Week - 1 - Consistency of Units

Aim:-

1. To convert the given SI unit values of given quantities to all different parameters.
2. To prepare consistent unit system table for different unit system.

Procedure:-

System of Units:

• A system of units is a set of realated units that are used for calculations. For example, in the MKS unit system, the base units are the meter, kilogram and second which represents the base dimensions of length, mass and time respectively. In this system, the unit of speed is the meter per second.

SI Units Of Fundamental Quantity:-

SI Units of Derived Quantity:-

Value of the following measurements are given as follows:

• Mass= 1 kg
• Length= 1m
• Time= 1s
• Force= 1N
• Stress= 1Pa
• Energy= 1Nm
• Density= 1Kg/m³
• Youngs Modulus= 210Gpa
• Velocity= 56.33kmph
• Gravity= 9.8 m/s²

Conversion of SI units to gm mm ms system:-

1) Mass = 1 Kg = 1000 gm

2) Length = 1m = 1000mm

3) Time = 1 sec = 1000ms

4) Force = 1 N F = Mass X Acceleration = 1 Kg * 1m/s² =(1000gm*1000mm)/(1000ms)² = 1 (gm*mm)/ms²

5) Stress = 1 Pa 1Pa = 1N/m 1N= 1(gm*mm/ms²) = {1(gm*mm/ms²)} / (1000mm²) = 1*10^-6gm/mm*ms²

Conversion Factor = 10^-6gm/mm*ms²

6) Energy = 1Nm = 1N*1m = {1gm*mm/ms²}* 1000mm = 1000 gm*mm²/ms² = 10³ gm mm²/ms²

Conversion Factor = 10³ gm mm²/ms²

7) Density = 1Kg/m³ = 1000gm/(1000mm) = 1 gm/1000000 mm³ = 10⁶ gm/mm³

Conversion Factor = 10⁶ gm/mm³

8) Youngs Modulud = 210 GPa 1 Pa= 10^-6 gm/mm ms² 1 Gpa= 10⁹*10^-6 gm/mm ms 210 GPa= 210*10³ gm/mm ms²

Conversion Factor = 10³

9) Velocity= 56.33 Kmph 1 Km = 1000000 mm = 10⁶ mm 1 Hr = 60 min*60sec*1000 = 36*10⁵ ms 1 Kmph = (10⁶)/(36*10⁵) = 0.277 mm/ms For 56.33 Kph; = 56.33* 0.277 mm/ms = 15.60 mm/ms

Conversion Factor= 0.277

10) Gravity = 9.88 m/s² 1m/s² = 1000mm/(1000ms²) = 10^-3 mm/ms² 9.88 m/s² = 9.8*10^-3 mm/ms²

Conversion Factor= 10^-3

Calculation Table:-

Unit System	MASS (1Kg)	LENGTH (1m)	TIME (1s)	FORCE (1N)	STRESS (1Pa)	ENERGY (1Nm)	DENSITY (1Kg/m3)	YOUNGS MODULUS (210GPa)	VELOCITY (56.33kmph)	GRAVITY (9.8m/s2)
Kg cm ms	1 kg	100 cm	1000 ms	10-4 (kg*cm)/ms2	10-8 kg/cm ms2	10-2 kg cm2/ms2	10-6 kg/cm3	210 * 106 kg/cm*ms2	0.1560 cm/ms	9.8*10-4 cm/ms2
Kg cm s	1 kg	100 cm	1 s	100 kg cm/s2	10-2 kg/cm s2	104 kg cm2/s2	10-4 kg/cm3	210 * 107 kg/cm*s2	156.03 cm/s	cm/s2
gm mm ms	1000 gm	1000 mm	1000 ms	1 (gm*mm)/ms2	1*10-6gm/mm*ms2	103 gm mm2/ms2	106 gm/mm3	210*103 gm/mm ms2	15.60 mm/ms	9.8*10-3 mm/ms2
kg m s	1 kg	1 m	1 s	1 kg m/s2	1 kg/m s2	1 kg m2/s2	10 kg/m3	210 * 109 kg/m s2	15.603 m/s	9.8*1 m/s2
g cm s	1000 gm	100 cm	1 s	105 g cm/s2	10 g/cm s2	107g cm2/s2	10-3 g/cm3	210 * 1010 g/cm s2	156.03 cm/s	9.8*100 cm/s2
g cm us	1000 gm	100 cm	106 us	10-1 g cm/us2	10-3 g/cm us2	10g cm2/us2	10-3 g/cm3	210 * 106 g/cm us2	0.000156 cm/us	9.8*10-10 cm/us2
g mm s	1000 gm	1000 mm	1 s	106 g mm/s2	1 g/mm s2	109 g mm2/s2	10-6 g/mm3	210 * 109 g/mm s2	15603 mm/s	9.8*1000 mm/s2
ton mm s	0.001 ton	1000 mm	1000 ms	10-6 ton mm/ms2	10-12 ton/mm ms2	10-3 ton mm2/ms2	10-12 ton/mm3	210 * 10-3 ton/mm ms2	15.60 mm/ms	9.8*10-3 mm/ms2
slug ft s	0.0068 slug	3.28 ft	1 s	0.22 slug ft/s2	0.0205 slug/ft s2	7216 slug ft2/s2	0019 slug/ft3	4.305*109 slug/ft s2	51.316 ft/s	32.14 ft/s2
kg mm s	1 kg	1000 mm	1 s	1000 kg mm/s2	10-3 kg/mm s2	106 kg mm2/s2	10-9 kg/mm3	210 * 106 kg/mm s2	15603 mm/s	9.8*1000 mm/s2
g cm ms	1000 gm	100 cm	1000 ms	10-1 gm cm/ms2	10-3 gm/cm ms2	10 gm cm2/ms2	10-3 g/cm3	210 * 106 g/cm ms2	1.5603 cm/ms	9.8*10-4 cm/ms2
kg mm ms	1 kg	1000 mm	1000 ms	10-3 (kg*mm)/ms2	10-9 kg/mm ms2	1 kg mm2/ms2	10-9 kg/mm3	210 * 1 kg/mm ms2	15.60 mm/ms	9.8*10-3 mm/ms2

Conclusion:-

1. Convert the given SI unit values of given quantities to all different parameters with detailed calculation.
2. Prepare the consistent unit system table for different unit system.