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Week - 1 - Consistency of Units

AAmmepalle Gangadhara17 Sept 2021

OBJECVTIVE:-

  • We has to be conversant with converting quantities from one system of units to another.

FUNDAMENTAL DIMENSIONS AND UNITS

All phiysical quantities are measured in the certain units. there are two type of units

  • Fundamental units
  • Derived units

Fundamental units

All the physical quanties are expressed in terms of the fllowing three fundamental units

  • Length(L)
  • Mass(M)
  • Time(T)

Derived unit

Some units called derived unuits are expressed in terms of fundamental units such as units of area,velcoity,accleration,pressure etc..

  • Area-m2
  • Density-kg/m3
  • velcoity-m/s
  • Acceleration-m/s2
  • Angular velcoity-rad/s
  • Force-N
  • pressure-N/m2
  • Torque,work,Energy-N-m or Joules

System of units

  • C.G.S. units
  • F.P.S. units
  • M.K.S. unit
  • S.I. units

S.I.units(International system of units)

This system has six basic units ,two supplementry units and twenty -seven derived units. the six basic units are as follows

Quantity Units Symbol
Length Metre m
Mass Kilogram kg
Time Second S
Electric current Ampere A
thermodynamic Temperture Degree Kelvin K
Luminous intensity Candala Cd

Value of the following measurements are given as follows

conversion of S.I unit to gm mm ms

MASS 1kg

  • 1000g

LENGTH 1m

  • 1000mm

TIME 1s

  • 1000ms

FORCE 1N

  • F=mass*acceleration

    =>1kg*1m/s2

    =>(1000g*1000mm)/(1000ms)2

    =>10^6/10^6 g mm/ms2

    =>1 g mm/ms2

Pressure 1Pa

  • 1Pa =1N/1M2

=>(1kg*1m/s2 )/1M2

=>((1000g*1000mm)/(1000ms)2)/(1000mm)2

=>(g*mm/ms2)*mm-2)

=>1000g/(1000)2ms2*1000mm

=>1*10-6g/ms2 mm

  • convertion factor is 10-6

ENERGY 1Nm=1 Joule

  • 1 Joule =1N*1M

1N =1 g mm/ms2{above derivation}

1Joule =>(1000g*1000mm/(1000ms)2)*1000mm

=>109g mm2/106ms2

=>109g mm2 *10-6 ms2

ANS =>103 g mm2/ms2

  • Conversion factor=103

DENSITY 1Kg/m3

=>1000g/(1000mm)3

=>g/(1000mm)2

Ans =>10-6g /mm2

  • Conversion factor=10-6

YOUNG'S Modulus 210GPa

1pa =>1*10-6g/ms2mm mm{above derivation}

1 Giga =>1*109

=>(1*10-6)*(1*109)

1Gpa =>1*103g/ms2 mm

210Gpa =>210*103 g/ms2mm

  • Conversion factor=10-3

Velocity 56.33KMPH

Velocity =Km/H

1Km =106mm

1 hour => 60 minutes

1 Minute =>60 seconds

=>60*60 seconds=3600 seconds

1ms =3600*1000

=>36*105

Km/H =>(106)/(36*105)

