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Pump Formulas — Imperial and SI Units

Pressure to Head

Imperial Units SI Units

 

 

H = head, ftP = pressure, psiSG = specific gravity

H = head, mP = pressure, barSG = specific gravity

Mass Flow to Volumetric Flow

Imperial Units SI Units

 

 

Q = flow, gpmṁ = mass flow, lbm/hSG = specific gravityρ = fluid density, lbm/ft

3 

Q = flow, m /hṁ

 

= mass flow, kg/hρ = fluid density, kg/m

3

Net Positive Suction HeadIn terms of head Imperial Units SI Units

               

NPSH = net positive suction head at reference point(usually center line of the impeller), ftHa = absolute pressure of the suction vessel, ftHvpa = fluid vapor pressure at pumping temperature, ftHst = static head to suction reference point (usually centerline of the impeller), ftHfs = suction line losses, ft

NPSH = net positive suction head at reference point(usually center line of the impeller), mHa = absolute pressure of the suction vessel, mHvpa = fluid vapor pressure at pumping temperature, mHst = static head to suction reference line (usually centerpoint of the impeller), mHfs = suction line losses, m

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In terms of pressure and head Imperial Units SI Units

 

   

 

   

NPSH = net positive suction head at reference point(usually center line of the impeller), ftPa = absolute pressure of the suction vessel, psiaPvpa = fluid vapor pressure at pumping temperature, psiaHst = static head at reference point (usually center line of

the impeller), ftHfs = suction line losses, ftSG = specific gravity

NPSH = net positive suction head at reference point(usually center line of the impeller), mPa = absolute pressure of the suction vessel, kPaPvpa = fluid vapor pressure at pumping temperature, kPaabsolute

Hst = static head to suction reference line (usually centerpoint of the impeller), mHfs = suction line losses, mρ = fluid density, kg/m

3 

g = gravitational constant, 9.81 m/s2 

Pump HeadImperial Units SI Units

 

   

 

   

H = pump head, ftHf = friction loss, ftPS = suction pressure, psiaPd = discharge pressure, psiaSG = specific gravityVs = suction velocity, ft/sVd = discharge velocity, ft/sZs = suction height from reference, ftZd = discharge head from reference, ftg = gravitational constant, 32.2 ft/s

2 

H = pump head, mHf = friction loss, mPS = suction pressure, barPd = discharge pressure, barSG = specific gravityVs = suction velocity, m/sVd = discharge velocity, m/sZs = suction height from reference, mZd = Discharge head from reference, mg = gravitational constant, 9.81 m/s

2 

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Pump PowerImperial Units SI Units

 

 

P = power, horse powerH = head, ftQ = flow, gpmSG = specific gravity

  = pump efficiency, decimal

P = power, kWH = head, mQ = flow, m

3 /hr

SG = specific gravity

  = pump efficiency, decimal

Pump TorqueImperial Units SI Units

 

 

τ = torque, ft-lbfP = pump power, hpN = pump speed, rpm

τ = torque, N-mP = pump power, kWN = pump speed, rpm

Temperature RiseImperial Units SI Units

 

 

 ΔT = temperature rise, °FH = total head, ftη = pump efficiency, decimal U = fluid specific heat, BTU/(lbm-°F)

 ΔT = temperature rise, °C or °K H = total head, mη = pump efficiency, decimal U = fluid specific heat, kJ/(kg-°K) or kJ/(kg-°C)

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Fluid VelocityImperial Units SI Units

 

 

V = velocity, ft/sQ = flow, gpmd = pipe inside diameter, in

V = velocity, m/sQ = flow, m

3 /h

d = pipe inside diameter, mm

Velocity HeadImperial Units SI Units

 

 

 

 

Hv = velocity head, ft of liquidV = fluid velocity, ft/sg = gravitational constant, 32.2 ft/s

2 

Q = flow, gpmd = pipe inside diameter, in

Hv = velocity head, mV = fluid velocity, m/sg = gravitational constant, 9.81 m/s

2 

Q = flow, m3 /h

d = pipe inside diameter, mm

Specific Speed at BEPImperial Units SI Units

 

 

Ns = specific speedN = pump speed, rpmQ = flow, gpm

H = head, ftValues are taken at best efficiency point (BEP)Pump flow is taken at the largest impeller diameterFor double suction impellers pump flow is divided by two

Ns = specific speedN = pump speed, rpmQ = flow, m

3 /h

H = head, mValues are taken at best efficiency point (BEP)Pump flow is taken at the largest impeller diameterFor double suction impellers pump flow is divided by two

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Suction Specific Speed at BEPImperial Units SI Units

 

 

Ns = specific speedN = pump speed, rpmQ = flow, gpm

NPSH = net positive suction head, ftValues are taken at best efficiency point (BEP)Pump flow is taken at the largest impeller diameterFor double suction impellers pump flow is divided by two

