Week - 1 - Consistency of Units
Objective
- Obtain the different conversion factors between the following systems of units:
Unit systems:
gm mm ms
Kg cm ms
Kg cm s
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
- Use those conversion factors in the following quantities
Procedure
From SI to g/mm/ms
The same procedure is applied for the rest of the unit systems with the use of the attached Matlab program. Which allows to choose the mass, length and time unit to create a consistent unit system to work with and gives the conversion factor between them.
From SI to kg/cm/ms
From SI to kg/cm/s
From SI to kg/m/s
From SI to g/cm/s
From SI to g/cm/us
From SI to g/mm/s
From SI to Ton/mm/s
From SI to slug/ft/s
The above coefficients can be simplified to:
|
SI Equivalent |
Conversion Factor |
|
Mass (Kg) |
0.07*[Slug] |
|
Length (m) |
3.28*[ft] |
|
Time (s) |
1*[s] |
|
Force (N) |
0.22*([ft]*[slug])/[s]^2 |
|
Stress (Pa) |
0.02*([slug]/([ft]*[s]^2)) |
|
Energy (Nm) |
0.74*(([ft]^2*[slug])/[s]^2) |
|
Density (Kg/m^3) |
0.00194032*([slug]/[ft]^3) |
|
Young's Modulus (Pa) |
4385941188.9*([slug]/([ft]*[s]^2)) |
|
Velocity (m/s) |
3.28*([ft]/[s]) |
|
Gravity (m/s^2) |
3.28*([ft]/[s]) |
From SI to kg/mm/s
From Si to g/cm/ms
From SI to kg/mm/ms
Conclusions
- Appropriate unit system must be selected according to the magnitude of the basic quantities (mass, time and length)
Matlab code
clc;
clear all;
format shortE
format bank
%Change Unit system
u = symunit;
SIUnits = baseUnits('SI')
Mass_Unit = input('Enter mass unit: ', 's');
Length_Unit = input('Enter length unit: ', 's');
Time_Unit = input('Enter time unit: ', 's');
newUnits = subs(SIUnits,[u.kg u.m u.s],[u.(Mass_Unit) u.(Length_Unit) u.(Time_Unit)])
newUnitSystem('SI_try',newUnits)
%Mass, length, time
Mass = rewrite(1*u.kg,'SI_try')
Length = rewrite(1*u.m,'SI_try')
Time = rewrite(1*u.s,'SI_try')
%Force
Force = rewrite(u.kg*u.m/u.s^2,'SI_try')
%stress
Stress = rewrite((u.kg*u.m/u.s^2)*(1/u.m^2),'SI_try')
%Energy
Energy = rewrite((u.kg*u.m/u.s^2)*(u.m),'SI_try')
%Density
Density = rewrite(u.kg/u.m^3,'SI_try')
%Youngs
E = rewrite(210e9*(u.kg*u.m/u.s^2)*(1/u.m^2),'SI_try')
%Velocity
Velocity = rewrite(u.m/u.s,'SI_try')
%Gravity
Gravity = rewrite(u.m/u.s^2,'SI_try')
% Display results in a table
T = table(Mass, Length, Time, Force, Stress, Energy, Density, E, Velocity, Gravity);
disp(T)