Week - 1 - Consistency of Units
Aim:-
- Convert given measurements into a different system of units and find their corresponding conversion factors.
Measurements Given:-
- 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
Conversions: (From SI unit to gm/mm/ms unit system)
MASS : 1kg = 1000gm
LENGTH : 1m = 1000mm
TIME : 1s = 1000ms
FORCE : 1N = 1kg*1 m/s
= (1000g*1000mm)/(1000ms)
= 10 *10 (g*mm)/ms
= 1 (g*mm)/ms
STRESS : 1Pa = 1N/m^2 = {1kg*(1 m/s^2)}/m^2 = 1 kg/ (m* s^2)
= 1000g/{1000mm*(1000ms)^2 }
= 10^-6 g/ (mm*ms^2 )
ENERGY : 1J = 1Nm = (1kg*1 m/s^2 ) * m 1 (kg*m^2 /s^2 )
= {1000g * (1000mm)^2 }/(1000ms)^2
= (10^9 g*mm^2 ) / (10^6 ms^2)
= 10^3 (g*mm^2 / ms^2 )
DENSITY : 1Kg/m3 = 1000g/(1000mm)^3
= 10^-6 g/mm^3
YOUNG'S MODULUS : 210GPa = 210e+9 kg/(m*s ) = 210e+9 * 10^-6 g/ (mm*ms^2 )
= 210e+3 g/ (mm*ms^2 ) = 210*10^3 g/ (mm*m s^2 )
VELOCITY : 56.33 Kmph = 56.33 * {10^6 mm/(3600*1000ms)}
= 15.647 mm/ms
GRAVITY : 9.8m/s2 = 9.8 * 1000mm/(1000ms)^2
= 9.8* 10^-3 mm/ms^2
Table unit systems as rows and measured quantities as columns :
CONCLUSION:
- Thus the given input measurements are converted into respective unit systems and this is used in
LS-DYNA calculation.