=0.277 Mm/ms

56.33Km/H =56.33*0.277

ANS =>15.60Mm/Ms

  • Conversion factor=1

GRAVITY 9.8m/s2

Gravity =M/s2

=>1000mm/(1000ms)2

=>1*10-3mm/ms2

9.8mm/ms2 =>9.8*10-3mm/ms2

ANS =>9.8*10-3mm/ms2

  • Conversion factor=1

Table of all consistency units

  • S.I unites

    Mass

    LENGTH

    TIME

    FORCE

    STRESS

    ENERGY

    DENSITY

    YOUNG'S Modulus

    Velocity 56.33

    GRAVITY 9.8

    kg m s

    1kg

    1m

    1s

    1kg*1m/s2

    1pa=kg/m*s2

    1Nm=1Joule =kg m2/s2

    Kg/m3

    210e+9kg/m s2

    15.64 m/s

    9.8 m/s2

    Kg cm ms

    1 kg

    102cm

    103ms

    1*10-4kg cm/ms2

    1*10-8 kg/cm*ms2

    1*10-3kg cm2/ms2

    10-6 kg/cm3

    2100 kg/cm ms2

    1.564cm/ms

    9.8*10-4 cm/ms2

    Kg cm s

    1kg

    102cm

    1s

    102 kg*cm/s2

    1*10-3 kg/cm*s2

    104kgcm2/s2

    10-6 kg/cm3

    210e+7kg/cm s2

    1564 cm/s

    9.8*102cm/s2

    gm mm ms

    103g

    103mm

    103ms

    1 gm*mm/ms2

    1*10-6g/ms2 mm

    103 g mm2/ms2

    10-6g /mm2

    210*103 g/ms2mm

    15.64mm/Ms

    9.8*10-3mm/ms2

    g cm s

    103g

    102cm

    1s

    105g*cm/s2

    10 g/cm*s2

    106g cm2/s2

    10-3g/cm3

    2.1*1012g/cm s2

    1564 cm/s

    9.8*102cm/s2

    g cm us

    103g

    102cm

    106us

    10-7 g*cm/us2

    10-11 g/cm*us2

    10-5g cm2/us2

    10-3g/cm3

    2.1 g/cm us2

    15.6*10-4 cm/us

    9.8*10-10 cm/us2

    g mm s

    103g

    103mm

    1s

    106g*mm/s2

    1 g/mm*s2

    109g mm2/s2

    10-6 g/mm3

    2.1*1011g/mm s2

    1564mm/s

    9.8*103mm/s2

    ton mm s

    10-3t

    103mm

    1s

    1 t/mm*s2

    10-6 t/mm*s2

    103t *mm2/s

    10-12 t/mm3

    210e+3t/mm s2

    15647 mm/s

    9.8*103mm/s2

    slug ft s

    0.068 slug

    3.28ft

    1s

    0.2246 slug/ft*s2

    0.0208 slug/s2ft

    0.7366 slug*ft2/s

    1.93*10-3 slug/ft3

    4.368e+9slug/ft s2

    51.32 ft/s

    32.144 ft/s2

    kg mm s

    1kg

    103mm

    1s

    103 kg*mm/s2

    10-3 kg/mm*s2

    106 g mm2/s2

    10-9 kg/mm3

    2.1*108 kg/mm s2

    1564mm/s

    9.8*103mm/s2

    g cm ms

    103g

    102cm

    103ms

    1*10-1g cm/ms2

    1*10-5 g/cm*ms2

    10 g cm2/ms2

    10-3 g/cm3

    2.1e+6g/cm ms2

    1.56cm/ms

    9.8*10-4 cm/ms2

    kg mm ms

    1kg

    103mm

    103ms

    10-3 kg*mm/ms2

    10-9 kg/mm*ms2

    1 kg mm2/ms2

    10-9 kg/mm3

    2.10e2kg/mm ms2

    15.647 mm/ms

    9.8*10 -3 mm/ms2

The conversion factor

Unit system=>Kg m s

  • FORCE 1N=>1kg*1m/s2
  • conversion factor =1
  • STRESS 1Pa=>kg/m*s2
  • conversion factor =1
  • ENERGY 1Nm=>kg m2/s2
  • conversion factor =1
  • DENSITY 1Kg/m3=>Kg/m3
  • conversion factor =1
  • YOUNG'S Modulus 210GPa=>210e+9kg/m s2
  • conversion factor =109
  • Velocity56.33kmph=>15.64 m/s
  • conversion factor =1
  • m/s2=>9.8 m/s2
  • conversion factor =1

Unit system=>kg cm ms

  • FORCE=>1*10-4kg cm/ms
  • conversion factor=10-4
  • STRESS=>1*10-8 kg/cm*ms2
  • conversion factor=10-8
  • ENERGY=>1*10-3kg cm2/ms2
  • conversion factor=10-3
  • DENSITY=>10-6 kg/cm3
  • conversion factor =10-6
  • YOUNG'S Modulus=>2100 kg/cm ms2
  • conversion factor =10
  • Velocity56.33=>1.564cm/ms
  • conversion factor =1
  • GRAVITY 9.8=>9.8*10-4 cm/ms2
  • conversion factor=10-4

Unit system=> Kg cm s

  • FORCE 1N=> 102 kg*cm/s2
  • conversion factor =102
  • STRESS 1Pa=> 10-3 kg/cm*s2
  • conversion factor =10-3
  • ENERGY 1Nm=>104kgcm2/s2
  • conversion factor =104
  • DENSITY 1Kg/m3=>10-6 kg/cm3.
  • conversion factor =10-6
  • YOUNG'S Modulus 210GPa=>210e+7kg/cm s2
  • conversion factor =107
  • Velocity56.33=>1564 cm/s
  • conversion factor =1
  • Gravity =>9.8*102cm/s2
  • conversion factor =102

Unit system=> gm mm ms

  • FORCE => 1 gm*mm/ms2
  • conversion factor =1
  • STRESS => 1*10-6g/ms2 mm
  • conversion factor =10-6
  • ENERGY =>103 g mm2/ms2
  • conversion factor =103
  • DENSITY =>10-6g /mm2
  • conversion factor =10-6
  • YOUNG'S Modulus 210=>210*103 g/ms2mm
  • conversion factor =103
  • Velocity56.33=>15.64mm/Ms
  • conversion factor =1
  • Gravity =>9.8*10-3 mm/ms2
  • conversion factor =10-3

