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
| S.No | Units | Derived Quantites | Remarks | ||||||||
| Mass | Length | Time | Force | Stress | Energy | Density | Youngs Modulus | Velocity | Gravity | ||
| 1 | kg | m | s | 1 N | 1 Pa | 1 Nm | 1 Kg/m3 | 210 Gpa | 56.33 KMPH | 9.81 m/s2 | |
| 2 | kg | cm | ms | 10^-4 | 10^-8 | 0.01 | 0.000001 | 2100 | 1.565 | 9.81X10^-4 | |
| 3 | kg | cm | s | 100 | 0.01 | 10000 | 0.000001 | 2.1E+9 | 1564.7 | 981 | |
| 4 | g | mm | ms | 1 | 0.000001 | 1000 | 0.000001 | 210000 | 15.647 | 0.00981 | |
| 5 | kg | m | s | 1 | 1 | 1 | 1 | 210 | 15.647 | 9.81 | |
| 6 | g | cm | s | 100000 | 10 | 10000000 | 0.001 | 2.1E+12 | 1564.7 | 9.81X10^-4 | |
| 7 | g | cm | us | 10^-7 | 1E-11 | 0.00001 | 0.001 | 2.1 | 0.002 | 9.81E-10 | |
| 8 | g | mm | s | 1000000 | 1 | 1E+10 | 0.000001 | 2.1E+11 | 15647.2 | 9810 | |
| 9 | Ton | mm | s | 1 | 0.000001 | 1000 | 1E-12 | 210000 | 15647.2 | 9810 | |
| 10 | Slug | Fts | s | 0.2236 | 2.24E-05 | 0.7333 | 0.223696 | 4697616 | 51.323 | 32.1768 | |
| 11 | kg | mm | s | 1000 | 0.1 | 1000000 | 1E-9 | 2.1E+10 | 15647.2 | 9810 | |
| 12 | g | cm | ms | 0.1 | 0.00001 | 10 | 0.001 | 2100000 | 1.565 | 0.000981 | |
| 13 | kg | mm | ms | 10^-9 | 1E-13 | 0.000001 | 01E-9 | 0.021 | 15.647 | 0.00981 | |
Learning Outcomes :
1. Converting the units from one systems to another system is understood clearly.