
kg mm s	1 Kg	1000 mm	1 sec	10^3 kg mm/Sec^2	10^-3 kg/(mm sec^2)	10^6 Kg mm^2/sec^2	10^-9 Kg/mm^3	210*10^6 kg/(mm sec^2)	15.64*10^3 mm/sec	9.81*10^3 mm/sec^2
g cm ms	10^3g	100 cm	1000 msec	10^-1 g cm/sec^2	10^-5 g/(cm ms^2)	10 g cm^2/ms^2	10^-3 g/cm^3	210*10^4 g/(cm ms^2)	1.564 cm/ms	9.81*10^-4 cm/ms^2
kg mm ms	1 Kg	1000 mm	1000 msec	10^-3 Kg mm/ms	10^-9 kg/(mm ms^2)	1 Kg mm^2/ms^2	10^-9 Kg/mm^3	210 kg/( mm ms^2)	15.64 mm/ms	9.81*10^-3 mm/ms^2

Conversion Factors are given below ( we have consider only derived quantities)

1) Kg m sec

quantity	conversion factor
force	1
stress	1
energy	1
density	1
youngs Modulus	10^9
velocity	1
gravity	1

2 Kg cm s

quantity	conversion factor
force	10^2
stress	10^-2
energy	10^4
density	10^-6
youngs Modulus	10^7
velocity	10^2
gravity	10^2

3)Kg cm ms

quantity	conversion factor
force	10^-4
stress	10^-8
energy	10^-2
density	10^-6
youngs Modulus	10
velocity	1
gravity	10^-4

4) kg cm sec

quantity	conversion factor
force	10^2
stress	10^-2
energy	10^4
density	10^-6
youngs Modulus	10^7
velocity	10^2
gravity	10^2

5) g cm sec

quantity	conversion factor
force	10^5
stress	10
energy	10^7
density	10^-3
youngs Modulus	10^10
velocity	10^2
gravity	10^2

6) g cm us

quantity	conversion factor
force	10^-7
stress	10^-11
energy	10^-5
density	10^-3
youngs Modulus	10^-2
velocity	10^-4
gravity	10^-10

7) g mm sec

quantity	conversion factor
force	10^6
stress	1
energy	10^9
density	10^-6
youngs Modulus	10^9
velocity	10^3
gravity	10^3

8) ton mm sec

quantity	conversion factor
force	1
stress	10^-6
energy	10^3
density	10^-12
youngs Modulus	10^3
velocity	10^3
gravity	10^3

9) slug ft sec

quantity	conversion factor
force	1
stress	1
energy	1
density	10^-3
youngs Modulus	10^9
velocity	1
gravity	1

10) kg mm sec

quantity	conversion factor
force	10^3
stress	10^-3
energy	10^6
density	10^-9
youngs Modulus	10^6
velocity	10^3
gravity	10^3

11) g cm ms

quantity	conversion factor
force	0.1
stress	10^-5
energy	10
density	10^-3
youngs Modulus	10^4
velocity	0.1
gravity	10^-4

12) kg mm sec

quantity	conversion factor
force	10^-3
stress	10^-9
energy	1
density	10^-9
youngs Modulus	1
velocity	1
gravity	10^3

Conclusion

We have understand how to convert the quantities from one unit system to another.