Week - 1 - Consistency of Units

Aim : To achieve the units conversions from one form of system to another form for given quantities as below,

Procedure :

1. Given parameters like Mass, Length, time, Force , energy, density, Youngs Modulus, Velocity , Gravity either fundamental or derived quantities are in Kg, m, sec.

2. Following are the basic fundamental quantities from system to another unit system, By using the below conversion we can convert the all derived quantities as mentioned in the below table

a. 1Kilo Gram = 1000 Grams

b. 1 Ton = 1000 kilo grams

c. 1 Slug = 14.593 Kilo Gram

d. 1 Mtr = 100cm

e. 1 Mtr = 1000mm

f. 1 Mtr = 3.28 Ft

g. 1 Kilo Meter = 1000mtr

h. 1Hr = 3600sec

i. 1 Sec = 1000 ms

j. 1 Sec = 10^6 um

k. 1N = 1(Kg-m)/s^2

l. 1 Pa = 1 N/m^2

m. 1GPa = 10^9 Pa

3. The following example is shown from conversion the units SI units to g/mm/ms

a. Force

1N = 1Kg-m/s^2

= 1000*1000/(1000)^2 g-mm/(ms)^2

1N = 1 g-mm/(ms)^2

b. Stress

1Pa = 1N/m^2

= 1 /(1000)^2 g-mm/(ms)^4

= 0.000001 g-mm/(ms)^4

c. Energy

1 N-m = 1 * 1000 g-mm^2/(ms^2)

= 1000 g-mm^2/(ms^2)

d. Density

1 Kg/m^3 = 1000/(1000)^3 g/mm^3

= 0.000001 g/mm^3

e. Youngs Modulus

210GPa = 210*10^9 Pa

= 210*10^9 * 10^-6 g-mm/(ms)^4

= 210*10^3 g-mm/(ms)^4

f. Velocity

56.33KMPH = 56.33*1000*1000/(60*60*1000) mm/ms

= 15.657 mm/ms

g. Gravity

9.81 m/s² = 9.81*1000/(1000*1000) mm/(ms)^2

= 0.00981 mm/(ms)^2

kg-m-s	kg-cm-ms	kg-cm-s	gm-mm-ms	g-cm-s	g-cm-us	g-mm-s	Ton-mm-s	slug-ft-s	kg-mm-s	g-cm-ms	kg-mm-ms
Mass(1kg)	1	1	1000	1000	1000	1000	0.001	0.06852	1	1000	1
Length(1m)	100	100	1000	100	100	1000	1000	3.28	1000	100	1000
Time(1s)	1000	1	1000	1	1000000	1	1	1	1	1000	1000
Force(1N)	0.0001	100	1	100000	1E-07	1000000	1	0.224746	1000	0.1	0.001
Stress(1Pa)	0.00000001	0.01	0.000001	10	1E-11	1	0.000001	0.02089	0.001	0.00001	1E-09
Energy(1N-m)	0.01	10000	1000	10000000	0.00001	1E+09	1000	0.737166	1000000	10	1
Density 1kg/m^3	0.000001	0.000001	0.000001	0.001	0.001	0.000001	1E-12	0.001942	1E-09	0.001	1E-09
young's modulus 210Gpa	21	2.1E+13	210000	2.1E+16	2.1E-08	2.1E+17	2.1E+11	4.72E+10	2.1E+14	21000	210
velocity 56.33 KMPH	1.56472222	1564.722	15.64722	1564.722	0.001565	15647.22	15647.22	51.32289	15647.22	1.564722	15.64722
Gravity 9.8m/s^2	0.00098	980	0.0098	980	9.8E-10	9800	9800	32.144	9800	0.00098	0.0098