Ns = specific speedN = pump speed, rpmQ = flow, m

3 /h

NPSH = net positive suction head, mValues are taken at best efficiency point (BEP)Pump flow is taken at the largest impeller diameterFor double suction impellers pump flow is divided by two

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Other Pump Formulas 

Affinity LawsChanges in Diameter Changes in Speed

 

  

 

  

 

  

 

  

D = diameter, in or mmQ = flow, gpm or m

3 /h

H = head, ft or mP = power, hp or kW

Q = flow, gpm or m /hH = head, ft or mP = power, hp or kWN = speed, rpm

Bernoulli’s Equation 

 

g = gravitational constantL = energy lossesPS = suction pressurePd = discharge pressureVs = suction velocityVd = discharge velocityW = work by the pumpZs = suction height from referenceZd = discharge head from referenceρ = fluid density

 

γ = fluid specific weight = g*ρ 

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Tables

Conversion FactorsImperial Conversions From To Multiply By

barrel (oil) – bbl gallon – US gal 42barrel (oil) – bbl cubic meter – m3  0.159 0British thermal unit – Btu Joule – J 1 055

British thermal unit per hour – Btu/h Watt – W 0.293 1cubic feet – ft3  cubic meter – m3  0.028 32cubic feet per minute – ft /min or cfm cubic meters per hour – m h 1.699feet – ft meter – m 0.304 8foot pounds force – ft-lbf Joule – J 1.356gallon (US) – US gal cubic meter – m3  0.003 785gallon (US) – US gal liter – l 3.785gallon (US) – US gal gallon (Imperial) – Imp gal 0.832 7gallon (US) per minute – gpm cubic meter per hour – m3 /h 0.227 1gallon (US) per minute – gpm barrel (oil) per day – b/d 34.28horsepower – hp kilowatt – kW 0.745 7horsepower hour – hp-h kilojoule – kJ 2 684horsepower hour – hp-h British thermal unit per hour – Btu 2 545inch – in millimeter – mm 25.4inch of mercury at 0°F – inHg kilopascal – kPa 3.386inch of water at 68°F – inH2O kilopascal – kPa 0.248 7mile kilometer – km 1.609pound force – lbf Newton – N 4.448pound mass – lbm kilogram – kg 0.453 6pound force per square inch – psi kilopascal – kPa 6.895pound force per square inch – psi bar 0.068 95ton (long) ton (short) 1.12ton (short) kilogram – kg 907.2

yard – yd meter – m 0.914 4Note

1.  Conversions less than four significant digits are exact.

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SI Conversions From To Multiply Bybar kilopascal – kPa 100bar pounds force per square inch – psi 14.50cubic meter – m3  gallons  – US gal 264.2cubic meter – m3  cubic feet – ft3  35.31cubic meter per hour – m /hr gallons per minute – gpm 4.403cubic meter per hour – m3 /hr barrel per day – b/d 337.3kilograms –  kg pounds mass – lbm 2.205

kilogram per square centimeter – kg/cm2

Bar 0.980 7kilogram per square centimeter – kg/cm2 pounds force per square inch – psi 14.22kilometer – km mile 0.621 4kilopascal – kPa pounds force per square inch – psi 0.145 0kilowatt – kW horsepower – hp 1.341kilowatt hour – kW-h British thermal units per hour – Btu 3.413kilowatt hours – kW-h Kilojoule – kJ 3 600meter – m feet – ft 3.281Newton – N pound force – lbf 0.224 8

SI PrefixesPower of Ten Name Symbol1012  tera T10 giga G106  mega M103  kilo k10 deca da10-1  deci d10-2  centi c10-3  milli m10-6  micro μ 10-   nano n

10-12

  pico p

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Symbols and NomenclatureSymbol Definition Imperial Units SI UnitsA Area ft2  m2 D, d Diameter inches mmg Gravitational constant 32.2 ft/s2  9.81 m/s2 H Head ft mh Time hour hourṁ  Mass flow rate lbm/h kg/hN Speed rpm rpmNs Specific speed Dimensionless DimensionlessNss Suction specific speed Dimensionless DimensionlessP Power horsepower kWP Pressure psi kPa or barQ Flow gpm m /hs Time seconds secondsU Specific heat btu/lbm-°F kJ/kg-°CV Velocity ft/s m/sW Work ft mZ Elevation ft mNPSH Net positive suction head ft mSG Specific gravity Dimensionless Dimensionless

η  Efficiency Dimensionless Dimensionlessρ  Density lbm/ft3  Kg/m3 τ  Torque ft-lbf N-m

 ΔT  Temperature change °F °Cγ Specific weight lbf/ft3  kN/m3