Week - 1 - Consistency of Units
AIM
To convert the given measurements such as (mass, length,time,force,stress, energy,youngs modulus,densiity, velocity, gravity) to system of units like (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) with suitable calculation and to develop the consistent of system of units table accordingly.Additionally calculation for gm mm ms has to be explained in detailed.
PROCEDURE
calculation to gm mm ms
SYSYTEM OF UNITS
1KG=1000g
1m=1000mm
1s=1000ms
FORCE
F=M*A
N=1000g*1000mm/(1000ms)^2
N=1000g*1000mm/10^6*ms^2
1N=1*g*mm/ms^2
STRESS
`σ`=1*N/M^2
`σ`=(1*g*mm/ms^2)/(1000mm)^2
`σ`=(1*g*mm/ms^2)/10^6*mm^2
`σ`= 10^-6*g/mm*ms^2
ENERGY
1NM=(1*g*mm/ms^2)*1000mm
1NM=10^3*g*mm^2/ms^2
DENSITY
`ρ`=1*kg/m^3
`ρ`=1*1000g/1000^3*mm^3
`ρ`=10^-6 gm/mm^3
YOUNG'S MODULUS
1pa=1*N/M^2=10^-6*g/mm*ms^2
1GPa=10^9*10^-6*g/mm*ms^2
210GPa=210 *10^3g/mm*ms^2
VELOCITY
velocity =56.33kmph
56.33kmph=56.33*10^6/36*10^5
velocity=15.65 mm/ms
GRAVITY
G=9.88M/S^2
G=9.88*1000mm/10^6*ms^2
G=9.8*10^-3 mm/ms^2
| LS-DYNA consistency of units table |
| UNIT SYSTEM | MASS (kg) | LENGTH (L) | TIME (s) | FORCE (N) | STRESS (Pa) | ENERGY (Nm) | DENSITY (kg/m^3) | YOUNG'S MODULUS (210 Gpa) | VELOCITY (56.33 KMPH) | GRAVITY (9.88 m/S^2) | |
| Kg cm ms | 1kg | 100 cm | 1000 ms | 10^-4kg*cm/ms^2 | 10^-8 kg/cm*ms^2 | 10^-2 kg*cm^2/ms^2 | 10^-6 kg/cm^3 | 210 *10^1kg/cm*ms^2 | 1.56 cm/ms | 9.8*10^-4 cm/ms^2 | |
| Kg cm s | 1kg | 100 cm | 1s | 10^2 kg*cm/s^2 | 10^-2 kg/cm*s^2 | 10^4 kg*cm^2/s^2 | 10^-6 kg/cm^3 | 210*10^11 kg*cm/s^2 | 1564.7 cm/s | 9.8*10^2 cm/s^2 | |
| gm mm ms | 1000g | 1000mm | 1000ms |
|
10^-6 gm/mm*ms^2 | 10^3 gm*mm^2/ms^2 | 10^-6 gm/mm^3 | 210 *10^3g/mm*ms^2 | 15.65 mm/ms | 9.8*10^-3 mm/ms^2 | |
| kg m s | 1kg | 1m | 1s | 1*kg*m/s^2 | kg/m*s^2 | 1*kg*m^2/s^2 | kg/m^3 | 210 *10^9kg/m*s^2 | 15.65m/s | 9.8 m/S^2 | |
| g cm s | 1000g | 100 cm | 1s | 10^5 g*cm/s^2 | 10^-3 g/cm*s^2 | 10^7 g*cm^2/s^2 | 10^-3 g/cm^3 | 210 *10^6g/cm*s^2 | 1564.7 cm/s | 9.8*10^2 cm/s^2 | |
| g cm us | 1000g | 100 cm | 10^6 | 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^-6g/cm*us^2 | 0.001565cm/us | 9.8*10^10 cm/us^2 | |
| g mm s | 1000g | 1000mm | 1s | 10^6 g*mm/s^2 | 10^-2 g/mm*s^2 | 10^9 g*mm^2/s^2 | 10^-9 g/mm^3 | 210*10^15 g*mm/s^2 | 15647.2mm/s | 9.8*10^3 mm/s^2 | |
| ton mm s | 0.001 ton | 1000mm | 1s | 1*ton*mm/s^2 | 10^6 ton/mm*s^2 | 10^3*ton*mm^2/s^2 | 10^-12 ton/mm^3 | 210*10^15 ton/mm*s^2 | 15647.2mm/s | 9.8*10^3 mm/s^2 | |
| slug ft s | 0.068 slug | 3.28ft | 1s | 0.22 slug*ft/s^2 | 0.0205 slug/ft*s^2 | 0.72 slug*ft^2/s^2 | 0.0019 slug/ft^3 | 0.399*10^9 slug*ft/s^2 | 51.32ft/s | 32.4ft/s^2 | |
| kg mm s | 1kg | 1000mm | 1s | 10^3 kg*mm/s^2 | 10^-2 kg/cm*s^2 | 10^6 kg*mm^2/s^2 | 10^-9 kg/mm^3 | 210 *10^6kg/mm*s^2 | 15647.2mm/s | 9.8*10^3 mm/s^2 | |
| g cm ms | 1000g | 100cm | 1000ms | 10^-1 g*cm/ms^2 | 10^-5 g/cm*ms^2 | 10 g*cm^2/ms^2 | 10^-3 g/cm^3 | 210 *10^8 g/cm*s^2 | 1.56 cm/ms | 9.8*10^-4 cm/ms^2 | |
| kg mm ms | 1kg | 1000mm | 1000ms | 10^-5 kg*mm/ms^2 | 10^-11 kg/mm*ms^2 | 10^-2 kg*mm^2/ms^2 | 10^-9 kg/mm^3 | 210*10^-2 kg/mm*ms^2 | 15.65 mm/ms | 9.8*10^-3 mm/ms^2 |
conclusion
In this challenge ,convert the SI unit systems of give measurements such as (mass, length,time,force,stress, energy,youngs modulus,densiity, velocity, gravity) to systemof units like (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).since ls-dyna is an unitless software, these conversion factors will be usefull to work with different units system.