Consistency of Units
OBJECTIVE : To convert the given measurements in the different system of units mentioned below along with the conversion factors.
Values 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
g 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
Detailed calculation for conversion from SI unit to gm/mm/ms unit system :
Mass –
`1 kg=1000 g`
Conversion factor = `10^3`
Length –
`1 m=1000 mm`
Conversion factor = `10^3`
Time –
`1 s=1000 ms`
Conversion factor = `10^3`
Force –
`1 N` is `1 kg.m/s^2`
`=(1000 g×1000 mm)/[ (1000×1000) ms^2]`
`=1 g.(mm)/(ms)^2=1 N`
Conversion factor = `1`
Stress –
`1Pa` is `1 N/m^2` i.e. `1 (kg)/(m.s^2)`
`=(1000 g)/ [1000 mm×(1000×1000) ms^2]`
`=10^(-6) g/(mm.ms^2)`
Conversion factor = `10^6`
As `1 Pa= 10^(-6) MPa`. Thus, we can express Stress value as MPa for this unit system.
Energy –
`1 N.m` is `1 kg.m^2/s^2`
`=[1000 g×(1000×1000) mm^2]/((1000×1000) ms^2)`
`=10^3 g.(mm^2)/(ms^2)`
Conversion factor = `10^3`
As `1 J=10^3 mJ`. Thus, we can express Energy value as mJ for this unit system.
Density –
`1 (kg)/m^3`
`=(1000 g)/((1000×1000×1000) mm^3)`
`=10^(-6) g/(mm^3)`
Conversion factor = `10^-6`
Young’s Modulus –
`210 Gpa` is `210×10^9 Pa` i.e. `210×10^9 (kg)/(m.s^2)`
`=210×10^9 {(1000 g)/ [1000 mm×(1000×1000) ms^2]}`
`=210×10^9×10^(-6) g/(mm.ms^2)`
`=210×10^3 g/(mm.ms^2)`
Conversion factor = `10^3`
Velocity –
`56.33 (km)/(hr)`
`1 km=1000 m=10^6 mm;`
`1 hr=3600 s=36×10^5`
`therefore` `(56.33×10^6)/(36×10^5 ) (mm)/(ms)=``15.65 (mm)/(ms)`
Conversion factor = `5/18`
Gravity –
`9.8 m/s^2`
`=9.8×(1000 mm)/ ((1000×1000) ms^2)`
`=9.8×10^(-3) (mm)/(ms^2)`
Conversion factor = `10^-3`
The conversion of measurements for remaining Unit Systems will be done in a tabulated form below along with conversion factors.
|
UNIT SYSTEM |
Mass |
Length |
Time |
Force (1N) |
Stress (1Pa) |
Energy (1Nm) |
Density |
Young’s Modulus (210 Gpa) |
Velocity (56.33 km/hr) |
Gravity |
|
kg-m-s |
1kg |
1m |
1s |
1 kg.m/s2 |
1 kg/m.s2 |
1 kg.m2/s2 |
1kg/m3 |
210x109 kg/m.s2 |
15.65 m/s |
9.8 m/s2 |
|
kg-cm-ms |
1kg |
102 cm |
103ms |
10-4 kg.cm/ms2 |
10-8 kg/cm.ms2 |
10-2 kg.cm2/ms2 |
10-6 kg/cm3 |
2100 kg.cm/ms2 |
1.565 cm/ms |
9.8x10-4 cm/ms2 |
|
kg-cm-s |
1kg |
102 cm |
1s |
102 kg.cm/s2 |
10-2 kg/cm.s2 |
104 kg.cm2/s2 |
10-6 kg/cm3 |
210x107 kg/cm.s2 |
1565 cm/s |
9.8x102 cm/s2 |
|
g-mm-ms |
103g |
103 mm |
103ms |
1 g.mm/ms2 |
10-6 g/mm.ms2 |
103 g.mm2/ms2 |
10-6 g/mm3 |
210x103 g/mm.ms2 |
15.65 mm/ms |
9.8x10-3 mm/ms2 |
|
g-cm-s |
103g |
102 cm |
1s |
105 g.cm/s2 |
10 g/cm.s2 |
107 g.cm2/s2 |
10-3 g/cm3 |
210x1010 g/cm.s2 |
1565 cm/s |
9.8x102 cm/s2 |
|
g-cm-ms |
103g |
102 cm |
106 ms |
10-7 g.cm/ms2 |
10-11 g/cm.ms2 |
10-5 g.cm2/ms2 |
10-3 g/cm3 |
2.10 g/cm.ms2 |
15.65x10-4 cm/ms |
9.8x10-10 cm/ms2 |
|
g-mm-s |
