Week - 1 - Consistency of units
Objective:
- To convert all the given SI unit quantities in to the mentioned quantities and unit systems. Along with this, mention the conversion factor that is used to convert into those particular quantities. Show a detailed calculation for the conversion of the quantity ‘gm/mm/ms’.
Introduction:
- The units that are widely used in the industry and engineering to measure the physical quantities are basically of two types. Fundamental units and derived units. The fundamental units are considered as independent units while the derived units are considered as dependent units. These derived units, as the name suggests, are derived quantities, which are derived from the fundamental units. Hence they are also called as dependent units.
- Fundamental Units: The measurement of physical quantities is done in terms of some arbitrary, but internationally accepted units, called fundamental units. All the fundamental units in engineering are expressed in the terms of following three fundamental quantities:
Length (L or l), Mass (M or m), Time (t).
- Derived Units: Some units are expressed in the terms of fundamental units known as derived units, e.g., the units of are, velocity, acceleration, pressure, force, etc.
- Systems of Units: There are only four systems of units, which are commonly used and universally recognized. These are known as:
- C.G.S. units
- F.P.S. units
- M.K.S. units, and
- S.I. units
The most commonly used and industry accepted system of units is the S.I. unit system.
- In this system of units, the fundamental units are meter (m), kilogram (kg), and second (s) respectively.
- Values of some of the units are given for the reference, which have to be converted into different 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
Calculations:
- The calculations for the above unit system when represented in the gm/mm/ms format are as follows.
|
Quantity |
S.I. Unit System |
gm/mm/ms System |
|
Mass |
1kg |
1000gm Conversion Factor – 103 |
|
Length |
1m |
1000mm Conversion Factor – 103 |
|
Time |
1s |
1000ms Conversion Factor – 103 |
|
Force |
1N |
Mass*acceleration 1000gm*(1000mm/1000ms2) 103*(103/106) gm*(mm/ms) 103*10-3 gm*mm/ms 1gm*mm/ms Conversion Factor – 1 |
|
Stress |
1Pa |
Pa=N/m2 1Pa=(1kg*m/s2)/(1m2) 1kg/(m*s2) 1000/(103*106) 10-6gm/(mm*ms2) Conversion Factor – 10-6 |
|
Energy |
1Nm |
1kg*(m/s2)*m 1kg*(m2/s2) 1000*(106/106) gm*(mm2/ms2) 103 gm*(mm2/ms2) Conversion Factor – 103 |
|
Density |
1kg/m3 |
1000/109 gm/mm3 10-6 gm/mm3 Conversion Factor – 10-6 |
|
Young’s Modulus |
210GPa |
210*109 Pa Since conversion factor for Pa is 10-6 (from above), 210*109*10-6 gm/(mm*ms2) Conversion Factor – 103 |
|
Velocity |
56.33kmph |
56.33*(1000m*3600s) 56.33*[106/(3600*1000)] mm*ms 15.647mm/ms Conversion Factor – 1 |
|
Gravity |
9.8m/s2 |
9.8*1000mm/(1000ms)2 9.8*10-3 mm/ms2 Conversion Factor –10-3 |
- Conversion of the above mentioned quantities in following units:
Kg cm ms
Kg cm s
Gm mm ms
Kg m s
Gm cm s
Gm cm μs
Gm mm s
Ton mm s
Slug ft s
Kg mm s
G cm ms
Kg mm ms
|
Units SI Units |
Mass |
Length |
Time |
Force |
Stress |
Energy |
Density |
Young’s Modulus |
Velocity 56.33kmph |
Gravity |
|
Kg m s |
1kg |
1m |
1s |
1N 1kg*m/s2 Conversion Factor=1 |
1Pa Conversion Factor=1 |
1Nm Conversion Factor=1 |
1kg/m3 Conversion Factor=1 |
210GPa Conversion Factor= 109 |
15.647 m/s Conversion Factor=1 |
9.8m/s2 Conversion Factor=1 |
|
Kg cm ms |
1kg |
102 cm |
103 ms |
10-4 kg*cm/ms2 Conversion Factor=10-4 |
10-8 kg/(cm*ms2) Conversion Factor=10-8 |
10-2 kg*cm2/ms2 Conversion Factor=10-2 |
