Week - 1 - Consistency of Units
Week 1-consistency of units
Aim:
The objective of this task was to familiarize with the unit system’s used in various fields. The unit systems used by the companied depends on the domain. The knowledge in the relationship between different unit systems will help to reduce errors and helps to interpret the results.
General conversion factors:
Kilogram to gram, ie 1 kg = 1000g
Meter to millimetre, ie 1m = 1000mm
Seconds to milliseconds, ie 1s = 1000ms
Input units are g, mm, ms.
SI units are kg, m, s.
Conversion of kg to g = 10^3
Mass 1kg = 10^3g
Conversion of m to mm = 10^3
Length 1m = 10^3 mm
Conversion of s to ms = 10^3
Time 1s = 10^3ms
The derived units like,
Acceleration, a =1 m/s^2 = 10^3/(10^6)
a = 10^-3 mm/ms^2
Force F = 1N= Kg*a = 10^3*10^-3
F = 1gmm/(ms^2)
Stress, S = Pa =F/A = 1/(10^6)
= 10^-6 g/(mm*ms^2)
Energy = 1N*m, unit in J = 1*10^3
= 10^3 g(mm^2)/(ms^2)
Density = 1kg/(m^3) = 10^3/(10^9)
= 10^-6 g/(mm^3).
Youngs modulus of steel, E = 2.1*10^11 Pa.= 2.1*10^11*10^-6
= 2.1*10^5 g/(mm*ms^2)
Velocity, v = 1m/s = 10^3/10^3 = 1mm/ms
Velocity = 56.33KmpH = 56.33*10^6/(3600*10^3) mm/ms.
= 15.64 mm/ms
Gravity = 9.81 m/s^2 = 9.81 *(10^3/(10^6))
= 9.81*10^-3 mm/ms^2.
The Figure 1 below explains the measurements to be converted.
Figure 1:measurements to be converted.
The Figure 2 below explains the various unit systems.
Figure 2:various systems of units
Table below illustrates the converted values of those measurements into various systems of units.
Table 1:converted values
|
Units |
Mass 1Kg |
Length 1m |
Time 1s |
Acceleration, |
Force, |
Stress, |
Energy, |
Density |
Youngs Modulus, |
Velocity, |
Gravity, |
|
kg,cm,ms |
1 |
100 |
1E+03 |
1E-04 |
1E-04 |
1E-08 |
1E-02 |
1E-06 |
2E+03 |
1.6 |
9.80E-04 |
|
kg,cm,s |
1 |
100 |
1 |
100 |
100 |
1.0E-02 |
1E+04 |
1E-06 |
2E+09 |
1.56E+03 |
9.8E+02 |
|
g,mm,ms |
1E+03 |
1E+03 |
1E+03 |
1.00E-03 |
1.00E+00 |
1.00E-06 |
1E+03 |
1E-06 |
2.10E+05 |
1.56E+01 |
9.80E-03 |
|
Kg,m,s |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
2E+11 |
15.6 |
9.8 |
|
g,cm,s |
1E+03 |
100 |
1 |
100.0 |
1E+05 |
10 |
1E+07 |
1E-03 |
2E+12 |
1.56E+03 |
9.8E+02 |
|
g,cm,us |
1E+03 |
100 |
1E+06 |
1.0E-10 |
1.0E-07 |
1.0E-11 |
1.0E-05 |
1E-03 |
2.10 |
1.6E-03 |
9.8E-10 |
|
g,mm,s |
1E+03 |
1E+03 |
1 |
1E+03 |
1E+06 |
1 |
1E+09 |
1E-06 |
2E+11 |
1.56E+04 |
9.8E+03 |
|
ton,mm,s |
0.001 |
1E+03 |
1 |
1E+03 |
1 |
1.0E-06 |
1E+03 |
1E-12 |
2E+05 |
1.56E+04 |
9.8E+03 |
|
slug,ft,s |
0.1 |
3.3 |
1 |
3.3 |
0.2 |
2.1E-02 |
0.7 |
1.9E-03 |
4E+09 |
51.3 |
32.2 |
|
Kg,mm,s |
1 |
1000 |
1 |
1E+03 |
1E+03 |
1.0E-03 |
1E+06 |
1.0E-09 |
2E+08 |
1.56E+04 |
9.8E+03 |
|
g,cm,ms |
1E+03 |
100 |
1E+03 |
1.0E-04 |
1.0E-01 |
1.0E-05 |
10.00 |
1.0E-03 |
2E+06 |
1.56E+00 |
9.8E-04 |
|
Kg,mm,ms |
1 |
1E+03 |
1E+03 |
1.0E-03 |
1.0E-03 |
1.0E-09 |
1.00 |
1.0E-09 |
210.0 |
15.6 |
9.8E-03 |
Results.
The task was performed according to the question. The unit conversion was performed according to the given system of units.