Week - 1 - Consistency of Units
AIM:
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 210. Thus the conversion factor is 10^-9.
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
Write the given measurements in the above different system of units. Also, mention the conversion factors.
DESCRIPTION:
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
CASE 1:
Kg cm ms
MASS 1kg=1KG
LENGTH 1m=100CM
TIME 1s=10^3ms
FORCE 1N=1kgm/sec^2=10^-4kgcm/ms2
STRESS 1Pa=1N/m2=1kgm/m2sec2=10^-7kg/cmms2
ENERGY 1Nm=1kgm.m/sec2=10^-2kgcm2/ms2
DENSITY 1Kg/m3=10^-6kg/cm3
YOUNG'S Modulus 210GPa=210*10^2kg/cmms2
Velocity 56.33KMPH=15.64m/sec=1.564cm/msec
GRAVITY 9.8m/s2=9.8*10^-4cm/ms^2
CASE 2:
Kg cm s
MASS 1kg=1KG
LENGTH 1m=100CM
TIME 1s=1S
FORCE 1N=100kgcm/sec2
STRESS 1Pa=10^-2kg/cmsec2
ENERGY 1Nm=10000kgcm2/sec2
DENSITY 1Kg/m3=10^-6kg/cm3
YOUNG'S Modulus 210GPa=210*10^7kg/cmsec2
Velocity 56.33KMPH=1564cm/sec
GRAVITY 9.8m/s2=9.8*10^2cm/sec2
CASE 3:
gm mm ms
MASS 1kg=1000GM
LENGTH 1m=1000MM
TIME 1s=1000MS
FORCE 1N=1GMMM/MS2
STRESS 1Pa=10^-6gm/mmms2
ENERGY 1Nm=1000GMMM/MS2
DENSITY 1Kg/m3=10^-6gm/ms3
YOUNG'S Modulus 210GPa=210*10^3gm/mmms2
Velocity 56.33KMPH=15.64mm/ms
GRAVITY 9.8m/s2=9.8*10^-3mm/ms2
CASE 4:
kg m s
MASS 1kg=1KG
LENGTH 1m=1M
TIME 1s=1S
FORCE 1N=1KGM/SEC2
STRESS 1Pa=1N/M2
ENERGY 1Nm=1kgm2/sec2
DENSITY 1Kg/m3
YOUNG'S Modulus 210GPa=210*10^9N/M2
Velocity 56.33KMPH=15.64m/sec
GRAVITY 9.8m/s2
CASE 5:
g cm s
MASS 1kg=1000G
LENGTH 1m=100CM
TIME 1s
FORCE 1N=10^5GCM/SEC2
STRESS 1Pa=10^1G/CMSEC2
ENERGY 1Nm=10^7gmcm2/sec2
DENSITY 1Kg/m3=10^-3gm/cm2
YOUNG'S Modulus 210GPa=210 * 10^10G/CMSEC2
Velocity 56.33KMPH=1564cm/sec
GRAVITY 9.8m/s29.8*100cm/sec2
CASE 6:
g cm us
MASS 1kg=1000G
LENGTH 1m=100CM
TIME 1s=10^6us
FORCE 1N=10^-7gmcm/us2
STRESS 1Pa=10^-11gm/cmus2
ENERGY 1Nm=10^-5gmcm2/us2
DENSITY 1Kg/m3=10^-3gm/cm3
YOUNG'S Modulus 210GPa=2.10gm/cmus2
Velocity 56.33KMPH=15.64*10^-4cm/us
GRAVITY 9.8m/s2=9.8*10^-10cm/us2
CASE 7:
g mm s
MASS 1kg=1000GM
LENGTH 1m=1000MM
TIME 1s
FORCE 1N=10^6GMMM/S2
STRESS 1Pa=1gm/mms2
ENERGY 1Nm=10^9GMMM2/S2
DENSITY 1Kg/m3=10^-6gm/mm3
YOUNG'S Modulus 210GPa= 210*10^9gm/mms2
Velocity 56.33KMPH=15.64*10^3mm/sec
GRAVITY 9.8m/s2=9.8*10^3mm/s2
CASE 8:
ton mm s
MASS 1kg=10^-3TON
LENGTH 1m=1000MM
TIME 1s
FORCE 1N=1TONmm/s2
STRESS 1Pa=10^-6ton/mms2
ENERGY 1Nm=10^3tonmm2/s2
DENSITY 1Kg/m3=10^-12ton/mm3
YOUNG'S Modulus 210GPa=210*10^3ton/mms2
Velocity 56.33KMPH=15.64*10^3mm/sec
GRAVITY 9.8m/s2=9.8*10^3mm/sec2
CASE 9:
slug ft s
MASS 1kg=0.0685slug
LENGTH 1m=3.28ft
TIME 1s
FORCE 1N=0.0685*3.28slug ft/s2
STRESS 1Pa=0.0685/3.28 slug/ft s2
ENERGY 1Nm= 0.0685*3.28*3.28 slug ft2/s2
DENSITY 1Kg/m3= 0.0685/3.28*3.28*3.28 slug/ft3
YOUNG'S Modulus 210GPa= 210 * 10^9 *0.0685/3.28 slug/ft s2
Velocity 56.33KMPH=15.64*3.28ft/sec
GRAVITY 9.8m/s2= 9.8*3.28 ft/s2
CASE 10:
kg mm s
MASS 1kg
LENGTH 1m=1000mm
TIME 1s
FORCE 1N=1000kgmm/s2
STRESS 1Pa=10^-3kg/mms2
ENERGY 1Nm=10^6kgmm2/s2
DENSITY 1Kg/m3=10^-9kg/mm3
YOUNG'S Modulus 210GPa=210*10^6kg/mms2
Velocity 56.33KMPH=15.64*1000mm/s
GRAVITY 9.8m/s2=9.8*1000mm/s2
CASE 11:
g cm ms
MASS 1kg=1000g
LENGTH 1m=100cm
TIME 1s=1000ms
FORCE 1N=0.1gmcm/ms2
STRESS 1Pa=10^-5gm/cmms2
ENERGY 1Nm=10gmcm2/ms2
DENSITY 1Kg/m3=10^-3gm/cm3
YOUNG'S Modulus 210GPa=210*10^4gm/cmms2
Velocity 56.33KMPH=15.64*10^-1cm/ms
GRAVITY 9.8m/s2=9.8*10^-4cm/ms2
CASE 12:
kg mm ms
MASS 1kg
LENGTH 1m=1000mm
TIME 1s=1000ms
FORCE 1N=10^-3kgmm/ms2
STRESS 1Pa=10^-9kg/mmms2
ENERGY 1Nm=1kgmm2/ms2
DENSITY 1Kg/m3=10^-9kg/mm3
YOUNG'S Modulus 210GPa=210*kg/mmms2
Velocity 56.33KMPH=15.64mm/ms
GRAVITY 9.8m/s2=9.8*10^-3mm/ms2
CONCLUSION:
THIS WEEK CHALLANGE HELPS ME TO LEARN UNIT CONVERSION FOR DIFFERENT DIFFERENT TYPES OF UNITS. AND HOW TO CONVERT INTO THEIR FUNDAMENTAL UNITS WHEN IT IS GIVEN IN OTHER FUNDAMENTAL UNITS.