Week - 1 - Consistency of Units

Aim: Writing a detailed report of unit conversion as per different standards followed in different industries.

Objective:

• To convert the unit to gm, mm, and ms in the calculation.
• Other Standards units can be formed in the table form.

Conversion of S.I units

gm, mm, ms

Given Units:

MASS = 1kg
LENGTH = 1m
TIME = 1s
FORCE = 1N
STRESS = 1Pa
ENERGY = 1Nm
DENSITY = 1Kg/m3
YOUNG'S Modulus = 210GPa
Velocity =56.33KMPH
GRAVITY = 9.8m/s2

Kg to gm:

1Kg = 1000gm

Mass -> 1kg -> 1*1000 = 1000gm

M to mm:

1M = 1000mm

Length -> 1m -> 1*1000 = 1000mm

Sec to ms:

1sec = 1000 ms

Time -> 1sec -> 1*1000 = 1000ms

Force:

Force is an external agent capable of changing a body's state of rest or motion. It has a magnitude and a direction.

F = m a;

Stress:

The force exerted on the unit area of a substance is known as stress.

It is also defined as the quantity of force we apply to an object divided by the cross-section area of the object on which the force acts.

Stress is a Scaler quantity, and it’s denoted by "σ".

Stress is measured in Pascal or N/m².

Energy:

The capacity for doing work, in this process of transfer from one body to another body.

Density:

Density is the measurement of how tightly a material is packed together. It is defined as the mass per unit volume.

ρ = m/V, where ρ is the density, m is the mass of the object and V is the volume of the object.

Young's Modulus:

Young's modulus (E) is a property of the material that tells us how easily it can stretch and deform and is defined as the ratio of tensile stress (σ) to tensile strain (ε).

The formula of Stress:

(σ = F/A)

The formula of Strain:

(ε = dl/l)

Velocity V:

It can be defined as the rate of change of the object’s position with respect to a frame of reference and time.

Its unit is m/s.

Gravity:

Gravity is a force that attracts a body towards the center of the earth or any other physical body having mass.

Unit needs to convert:

1. Kg cm ms
2. Kg cm s
3. gm mm ms
4. kg m s
5. g cm s
6. g cm us
7. g mm s
8. ton mm s
9. slug ft s
10. kg mm s
11. g cm ms
12. kg mm

Basic calculation of SI units to gm/mm/ms unit:

Kg to gm:

1Kg = 1000gm

Mass -> 1kg -> 1*1000 = 1000gm

M to mm:

1M = 1000mm

Length -> 1m -> 1*1000 = 1000mm

Sec to ms:

1sec = 1000 ms

Time -> 1sec -> 1*1000 = 1000ms

Force:

1N = kg*m/ms^2

1N = 1000*1000/ (1000^2)

1N = 1 gm*m/ms^2

Conversion factor = 1

Stress:

1Pa = Kg/m*s^2

1Pa = 1000 / 1000*(1000*1000)

1Pa = 1/1000000 = 1/10^6

Conversion factor = 10^-6

Energy:

1Nm = 1kg*m^2/s^2

1Nm = 1000*(1000*1000)/(1000*1000)

1Nm = 1000 gm*mm^2 / ms ^2

Conversion factor = 10^3

Density:

1ρ = kg/m^3

1ρ = 1000/ (1000*1000*1000)

1ρ = 1/1000000

Conversion factor = 10^-6

Young's Modulus:

210 Gpa = 210 * [ 10^9 * 10^-6 ]

where 1Gpa = 10^9 N/m^2, whereas 1N is 10^-6

210 Gpa = 210 * 10^3 = 210000

Conversion factor = 10^3

Velocity:

1KMPH = 10^6 (mm) / (3600 * 1000) = 0.277 mm/ms

56.33KMPH = 56.33 * 0.277

56.33 Kmph = 15.64 mm/ms

Conversion factor = 0.277 mm/ms

Gravity:

1m/s^2 = 1000/(1000 * 1000) = 1/10^3 = 10^-3

9.81 m/s^2 = 9.81* 10^-3 mm/ms^2

Conversion factor = 10^-3

Tabulation:

UNITS	MASS	LENGTH	TIME	FORCE	STRESS	ENERGY	DENSITY	YOUNG'S MODULUS	VELOCITY	GRAVITY
SI UNITS	1KG	1M	1SEC	1NEWTON	1 PASCAL	1 N-M	1 KG/M^3	210 GPA	56.33 KMPH	9.8 M/S^2
Kg, cm, ms	1 kg	10^2	10^3	10^-4	10^-8	10^-2	10^-6	210*10^1	1.564 cm/ms	9.8*10^-4
Kg, cm , s	1 kg	10^2	1	10^2	10^-2	10^4	10^-6	210*10^7	1.5*10^6 cm/s	9.8*10^2
gm, mm, ms	10^3	10^3	10^3	1	10^-6	10^3	10^-6	210*10^3	15.64 mm/ms	9.8*10^-3
kg, m, s	1	1	1	1	1	1	1	210*10^9	15.64	9.8
gm, cm, s	10^3	10^2	1	10^5	10	10^7	10^-3	210*10^8	15.64*10^2	9.8*10^2
gm, cm, us	10^3	10^2	10^6	10^-6	10^-11	10^-5	10^-3	210*10^-2	1.5*10^-3	9.8*10^-10
gm, mm, s	10^3	10^3	1	10^6	1	10^9	10^-6	210*10^9	1.5*10^3	9.8*10^3
ton, mm, s	10^-3	10^3	1	1	10^-6	10^3	10^-12	210*10^3	1.5*10^3	9.8*10^3
slug, ft, s	0.068	3.28	1	0.22304	0.0207	0.732	2.4	4.3*10^9	51.34	32.144
kg, mm, s	1	10^3	1	10^3	10^-3	10^6	10^-9	210*10^6	5.6*10^7	9.8*10^3
g, cm, ms	10^3	10^2	10^3	10^-1	10^-5	10^1	10^-3	210*10^4	1.564	9.8*10^-4
kg, mm, ms	1	10^3	10^3	10^-3	10^-9	1	10^-9	210	15.64	9.8*10^-3

Conclusion:

As per the different standards, the unit conversion are calculated with proper calculations.