Week - 1 - Consistency of Units
AIM: Different industries use different system of units as per their convenience. Lsdyna doesnt have a default system of units. so, in this challenge we need to convert given measurements to different system of units and also to denote their coversion factors.
Measurements
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
Now a detailed calculation for one of the system of units
gm/mm/ms
MASS,1kg = 1000gm = 10^3gm
LENGTH,1m = 1000mm = 10^3mm
TIME,1s = 1000ms = 10^3ms
FORCE,1N = (1Kg.m)/s^2
= (1000gm.1000mm)/(1000ms.1000ms)
= 10^6.10^-6 (gm.mm)/ms^2
= 1 (gm.mm)/ms^2
conversion factor = 1
STRESS,1Pa = N/m^2 = (Kg.m/s^2)/m^2 = (Kg.m/s^2). m^-2
=kg.m^-1.s^-2
=Kg/m.s^2
=1000gm/(1000mm.(1000ms^2))
=10^3.10^-9(gm/mm.ms^2)
=10^-6(gm/mm.ms^2)
conversion factor = 10^-6
ENERGY,1Nm = (1Kg.m/s^2).m
=1Kg.m^2/s^2
=1000gm.(1000mm)^2/(1000ms)^2
=10^3(gm.(mm)^2)/ms^2
conversion factor = 10^3
DENSITY,1Kg/m^3 = (1000gm)/(1000mm)^3
=10^-6(gm/mm^3)
conversion factor = 10^-6
YOUNGS MODULUS,210GPa = 210(10^9.Kg.m^-1.s^-2)
= 210e^9. 10^-6(gm/mm.ms^2)
=210e^3 or 210(10^3). (gm/mm.ms^2)
conversion factor = 10^3
VELOCITY,56.33KMPH, (1Km = 10^6mm), (1hr = 3600x1000ms)
=56.33(10^6mm/(3600x1000ms))
=(1000mm)^6/3600x(1000ms)^2
=10/36 = 5/18
1Kmph=0.277mm/ms
conversion factor = 0.277mm/ms
56.33Kmph = 56.33x0.277
=15.6mm/ms
GRAVITY,9.8m/s^2
m/s^2 = (1000mm)/(1000ms.1000ms)
=10^-3(mm/(ms)^2)
9.8m/s^2 = 9.8x10^-3 mm/(ms)^2
conversion factor = 10^-3
Unit systems with measured quantities:
Conclusion:
Hence, the conversion of unit systems is understood further.