Pump Formulas — Imperial and SI Units Pressure to Head Imperial Units
SI Units
H = head, ft P = pressure, psi SG = specific gravity
H = head, m P = pressure, bar SG = specific gravity
Mass Flow to Volumetric Flow Imperial Units
SI Units
Q = flow, gpm ṁ = mass flow, lbm/h SG = specific gravity 3 ρ = fluid density, lbm/ft
Q = flow, m /h ṁ = mass flow, kg/h 3 ρ = fluid density, kg/m
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Net Positive Suction Head In terms of head Imperial Units
SI Units
NPSH = net positive suction head at reference point (usually center line of the impeller), ft Ha = absolute pressure of the suction vessel, ft Hvpa = fluid vapor pressure at pumping temperature, ft Hst = static head to suction reference point (usually center line of the impeller), ft Hfs = suction line losses, ft
NPSH = net positive suction head at reference point (usually center line of the impeller), m Ha = absolute pressure of the suction vessel, m Hvpa = fluid vapor pressure at pumping temperature, m Hst = static head to suction reference line (usually center point of the impeller), m Hfs = 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), ft Pa = absolute pressure of the suction vessel, psia Pvpa = fluid vapor pressure at pumping temperature, psia Hst = static head at reference point (usually center line of the impeller), ft Hfs = suction line losses, ft SG = specific gravity
NPSH = net positive suction head at reference point (usually center line of the impeller), m Pa = absolute pressure of the suction vessel, kPa Pvpa = fluid vapor pressure at pumping temperature, kPa absolute Hst = static head to suction reference line (usually center point of the impeller), m Hfs = suction line losses, m 3 ρ = fluid density, kg/m 2 g = gravitational constant, 9.81 m/s
Pump Head Imperial Units
SI Units
H = pump head, ft Hf = friction loss, ft PS = suction pressure, psia Pd = discharge pressure, psia SG = specific gravity Vs = suction velocity, ft/s Vd = discharge velocity, ft/s Zs = suction height from reference, ft Zd = discharge head from reference, ft 2 g = gravitational constant, 32.2 ft/s
H = pump head, m Hf = friction loss, m PS = suction pressure, bar Pd = discharge pressure, bar SG = specific gravity Vs = suction velocity, m/s Vd = discharge velocity, m/s Zs = suction height from reference, m Zd = Discharge head from reference, m 2 g = gravitational constant, 9.81 m/s
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Pump Power Imperial Units
SI Units
P = power, horse power H = head, ft Q = flow, gpm SG = specific gravity = pump efficiency, decimal
P = power, kW H = head, m 3 Q = flow, m /hr SG = specific gravity = pump efficiency, decimal
Pump Torque Imperial Units
SI Units
τ = torque, ft-lbf P = pump power, hp N = pump speed, rpm
τ = torque, N-m P = pump power, kW N = pump speed, rpm
Temperature Rise Imperial Units
SI Units
ΔT = temperature rise, °F H = total head, ft η = pump efficiency, decimal U = fluid specific heat, BTU/(lbm-°F)
ΔT = temperature rise, °C or °K H = total head, m η = pump efficiency, decimal U = fluid specific heat, kJ/(kg-°K) or kJ/(kg-°C)
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Fluid Velocity Imperial Units
SI Units
V = velocity, ft/s Q = flow, gpm d = pipe inside diameter, in
V = velocity, m/s 3 Q = flow, m /h d = pipe inside diameter, mm
Velocity Head Imperial Units
SI Units
Hv = velocity head, ft of liquid V = fluid velocity, ft/s 2 g = gravitational constant, 32.2 ft/s Q = flow, gpm d = pipe inside diameter, in
Hv = velocity head, m V = fluid velocity, m/s 2 g = gravitational constant, 9.81 m/s 3 Q = flow, m /h d = pipe inside diameter, mm
Specific Speed at BEP Imperial Units
SI Units
Ns = specific speed N = pump speed, rpm Q = flow, gpm H = head, ft Values are taken at best efficiency point (BEP) Pump flow is taken at the largest impeller diameter For double suction impellers pump flow is divided by two
Ns = specific speed N = pump speed, rpm 3 Q = flow, m /h H = head, m Values are taken at best efficiency point (BEP) Pump flow is taken at the largest impeller diameter For double suction impellers pump flow is divided by two
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Suction Specific Speed at BEP Imperial Units
SI Units
