Week - 1 - Consistency of Units

Week - 1 - Consistency of Units

AIM: Converting given measurements to the required unit systems

Explanation: Here the detailed calculation is shown for conversion to gm/mm/ms unit system

Mass:

1Kg = 1000 gm

1m = 1000 mm

1s = 1000 ms

Force:

Given Force = 1 N

Since 1 N = 1 `(Kg*m)/(s2)` and conversion by replacing the terms as given above

1 N = 1 `(1000 gm * 1000 mm)/(1000 ms*1000ms)`

Force in gm/mm/ms = 1 `(gm*mm)/(ms2)`

STRESS:

Given Stress = 1 Pa

Since 1 Pa = 1 `N/(m2)` = 1 `Kg/(m*s2)` and conversion by replacing the terms as given above

1 `N/(m2)` = 1 `(1000 gm)/(1000mm*1000 ms*1000ms)`

Force in gm/mm/ms = 1.00E-06 `gm/(mm*ms2)`

Energy:

Given Energy = 1 Nm

Since 1 Nm = 1 `(Kg*m2)/(s2)` and conversion by replacing the terms as given above

1 Nm = 1 `(1000 gm * 1000 mm * 1000 mm)/(1000 ms*1000ms)`

Force in gm/mm/ms = 1000 `(gm*mm2)/(ms2)`

Density:

Given Density = 1 `(Kg)/(m3)`

conversion by replacing the terms as given above

1 `(Kg)/(m3)` = 1 `(1000 gm)/(1000 mm*1000 mm*1000mm)`

Force in gm/mm/ms = 1.00E-06 `(gm)/(mm2)`

Young's Modulus:

Given Young's Modulus = 210 GPa = 2.10E+11 Pa

Since 1 Pa = 1 `N/(m2)` = 1 `Kg/(m*s2)` and conversion by replacing the terms as given above

1 `N/(m2)` = 1 `(1000 gm)/(1000mm*1000 ms*1000ms)`

Young's Modulus in gm/mm/ms = 2.10E+11*1.00E-06 `gm/(mm*ms2)` = 2.10E+05 `gm/(mm*ms2)`

Velocity:

Given Velocity = 56.33 `(Km)/(Hour)`

Converting it by replacing 1Km = 1.00E+06 mm, 1Hour = 3.60+E06 ms

So, Velocity in gm/mm/ms = 15.6 mm/ms

Gravity:

Given graity = 9.8 `m/(s2)`. conversion by replacing the terms as given above

1 `m/(s2)` = 1 `(1000 mm)/(1000 ms*1000ms)`

So, gravity in gm/mm/ms = 0.0098 `(mm)/(ms2)`

	MASS	LENGTH	TIME	FORCE	STRESS	ENERGY	DENSITY	YOUNG'S MODULUS	VELOCITY	GRAVITY
Given System	1 Kg	1 m	1 s	1 N	1 Pa	1 Nm	1 Kg/m3	210 Gpa	56.33	9.8 m/s2
Kg cm ms	1	100	1000	0.0001	1.00E-08	0.01	1.00E-06	2.10E+03	1.56E+00	0.00098
Kg cm s	1	100	1	100	0.01	1.00E+04	1.00E-06	2.10E+09	1.56E+03	980
gm mm ms	1000	1000	1000	1	1.00E-06	1.00E+03	1.00E-06	2.10E+05	1.56E+01	0.0098
kg m s	1	1	1	1	1	1	1.00E+00	2.1E+11	1.56E+01	9.8
g cm s	1000	100	1	1.00E+05	10	1.00E+07	1.00E-03	2.1E+12	1.56E+03	980
g cm us	1000	100	1.00E+06	1.00E-07	1.00E-11	0.00001	1.00E-03	2.1	1.56E-03	9.8E-10
g mm s	1000	1000	1	1.00E+06	1	1.00E+09	1.00E-06	2.1E+11	1.56E+04	9800
ton mm s	0.001	1000	1	1	1.00E-06	1.00E+03	1.00E-12	2.10E+05	1.56E+04	9800
slug ft s	0.0685	328	1	22.468	2.09E-04	7.37E+03	1.94E-09	4.39E+07	5.13E+03	3214.4
kg mm s	1	1000	1	1000	1.00E-03	1.00E+06	1.00E-09	2.10E+08	1.56E+04	9800
g cm ms	1000	100	1000	0.1	1.00E-05	10	1.00E-03	2.10E+06	1.56E+00	0.00098
kg mm ms	1	1000	1000	0.001	1.00E-09	1	1.00E-09	210	1.56E+01	0.0098