Week - 1 - Consistency of units
Aim:-To maintain unit consistency with a change in the unit system.
UNIT SYSTEM:
Unit system is divided into fundamental and derived unit system
- The units which are independent of each other are known as Fundamental Units
- Derived Units are derived from Fundamental Units.
- The system of units measures the physical quantities
SYSTEM OF UNITS
- C.G.S system(metric system)
- F.P.S system (British system)
- M.K.S system.
- S.I system (International system
Basic conversion of units
Length
1 meter = 100 centimeters
1 meter = 1000millimeters
1 foot = 304.8 mm
1 foot = 12 inch
1 inch =2.54 cm
Time
1 hour =3600 sec
1 sec = 1000 millisec
1 sec = 10^6 microsec
1 sec = 10^9 nano sec
Weight
1 Kg = 1000 gms
1 Ton = 1000 kgs
1kg = 0.068 slug
Pressure
1pa = 1N/m^2
Velocity
1 km = 1000m
1 h = 3600 s
So 1km /h = 1000/3600 = 5/18 = 0.28 m/sec
So to convert km/h to m/s we multiply the given number by 5/18 or 0.28m/sec
| S.I UNITS | 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 | 1kg | 1kg | 1 kg | 10^3 g | 10^3 g | 10^3 g | 10^3 g | 10^-3 ton | 0.068 slug | 1 kg | 10^3g | 1 kg |
| LENGTH 1m | 1m | 10^2cm | 10^2cm | 10^3mm | 10^2cm | 10^2cm | 10^3mm | 10^3mm | 3.28ft | 10^3mm | 10^2cm | 10^3mm |
| TIME 1s | 1s | 10^3ms | 1s | 10^3ms | 1s | 10^6us | 1s | 1s | 1s | 1s | 10^3ms | 10^3ms |
| FORCE 1N | 1kg*m/s^2 | 0.0001 kg*cm/ms^2 | 100kg*cm/s^2 | 1 gm*mm/ms^2 | 100000g*cm/s^2 | 10^-7g*cm/us^2 | 10^6g*mm/s^2 | 1t*mm/s^2 | 0.2246slug*ft/s^2 | 1000kg*mm/s^2 | 0.1g*cm/ms^2 | 0.001kg*mm/ms^2 |
| STRESS 1Pa | 1kg/m*s^2 | 10^-8 kg/cm*ms^2 | 0.001kg/cm*s^2 | 10^-6gm/mm*ms^2 | 10gm/cm*s^2 | 10^-11gm/cm*us^2 | 1gm/mm*s^2 | 10^-6ton/mm*s^2 | 0.0208slug/ft*s^2 | 0.001kg/mm8s^2 | 0.00001gm/cm*ms^2 | 0.00000001kg/mm*ms^2 |
| ENERGY 1Nm | 1Nm=1Joule =kg*m^2/s^2 | 0.001kg*cm^2/ms^2 | 10000kg*cm^2/s^2 | 1000g*mm^2/ms^2 | 1E+6g*cm^2/s^2 | 10^ -5g*cm^2/us^2 | 1E+kg*mm^2/s^2 | 1000ton*mm^2/s^2 | 0.736688slug*ft^2/s^2 | 1E+6kg*mm^2/s^2 | 10g*cm^2/ms^2 | 1kg*mm^2/ms^2 |
| DENSITY 1Kg/m3 | 1Kg/m^3 | 10^-6Kg/cm^3 | 10^-6Kg/cm^3 | 10^-6g/mm^3 | 10^-3g/cm^3 | 10^-3g/cm^3 | 10^-6g/mm^3 | 10^-12ton/mm^3 | 1.92*10^-3slug/ft^3 | 10^-9Kg/mm^3 | 0.001g/cm^3 | 10^-9Kg/mm^3 |
| YOUNG'S Modulus 210GPa | 21E+10kg/m*s^2 | 2100kg/cm*ms^2 | 21E+8kg/cm*s^2 | 21*10^4gm/mm*ms^2 | 21E+11gm/cm*s^2 | 2.1gm/cm*us^2 | 21E+10gm/mm*s^2 | 21E+4ton/mm*s^2 | 4368E+6slug/ft*s^2 | 21E+9kg/mm8s^2 | 21E+5gm/cm*ms^2 | 2100kg/mm*ms^2 |