103g |
103 mm |
1s |
106 g.mm/s2 |
1 g/mm.s2 |
109 g.mm2/s2 |
10-6 g/mm3 |
210x109 g/mm.s2 |
15650 mm/s |
9.8x103 mm/s2 |
|
ton-mm-s |
10-3 ton |
103 mm |
1s |
1 ton.mm/s2 |
10-6 ton/mm.s2 |
103 ton.mm2/s2 |
10-12 ton/mm3 |
210x103 ton/mm.s2 |
15650 mm/s |
9.8x103 mm/s2 |
|
slug-ft-s |
0.068 slug |
3.28 ft |
1s |
0.22 slug.ft/s2 |
0.02 slug/ft.s2 |
0.73 slug.ft2/s2 |
1.93x10-3 slug/ft3 |
4.2x109 slug/ft.s2 |
51.33 ft/s |
32.14 ft/s2 |
|
kg-mm-s |
1kg |
103 mm |
1s |
103 kg.mm/s2 |
10-3 kg/mm.s2 |
106 kg.mm2/s2 |
10-9 kg/mm3 |
210x106 kg/mm.s2 |
15650 mm/s |
9.8x103 mm/s2 |
|
g-cm-ms |
103g |
102 cm |
103ms |
10-1 g.cm/ms2 |
10-5 g/cm.ms2 |
10 g.cm2/ms2 |
10-3 g/cm3 |
210x104 g/cm.ms2 |
1.565 cm/ms |
9.8x10-4 cm/ms2 |
|
kg-mm-ms |
1kg |
103 mm |
103ms |
10-3 kg.mm/ms2 |
10-9 kg/mm.ms2 |
1 kg.mm2/ms2 |
10-9 kg/mm3 |
210 kg/mm.ms2 |
15.65 mm/ms |
9.8x10-3 mm/ms2 |
For software input, 109 can also be entered as e+9 and 10-9 can be entered as e-9.
To enter the values for each parameter in the software, we will not multiply the conversion factor each and every time for every unit system. So we will use measurement conversion for the above calculated values such as “1N = 105 dyne. Thus we will use dyne as unit for Force in g-cm-s”. Also,
`1N = 10^(-4) (kg.cm)/(ms^2)` (…..For kg-cm-ms)
`therefore` `1 (kg.cm)/(ms^2)=10^4 N`
The other units for the above calculated values are tabulated below.
|
Unit System |
Mass |
Length |
Time |
Force |
Stress |
Energy |
Density |
Young’s Modulus of Steel |
Velocity 35mph 56.33 km/hr |
Gravity |
|
kg-m-s |
kg |
m |
s |
N |
Pa |
J |
kg/m3 |
2.1e+11 |
15.65 |
9.8 |
|
kg-cm-ms |
kg |
cm |
ms |
1e+4N |
1e+2MPa |
1e+2J |
1e-6 kg/cm3 |
2.1e+3 |
1.565 |
9.8e-4 |
|
kg-cm-s |
kg |
cm |
s |
1e-2N |
1e+2Pa |
1e-4J |
1e-6 kg/cm3 |
2.1e+9 |
1565 |
980 |
|
g-mm-ms |
g |
mm |
ms |
N |
MPa |
mJ |
1e-6 g/mm3 |
2.1e+5 |
15.65 |
9.8e-3 |
|
g-cm-s |
g |
cm |
s |
dyne |
dyne/cm2 |
erg |
1e-3 g/cm3 |
2.1e+12 |
1565 |
980 |
|
g-cm-ms |
g |
cm |
ms |
1e+7N |
100GPa |
1e+5J |
1e-3 g/cm3 |
2.1 |
1.56e-3 |
9.8e-10 |
|
g-mm-s |
g |
mm |
s |
1e-6N |
Pa |
1e-9J |
1e-6 g/mm3 |
2.1e+11 |
1.56e+4 |
9800 |
|
ton-mm-s |
ton |
mm |
s |
N |
MPa |
mJ |
1e-12 ton/mm3 |
2.1e+5 |
1.56e+4 |
9800 |
|
slug-ft-s |
slug |
ft |
s |
4.54N |
50Pa |
1.37J |
1.93e-3 slug/ft3 |
4.2e+9 |
51.33 |
32.14 |
|
kg-mm-s |
kg |
mm |
s |
1e-3N |
kPa |
1e-6J |
1e-9 kg/mm3 |
2.1e+8 |
1.56e+4 |
9800 |
|
g-cm-ms |
g |
cm |
ms |
10N |
0.1MPa |
0.1J |
1e-3 g/cm3 |
2.1e+6 |
1.565 |
9.8e-4 |
|
kg-mm-ms |
kg |
mm |
ms |
kN |
GPa |
J |
1e-9 kg/mm3 |
2.1e+2 |
15.65 |
9.8e-3 |
CONCLUSION : The conversion of units for different unit systems have been calculated and tabulated. This tabulated result will help us to input values for any parameter, from the above calculated results.