Week - 1 - Consistency of Units
Week - 1 - Consistency of Units
Aim: Write a detailed report of unit conversion while converting given measurement values to different unit systems and write its conversion factor.
Objective: The main objective of this challenge is to convert unit values in different unit system, with which we deal while using LS-Dyna.
Values of the following measurements are as 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
Below are some units convert the above parameters to below 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
Note:
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.
Report:
1.Conversion of given SI unit to Kg,cm,ms
- Mass = 1 Kg The conversion factor is 1
- Length= 1m = 100cm the conversion factor is 100
- Time= 1s = 1000ms the conversion factor is 1000
- Force=1N=1kg*m/s^2 =1kg*100cm/(1000)^2ms^2 =1kg*100cm/10^6ms^2 =1kg*1cm/10^4ms^2 = 10^-4 kg*cm/ms^2 The conversion factor = 10^-4
- Stress=1pa=1n/m^2 =1(kg*m/s^2)/m^2 =1kg/m*s^2 =1kg/100cm*(1000)^2ms^2 =1kg/100cm*10^6ms^2 = 10^-8 kg/cm*ms^2 The conversion factor = 10^-8
- Energy=1Nm=1(kgm/s^2)*m =1kg*m^2/s^2 =1kg*(100)^2cm^2/(1000)^2ms^2 =1kg*10^4cm^2/10^6ms^2 = 10^-2 kg*cm^2/ms^2 The conversion factor = 10^-2
- Density=1kg/m^3 =1kg/(100cm)^3cm^3 =1kg/10^6cm^3 = 10^-6 kg/cm^3 The conversion factor = 10^-6
- Youngs modulus=210Gpa =210*10^9pa =210*10^9n/m^2 =210*10^9kg*m/s^2/m^2 =210*10^9kg/m*s^2 =210*10^9kg/100cm*1000^2 ms^2 =210*10^9kg/100cm*10^6ms^2 =210*10kg/cm*ms = 2100 kg/cm*ms The conversion factor = 10
- Velocity=56.33KMPH =56.33Km/h = 56.33*(1000*100*cm)/(60*60*1000ms) =56.33*10^5cm/36*10^5ms =56.33*0.02778cm/ms = 1.5648 cm/ms The conversion factor = 0.02778
- Gravity=9.8m/s^2 =9.8*100cm/1000^2ms^2 =9.8*100cm/10^6ms^2 = 9.8*10^-4 cm/ms^2 The conversion factor = 10^-4
In the Below Table the value from given SI unit to other units are converted and their converging factor are also given
|
Unit System |
Mass |
Mass converging factor |
Length |
Length converging factor |
Time |
Time converging factor |
Force |
Force converging factor |
Stress |
Stress converging factor |
Energy |
Energy converging factor |
Density |
Density converging factor |
Young's Modulus |
Young's Modulus converging factor |
Velocity |
Velocity converging factor |
Gravity |
Gravity converging factor |
|
kg cm s |
1 Kg |
1 |
100 cm |
100 |
1 s |
1 |
100 kg*cm/s^2 |
100 |
10^-2 kg/cm*s^2 |
10^-2 |
10^4 kg*cm^2/s^2 |
10^4 |
10^-6 kg/cm^3 |
10^-6 |
210*10^7 kg/cm*s^2 |
10^7 |
1,564.72 cm/s |
27.7778 |
980 cm/s^2 |
100 |
|
gm mm ms |
1000 gm |