Ns = specific speed N = pump speed, rpm Q = flow, gpm NPSH = net positive suction head, ft Values are taken at best efficiency point (BEP) Pump flow is taken at the largest impeller diameter For double suction impellers pump flow is divided by two
Ns = specific speed N = pump speed, rpm 3 Q = flow, m /h NPSH = net positive suction head, m Values are taken at best efficiency point (BEP) Pump flow is taken at the largest impeller diameter For double suction impellers pump flow is divided by two
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Other Pump Formulas Affinity Laws Changes in Diameter
Changes in Speed
D = diameter, in or mm 3 Q = flow, gpm or m /h H = head, ft or m P = power, hp or kW
Q = flow, gpm or m /h H = head, ft or m P = power, hp or kW N = speed, rpm
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Bernoulli’s Equation g = gravitational constant L = energy losses PS = suction pressure Pd = discharge pressure Vs = suction velocity Vd = discharge velocity W = work by the pump Zs = suction height from reference Zd = discharge head from reference ρ = fluid density γ = fluid specific weight = g*ρ
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Tables Conversion Factors Imperial Conversions From To barrel (oil) – bbl gallon – US gal barrel (oil) – bbl cubic meter – m3 British thermal unit – Btu Joule – J British thermal unit per hour – Btu/h Watt – W cubic feet – ft3 cubic meter – m3 3 cubic feet per minute – ft /min or cfm cubic meters per hour – m3/h feet – ft meter – m foot pounds force – ft-lbf Joule – J gallon (US) – US gal cubic meter – m3 gallon (US) – US gal liter – l gallon (US) – US gal gallon (Imperial) – Imp gal gallon (US) per minute – gpm cubic meter per hour – m3/h gallon (US) per minute – gpm barrel (oil) per day – b/d horsepower – hp kilowatt – kW horsepower hour – hp-h kilojoule – kJ horsepower hour – hp-h British thermal unit per hour – Btu inch – in millimeter – mm inch of mercury at 0°F – inHg kilopascal – kPa inch of water at 68°F – inH2O kilopascal – kPa mile kilometer – km pound force – lbf Newton – N pound mass – lbm kilogram – kg pound force per square inch – psi kilopascal – kPa pound force per square inch – psi bar ton (long) ton (short) ton (short) kilogram – kg yard – yd meter – m Note 1. Conversions less than four significant digits are exact.
Multiply By1 42 0.159 0 1 055 0.293 1 0.028 32 1.699 0.304 8 1.356 0.003 785 3.785 0.832 7 0.227 1 34.28 0.745 7 2 684 2 545 25.4 3.386 0.248 7 1.609 4.448 0.453 6 6.895 0.068 95 1.12 907.2 0.914 4
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SI Conversions From bar bar cubic meter – m3 cubic meter – m3 cubic meter per hour – m3/hr cubic meter per hour – m3/hr kilograms – kg kilogram per square centimeter – kg/cm2 kilogram per square centimeter – kg/cm2 kilometer – km kilopascal – kPa kilowatt – kW kilowatt hour – kW-h kilowatt hours – kW-h meter – m Newton – N
To kilopascal – kPa pounds force per square inch – psi gallons – US gal cubic feet – ft3 gallons per minute – gpm barrel per day – b/d pounds mass – lbm Bar pounds force per square inch – psi mile pounds force per square inch – psi horsepower – hp British thermal units per hour – Btu Kilojoule – kJ feet – ft pound force – lbf
Multiply By 100 14.50 264.2 35.31 4.403 337.3 2.205 0.980 7 14.22 0.621 4 0.145 0 1.341 3.413 3 600 3.281 0.224 8
SI Prefixes Power of Ten 1012 109 106 103 10 10-1 10-2 10-3 10-6 10-9 10-12
Name tera giga mega kilo deca deci centi milli micro nano pico
Symbol T G M k da d c m μ n p
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Symbols and Nomenclature Symbol A D, d g H h ṁ N Ns Nss P P Q s U V W Z NPSH SG η ρ τ ΔT γ
Definition Area Diameter Gravitational constant Head Time Mass flow rate Speed Specific speed Suction specific speed Power Pressure Flow Time Specific heat Velocity Work Elevation Net positive suction head Specific gravity Efficiency Density Torque Temperature change Specific weight
Imperial Units ft2 inches 32.2 ft/s2 ft hour lbm/h rpm Dimensionless Dimensionless horsepower psi gpm seconds btu/lbm-°F ft/s ft ft ft Dimensionless Dimensionless lbm/ft3 ft-lbf °F lbf/ft3
SI Units m2 mm 9.81 m/s2 m hour kg/h rpm Dimensionless Dimensionless kW kPa or bar m3/h seconds kJ/kg-°C m/s m m m Dimensionless Dimensionless Kg/m3 N-m °C kN/m3
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