10-6 kg/cm3 Conversion Factor=10-6 |
2100 kg/(cm*ms2) Conversion Factor=10 |
1.5647 cm/ms Conversion Factor=0.1 |
9.8*10-4 cm/ms2 Conversion Factor=10-4 |
|
Kg cm s |
1kg |
102 cm |
1s |
102 kg*cm/s2 Conversion Factor=102 |
10-2 kg/(cm*s2) Conversion Factor=10-2 |
104 kg*cm2/s2 Conversion Factor=104 |
10-6 kg/cm3 Conversion Factor=10-6 |
210*107 kg/(cm*s2) Conversion Factor=107 |
1564.7 cm/s Conversion Factor=100 |
9.8*102 cm/s2 Conversion Factor=102 |
|
g mm ms |
103 g |
103 mm |
103 ms |
1 g*mm/ms2 Conversion Factor=1 |
10-6 g/(mm*ms2) Conversion Factor=10-6 |
103 g*mm2/ms2 Conversion Factor=103 |
10-6 g/mm3 Conversion Factor=10-6 |
210*103 g/(mm*ms2) Conversion Factor= 10-6 |
15.647 mm/ms Conversion Factor=1 |
9.8*10-3 mm/ms2 Conversion Factor=10-3 |
|
g cm s |
103 g |
102 cm |
1s |
105 g*cm/s2 Conversion Factor=105 |
10g/(cm*s2) Conversion Factor= 10 |
107 g*cm2/s2 Conversion Factor=107 |
10-3 g/cm3 Conversion Factor=10-3 |
210*1010 g/(cm*s2) Conversion Factor=10-1 |
1564.7 cm/s Conversion Factor=100 |
9.8*102 cm/s2 Conversion Factor=102 |
|
g cm μs |
103 g |
102 cm |
106 μs |
10-7 g*cm/μs2 Conversion Factor=10-7 |
10-11 g/(cm*μs2) Conversion Factor=10-11 |
10-5 g*cm2/μs2 Conversion Factor=10-5 |
10-3 g/cm3 Conversion Factor=10-3 |
2.10 g/(cm*μs2) Conversion Factor=10-11 |
15.647*10-4 cm/μs Conversion Factor=10-2 |
9.8*10-10 cm/μs2 Conversion Factor=10-10 |
|
g mm s |
103 g |
103 mm |
1s |
106 g*mm/s2 Conversion Factor=106 |
1 g/(mm*s2) Conversion Factor=1 |
109 g*mm2/s2 Conversion Factor=109 |
10-6 g/mm3 Conversion Factor=10-6 |
210*109 g/(mm*s2) Conversion Factor=1 |
15647 mm/s Conversion Factor=103 |
9.8*103 mm/s2 Conversion Factor=103 |
|
ton mm s |
10-3 ton |
103 mm |
1s |
1 ton*mm/s2 Conversion Factor=1 |
10-6 ton/(mm*ms2) Conversion Factor=10-6 |
103 ton*mm2/s2 Conversion Factor=103 |
10-12 g/mm3 Conversion Factor=10-12 |
210*103 ton/(mm*s2) Conversion Factor=10-6 |
15647 mm/s Conversion Factor=103 |
9.8*103 mm/s2 Conversion Factor=103 |
|
slug ft s |
0.068 slug |
3.28 ft |
1s |
0.2246 slug*ft/s2 Conversion Factor=0.2246 |
0.0208 slug/(ft*s2) Conversion Factor=0.0208 |
0.7366 slug*ft2/s2 Conversion Factor=0.7366 |
1.93*10-3 slug/ft3 Conversion Factor=1.93*10-3 |
4.368*109 slug/(ft*s2) Conversion Factor=0.0208 |
51.322 ft/s Conversion Factor=0.9947 |
32.144 ft/s2 Conversion Factor=3.28 |
|
kg mm s |
1 kg |
103 mm |
1s |
103 kg*mm/s2 Conversion Factor=103 |
10-3 kg/(mm*s2) Conversion Factor=10-3 |
106 kg*mm2/s2 Conversion Factor=106 |
10-9 kg/mm3 Conversion Factor=10-9 |
210*106 kg/(mm*s2) Conversion Factor=10-3 |
15647 mm/s Conversion Factor=103 |
9.8*103 mm/s2 Conversion Factor=103 |
|
g cm ms |
103 g |
102 cm |
103 ms |
10-1 g/(cm*ms2) Conversion Factor=10-1 |
10-5 g/(cm*ms2) Conversion Factor=10-5 |
10 g*cm2/ms2 Conversion Factor=10 |
10-3 g/cm3 Conversion Factor=10-3 |
210*104 g/(cm*ms2) Conversion Factor=10-5 |
1.5647 cm/ms Conversion Factor=10 |
9.8*10-4 cm/ms2 Conversion Factor=10-4 |
|
kg mm ms |
1 kg |
103 mm |
103 ms |
10-3 kg/(mm*ms2) Conversion Factor=10-3 |
10-9 kg/(mm*ms2) Conversion Factor=10-9 |
1 kg*mm2/ms2 Conversion Factor=1 |
10-9 kg/mm3 Conversion Factor=10-9 |
210 kg/(mm*ms2) Conversion Factor=10-9 |
15.647 cm/ms Conversion Factor=1 |
9.8*10-3 mm/ms2 Conversion Factor=10-3 |
Conclusion:
- All the quantities mentioned in the challenge were successfully converted into different types of unit systems that are widely used in the industries.
- Along with this, the conversion factor which is used to convert these units has also been mentioned in the table above.