1000 |
1000 mm |
1000 |
1000 ms |
1000 |
1 gm*mm/ms^2 |
1 |
10^-6 gm/mm*ms^2 |
10^-6 |
10^3 gm*mm^2/ms^2 |
10^3 |
10^-6 gm/mm^3 |
10^-6 |
210*10^3 gm/mm*ms^2 |
10^3 |
15.6484 mm/ms |
0.2778 |
9.8*10^-3 mm/ms^2 |
10^-3 |
|
kg m s |
1 kg |
1 |
1 m |
1 |
1 s |
1 |
1 kg*m/s^2 |
1 |
1kg/m*s^2 |
1 |
1 kg*m^2/s^2 |
1 |
1 kg/m^3 |
1 |
210*10^9 kg/m*s^2 |
10^9 |
15.6484 m/s |
0.2778 |
9.8 m/s^2 |
1 |
|
g cm s |
1000 gm |
1000 |
100 cm |
100 |
1 s |
1 |
10^5 gm*cm/s^2 |
10^5 |
10 gm/cm*s^2 |
10 |
10^7 gm*cm^2/s^2 |
10^7 |
10^-3 gm/cm^3 |
10^-3 |
210*10^10 gm/cm*s^2 |
10^10 |
1,564.72 cm/s |
27.7778 |
9.8*10^2 cm/s^2 |
10^2 |
|
g cm us |
1000 gm |
1000 |
100 cm |
100 |
10^6 us |
10^6 |
10^-7 gm*cm/us^2 |
10^-7 |
10^-11 gm/cm*us^2 |
10^-11 |
10^-7 gm*cm^2/us^2 |
10^-7 |
10^-3 gm/cm^3 |
10^-3 |
210*10^-2 gm/cm*us^2 |
10^-2 |
0.001564 cm/us |
0.00002778 |
9.8*10^-10 cm/us^2 |
10^-10 |
|
g mm s |
1000 gm |
1000 |
1000 mm |
1000 |
1 s |
1 |
10^6 gm*mm/s^2 |
10^6 |
1 gm/mm*s^2 |
1 |
10^9 gm*mm^2/s^2 |
10^9 |
10^-6 gm/mm^3 |
10^-6 |
210*10^9 gm/mm*s^2 |
10^9 |
15,647.22 mm/s |
277.7778 |
9.8*10^3 mm/s^2 |
10^3 |
|
ton mm s |
0.001 ton |
10^-3 |
1000 mm |
1000 |
1 s |
1 |
1 ton*mm/s^2 |
1 |
10^-6 ton/mm*s^2 |
10^-6 |
1 ton*mm^2/s^2 |
1 |
10^-12 gm/mm^3 |
10^-12 |
210*10^3 ton/mm*s^2 |
10^3 |
15,647.22 mm/s |
277.7778 |
9.8*10^3 mm/s^2 |
10^3 |
|
slug ft s |
0.0685 slug |
0.0685 |
3.28 ft |
3.28 |
1 s |
1 |
0.2246 slug*ft/s^2 |
0.2246 |
0.0208 slug/ft*s^2 |
0.0208 |
0.7369 slug*ft^2/s^2 |
0.7369 |
0.001941 slug/ft^3 |
0.001941 |
438.5670*10^7 slug/ft*s^2 |
2.0884*10^7 |
51.33 ft/s |
0.9113 |
32.144 ft/s^2 |
3.28 |
|
kg mm s |
1 kg |
1 |
1000 mm |
1000 |
1 s |
1 |
10^3 kg*mm/s^2 |
10^3 |
10^-3 kg/mm*s^2 |
10^-3 |
10^6 kg*mm^2/s^2 |
10^6 |
10^-9 kg/mm^3 |
10^-9 |
210*10^6 kg/mm*s^2 |
10^6 |
15,647.22 mm/s |
277.7778 |
9.8*10^3 mm/s^2 |
10^3 |
|
g cm ms |
1000 gm |
1000 |
100 cm |
100 |
1000 ms |
1000 |
0.1 gm*cm/ms^2 |
0.1 |
10^-5 kg/cm*ms^2 |
10^-5 |
10 gm*cm^2/ms^2 |
10 |
10^-3 gm/cm^3 |
10^-3 |
210*10^4 gm/cm*ms |
10^4 |
1.5648 cm/ms |
0.02778 |
9.8*10^-4 cm/ms |
10^-4 |
|
kg mm ms |
1 kg |
1 |
1000 mm |
1000 |
1000 ms |
1000 |
10^-3 kg*mm/ms^2 |
10^-3 |
10^-9 kg/mm*ms^2 |
10^-9 |
1 kg*mm^2/ms^2 |
1 |
10^-9 gm/mm^3 |
10^-9 |
210 kg/ms*mm |
1 |
15.6484 mm/ms |
0.2778 |
9.8*10^-3 mm/ms^2 |
10^-3 |
Conclusion: These given measurement values have been converted to different unit system given in the data and found out the conversion factor.
Learning outcomes:
- Fundamental and derived quantity.
- Converting one unit system to other.