Unit system=> gm cm s

  • FORCE => 105g*cm/s2
  • conversion factor =105
  • STRESS => 10 g/cm*s2
  • conversion factor =10
  • ENERGY =>106g cm2/s2
  • conversion factor =106
  • DENSITY =>10-3g/cm3
  • conversion factor =10-3
  • YOUNG'S Modulus 210=>2.1*1012g/cm s2
  • conversion factor =1012
  • Velocity56.33=> 1564 cm/s
  • conversion factor =1
  • Gravity =>9.8*102cm/s2
  • conversion factor =102

Unit system=> g cm us

  • FORCE => 10-7 g*cm/us2
  • conversion factor =10-7
  • STRESS => 10-11 g/cm*us2
  • conversion factor =10-11
  • ENERGY =>10-5g cm2/us2
  • conversion factor =10-5
  • DENSITY =>10-3g/cm3
  • conversion factor =10-3
  • YOUNG'S Modulus 210=>2.1 g/cm us2
  • conversion factor =1
  • Velocity56.33=> 15.6*10-4 cm/us
  • conversion factor =10-4
  • Gravity =>9.8*10-10 cm/us2
  • conversion factor =10-10

Unit system=> g mm s

  • FORCE => 106g*mm/s2
  • conversion factor =106
  • STRESS => 1 g/mm*s2
  • conversion factor =1
  • ENERGY =>109g mm2/s2
  • conversion factor =109
  • DENSITY => 10-6 g/mm3
  • conversion factor =10-6
  • YOUNG'S Modulus 210=>2.1*1011g/mm s2
  • conversion factor =1011
  • Velocity56.33=> 1564mm/s
  • conversion factor =1
  • Gravity =>9.8*103mm/s2
  • conversion factor =103

Unit system=> ton mm s

  • FORCE => 1 t/mm*s2
  • conversion factor =1
  • STRESS => 10-6 t/mm*s2
  • conversion factor =10-6
  • ENERGY =>103t *mm2/s
  • conversion factor =103
  • DENSITY => 10-12 t/mm3
  • conversion factor =10-12
  • YOUNG'S Modulus 210=>210e+3t/mm s2
  • conversion factor =103
  • Velocity56.33=> 15647 mm/s
  • conversion factor =1
  • Gravity =>9.8*103mm/s2
  • conversion factor =103

Unit system=> slug ft s

  • FORCE => 0.2246 slug/ft*s2
  • conversion factor =1
  • STRESS => 0.0208 slug/s2ft
  • conversion factor =1
  • ENERGY =>0.7366 slug*ft2/s
  • conversion factor =1
  • DENSITY => 1.93*10-3 slug/ft3
  • conversion factor =10-3
  • YOUNG'S Modulus 210=>4.368e+9slug/ft s2
  • conversion factor =109
  • Velocity56.33=> 51.32 ft/s
  • conversion factor =1
  • Gravity =>32.144 ft/s2
  • conversion factor =1

Unit system=> kg mm s

  • FORCE => 103 kg*mm/s2
  • conversion factor =103
  • STRESS => 10-3 kg/mm*s2
  • conversion factor =10-3
  • ENERGY => 106 g mm2/s2
  • conversion factor =106
  • DENSITY => 10-9 kg/mm3
  • conversion factor =10-9
  • YOUNG'S Modulus 210=>2.1*108 kg/mm s2
  • conversion factor =108
  • Velocity56.33=> 1564mm/s
  • conversion factor =1
  • Gravity =>9.8*103mm/s2
  • conversion factor =103

Unit system=> g cm ms

  • FORCE => 1*10-1g cm/ms2
  • conversion factor =10-1
  • STRESS => 1*10-5 g/cm*ms2
  • conversion factor =10-5
  • ENERGY => 10 g cm2/ms2
  • conversion factor =10
  • DENSITY => 10-3 g/cm3
  • conversion factor =10-3
  • YOUNG'S Modulus 210=> 2.1e+6g/cm ms2
  • conversion factor =106
  • Velocity56.33=> 1.56cm/ms
  • conversion factor =1
  • Gravity =>9.8*10-4 cm/ms2
  • conversion factor =10-4

Unit system=> kg mm ms

  • FORCE => 10-3 kg*mm/ms2
  • conversion factor =10-3
  • STRESS => 10-9 kg/mm*ms2
  • conversion factor =10-9
  • ENERGY => 1 kg mm2/ms2
  • conversion factor =1
  • DENSITY => 10-9 kg/mm3
  • conversion factor =10-9
  • YOUNG'S Modulus 210=> 2.10e2kg/mm ms2
  • conversion factor =102
  • Velocity56.33=> 15.647 mm/ms
  • conversion factor =1
  • Gravity =>9.8*10 -3 mm/ms2
  • conversion factor =10-3

CONCLUSION :

Thus, the given measurements were converted to the provided different system of units and the conversion factors for the same was also provided with respect to the guidelines.

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