| Velocity 56.33KMPH | 15.647m/s | 1.5647cm/ms | 1564.7cm/s | 15.647mm/s | 1564.7cm/s | 0.0015647cm/us | 15647.2mm/s | 15647mm/s | 51.32ft/s | 15647.2mm/s | 1.5647cm/ms | 15.647mm/ms |
| GRAVITY 9.8m/s2 | 1m/s2 | 0.0001cm/ms^2 | 100cm/s^2 | 0.001mm/ms^2 | 100cm/s^2 | 10^-10cm/us^2 | 1000mm/s^2 | 1000mm/s^2 | 3.28ft/s^2 | 1000mm/s^2 | 0.0001cm/ms^2 | 0.001mm/ms^2 |
CONVERSION FACTOR :
FORCE=1N
N=kg*m/s^2
=1000g*1000mm/1000*1000 ms^2
=1 g*mm/ms^2
conversion factor is 1
N=1000g*100cm/10^6*10^6 ms^2
N=10^-7g*cm/ms^2
conversion factor =10^-7
N= 0.068slug *3.28ft/1s^2
= 0.244 slug*ft/s^2
conversion factor is 0.244
STRESS= 1Pa
= 1 kg/m*s^2
= 1000 g/1000mm*1000*1000ms^2
=10^-6 g/mm*ms^2
Conversion factor =10^-6
pa=0.068 slug/3.28ft*s^2
=0.0208 slug/ft*s^2
Conversion factor = 0.0208
DENSITY=1 kg/m^3
=1000g/1000*1000*1000 mm^3
=10^-6 g/mm^3
Conversion factor = 10^-6
1 Kg/m^3=0.068 slug/3.28^3ft^3
=1.92*10^-3 slug/ft^3
E=210Gpa
1Gpa =10^9 pa
= 1*10^9 kg/m*s^2
= 10^9*1000 g/1000mm*1000*1000ms^2
= 1000 g/mm*ms^2
210Gpa = 21E+4 g/mm*ms^2
Conversion factor =10^3
1Gpa =10^9*0.068 slug/3.28ft*s^2
=0.0208E+09 slug/ft*s^2
Conversion factor = 0.0208*10^9
VELOCITY 56.33KMPH= 56.33*1000/3600=56.33*5/18=15.64m/s
=15.64*1000mm/1000ms
=15.64 mm/ms
conversion factor = 1
CONVERSION FACTOR TABEL
| S.I UNITS | 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 | 1 | 1 | 10^3 | 1 | 10^3 | 10^3 | 10^3 | 10^-3 | 0.06854 | 1 | 10^3 | 1 |
| LENGTH | 1 | 10^2 | 10^3 | 10^2 | 10^2 | 10^2 | 10^3 | 10^3 | 3.28 | 10^3 | 10^2 | 10^3 |
| TIME | 1 | 1 | 10^3 | 10^3 | 1 | 10^6 | 1 | 1 | 1 | 1 | 10^3 | 10^3 |
| FORCE | 1 | 10^2 | 1 | 10^-4 | 10^5 | 10^-7 | 10^6 | 1 | 0.224 | 10^3 | 0.1 | 10^-3 |
| STRESS | 1 | 10^-2 | 10^-6 | 10^-8 | 10 | 10^-5 | 1 | 10^-6 | 0.021 | 10^-3 | 10^-5 | 10^-9 |
| ENERGY | 1 | 10^4 | 10^3 | 10^-2 | 10^7 | 10^-11 | 10^9 | 10^3 | 0.735 | 10^6us | 10 | 1 |
| DENSITY | 1 | 10^-6 | 10^-6 | 10^-6 | 10^-3 | 10^-3 | 10^-6 | 10^-12 | 0.002 | 10^-9 | 10^-3 | 10^-9 |
| YOUNG'S Modulus | 1 | 10^-2 | 10^-6 | 10^-8 | 10 | 10^-11 | 1 | 10^-6 | 0.21 | 10^-3 | 10^-5 | 10^-9 |
| Velocity | 1 | 10^2 | 1 | 0.1 | 10^2 | 10^-4 | 10^3 | 10^3 | 51.29 | 10^3 | 10^-1 | 1 |
| GRAVITY | 1 | 10^2 | 10^-3 | 10^-4 | 10^2 | 10^-10 | 10^3 | 10^3 | 3.282 | 10^3 | 10^-4 | 10^-3 |
CONCLUSION:
- understood conversion of units
- understood the use of conversion factor
- understood the different type of unit system