Week - 1 - Consistency of Units
Assignment 1 : Consistency of units
Aim :- To convert the given SI unit values of the given quantities to gm/mm/ms units and also to prepare consistent unit system table for different unit system.
Problem statement :-
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.
**The assignment should show detailed calculation for conversion from SI unit to gm/mm/ms unit system. For others only the answers in the form of a table is sufficient with the unit systems as rows and measured quantities as columns.**
Calculation of the conversion from SI unit to g,mm,ms :-
|
SI Unit system (kg, m, s) |
Conversion to (g, mm, ms) |
|
MASS 1kg |
1000g |
|
LENGTH 1m |
1000mm |
|
TIME 1s |
1000ms |
|
FORCE 1N |
1N = 1mass*1acceleration = 1kg*1 m/s2 = (1000g*1000mm)/(1000ms)2 = 106*10-6 (g*mm)/ms2 = 1 (g*mm)/ms2 Conversion factor = 1 |
|
STRESS 1Pa |
1 Pa = 1N/m2 = {1kg*(1 m/s2)}/m2 = 1 kg/ (m* s2) So, 1 kg/ (m* s2) = 1000g/{1000mm*(1000ms)2} = 10-6 g/ (mm*ms2) Conversion factor = 10-6 |
|
ENERGY 1Nm |
1 J = 1Nm = (1kg*1 m/s2) * m = 1 (kg*m2/s2) Now, 1 (kg*m2/s2) = {1000g * (1000mm)2}/(1000ms)2 = (109 g*mm2) / (106 ms2) = 103 (g*mm2/ ms2) Conversion factor = 103 |
|
DENSITY 1Kg/m3 |
1Kg/m3 = 1000g/(1000mm)3 = 10-6 g/mm3 Conversion factor = 10-6
|
|
YOUNG'S Modulus 210GPa |
210 GPa = 210e+9 kg/(m*s2) Here we already have 1 kg/ (m* s2) while calculating the stress 1 kg/ (m* s2) = 1000g/{1000mm*(1000ms)2} = 10-6 g/(mm*m s2) Therefore, 210e+9 kg/(m*s2) = 210e+9 * 10-6 g/ (mm*m s2) = 210e+3 g/ (mm*m s2) = 210*103 g/ (mm*m s2) Conversion factor = 103
|
|
Velocity 56.33Kmph |
56.33 Kmph = 56.33 * {106mm/(3600*1000ms)} = 15.647 mm/ms Conversion factor = 1 |
|
GRAVITY 9.8m/s2 |
9.8m/s2 = 9.8 * 1000mm/(1000ms)2 = 9.8* 10-3 mm/ms2 Conversion factor = 10-3 |
Consistent unit system table
|
Units |
Mass |
Length |
Time |
Force |
Stress |
Energy |
Density |
Young’s Modulus |
Velocity |
Gravity |
|
Kg cm ms |
1 Kg |
102cm |
103ms |
10-4kg cm/ms2 |
10-8kg /cm*ms2 |
10-2kg*cm2/ms2 |
10-6kg/cm3 |
2100kg/cm*ms2 |
1.56472 cm/ms |
9.8*10-4 cm/ms2 |
|
Kg cm s |
1 Kg |
102cm |
1s |
102kg*cm/s2 |
10-2kg/cm*s2 |
104kg*cm2/s2 |
10-6kg/cm3 |
210*107kg/cm*s2 |
1564.72 cm/s |
9.8*102 cm/s2 |
|
gm mm ms |
103 gm |
103mm |
103ms |
1gm*mm/m10-8kg |
10-6 gm/mm*ms2 |
103gm*mm2/ms2 |
10-6gm/mm3 |
210*103gm/mm*ms2 |
15.6472 mm/ms |
9.8*10-3 mm/ms2 |
|
kg m s |
103 gm |
1m |
1s |
1kg*m/s2 |
1 kg/m*s2 |
1 kg*m2/s2 |
1kg/m3 |
210*109N/m2 |
15.6472 m/s |
9.8 m/s2 |
|
gm cm s |
103 gm |
102cm |
1s |
105gm*cm/s2 |
10 gm/cm*s2 |
107gm*cm2/s2 |
10-3gm/cm3 |
210*1010gm/cm*s2 |
1564.72cm/s |
9.8*102 cm/s2 |
|
gm cm μs |
103 gm |
102cm |
106μs |
10-7gm*cm/μs2 |
10-11gm/cm*μs2 |
10-5gm*cm2/μs2 |
10-3gm/cm3 |
2.1gm/cm*μs2 |
15.6472 *10-4cm/μs |
9.8*10-10 cm/μs2 |
|
gm mm s |
103 gm |
103mm |
1s |
106gm*mm/s2 |
1gm/mm*s2 |
109gm*mm2/s2 |
10-6gm/mm3 |
210*1011gm/mm*s2 |
156472 mm/s |
9.8*103 mm/s2 |
|
ton mm s |
10-3 gm |
103mm |
1s |
1 ton mm/s2 |
10-6ton /mm*s2 |
103ton*mm2/s2 |
10-12ton/mm3 |
210*103ton/mm*s2 |
156472 mm/s |
9.8*103 mm/s2 |
|
kg mm s |
1 Kg |
103mm |
1s |
103kg mm/s2 |
10-3kg/mm*s2 |
106kg*mm2/s2 |
10-9kg/mm3 |
210*106kg/mm*s2 |
156472 mm/s |
9.8*103 mm/s2 |
|
gm cm ms |
103 gm |
102cm |
103ms |
10-1 gm cm/ms2 |
10-5gm/cm*ms2 |
10gm*cm2/ms2 |
10-3gm/cm3 |
210*104gm/cm*ms2 |
1.56472 cm/ms |
9.8*10-4 cm/ms2 |
|
kg mm ms |
1 Kg |
103mm |
103ms |
10-3 kg*mm/ms2 |
10-9kg/mm*ms2 |
1kg*mm2/ms2 |
10-9 kg/mm3 |
210kg/mm*ms2 |
15.6472 mm/ms |
9.8*10-3 mm/ms2 |
Conclusion :- As we know that LS-Dyna has no unit system, so we have to convert each units as per our requirements. So above conversions can be used with help of conversion factor.