Pump Formulas Imperial and SI Units

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1 Pump Formulas Imperial and Pressure to Head H = head, ft P = pressure, psi H = head, m P = pressure, bar Mass Flow to Volumetric Flow ṁ = mass flow, lbm/h ρ = fluid density, lbm/ft 3 ṁ = mass flow, kg/h ρ = fluid density, kg/m 3 Net Positive Suction Head In terms of head NPSH = net positive suction head at reference point (usually center line of the impeller), ft H a = absolute pressure of the suction vessel, ft H vpa = fluid vapor pressure at pumping temperature, ft H st = static head to suction reference point (usually center line of the impeller), ft H fs = suction line losses, ft NPSH = net positive suction head at reference point (usually center line of the impeller), m H a = absolute pressure of the suction vessel, m H vpa = fluid vapor pressure at pumping temperature, m H st = static head to suction reference line (usually center point of the impeller), m H fs = suction line losses, m 1

2 In terms of pressure and head NPSH = net positive suction head at reference point (usually center line of the impeller), ft P a = absolute pressure of the suction vessel, psia P vpa = fluid vapor pressure at pumping temperature, psia H st = static head at reference point (usually center line of the impeller), ft H fs = suction line losses, ft NPSH = net positive suction head at reference point (usually center line of the impeller), m P a = absolute pressure of the suction vessel, kpa P vpa = fluid vapor pressure at pumping temperature, kpa absolute H st = static head to suction reference line (usually center point of the impeller), m H fs = suction line losses, m ρ = fluid density, kg/m 3 g = gravitational constant, 9.81 m/s 2 Pump Head H = pump head, ft H f = friction loss, ft P S = suction pressure, psia P d = discharge pressure, psia V s = suction velocity, ft/s V d = discharge velocity, ft/s Z s = suction height from reference, ft Z d = discharge head from reference, ft g = gravitational constant, 32.2 ft/s 2 H = pump head, m H f = friction loss, m P S = suction pressure, bar P d = discharge pressure, bar V s = suction velocity, m/s V d = discharge velocity, m/s Z s = suction height from reference, m Z d = Discharge head from reference, m g = gravitational constant, 9.81 m/s 2 2

3 Pump Power P = power, horse power H = head, ft = pump efficiency, decimal P = power, kw H = head, m r = pump efficiency, decimal Pump Torque τ = torque, ft-lbf P = pump power, hp τ = torque, N-m P = pump power, kw Temperature Rise 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) 3

4 Fluid Velocity V = velocity, ft/s d = pipe inside diameter, in V = velocity, m/s d = pipe inside diameter, mm Velocity Head H v = velocity head, ft of liquid V = fluid velocity, ft/s g = gravitational constant, 32.2 ft/s 2 d = pipe inside diameter, in H v = velocity head, m V = fluid velocity, m/s g = gravitational constant, 9.81 m/s 2 d = pipe inside diameter, mm Specific Speed at BEP Ns = specific speed 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 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 4

5 Suction Specific Speed at BEP Ns = specific speed 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 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 5

6 Other Pump Formulas Affinity Laws Changes in Diameter Changes in Speed D = diameter, in or mm or m 3 /h H = head, ft or m P = power, hp or kw or m 3 /h H = head, ft or m P = power, hp or kw N = speed, rpm Bernoulli s Equation g = gravitational constant L = energy losses P S = suction pressure P d = discharge pressure V s = suction velocity V d = discharge velocity W = work by the pump Z s = suction height from reference Z d = discharge head from reference ρ = fluid density γ = fluid specific weight = g*ρ 6

7 Tables Conversion Factors Imperial Conversions From To Multiply By 1 barrel (oil) bbl gallon US gal 42 barrel (oil) bbl cubic meter m British thermal unit Btu Joule J British thermal unit per hour Btu/h Watt W cubic feet ft 3 cubic meter m cubic feet per minute ft 3 /min or cfm cubic meters per hour m 3/ h feet ft meter m foot pounds force ft-lbf Joule J gallon (US) US gal cubic meter m gallon (US) US gal liter l gallon (US) US gal gallon (Imperial) Imp gal gallon (US) per minute gpm cubic meter per hour m 3 /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 25.4 inch of mercury at 0 F inhg kilopascal kpa inch of water at 68 F inh 2 O 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) 1.12 ton (short) kilogram kg yard yd meter m Note 1. Conversions less than four significant digits are exact. 7

8 SI Conversions From To Multiply By bar kilopascal kpa 100 bar pounds force per square inch psi cubic meter m 3 gallons US gal cubic meter m 3 cubic feet ft cubic meter per hour m 3 /hr gallons per minute gpm cubic meter per hour m 3 /hr barrel per day b/d kilograms kg pounds mass lbm kilogram per square centimeter kg/cm 2 Bar kilogram per square centimeter kg/cm 2 pounds force per square inch psi kilometer km mile kilopascal kpa pounds force per square inch psi kilowatt kw horsepower hp kilowatt hour kw-h British thermal units per hour Btu kilowatt hours kw-h Kilojoule kj meter m feet ft Newton N pound force lbf SI Prefixes Power of Ten Name Symbol tera T 10 9 giga G 10 6 mega M 10 3 kilo k 10 deca da 10-1 deci d 10-2 centi c 10-3 milli m 10-6 micro μ 10-9 nano n pico p 8

9 Symbols and Nomenclature Symbol Definition A Area ft 2 m 2 D, d Diameter inches mm g Gravitational constant 32.2 ft/s m/s 2 H Head ft m h Time hour hour ṁ Mass flow rate lbm/h kg/h N Speed rpm rpm Ns Specific speed Dimensionless Dimensionless Nss Suction specific speed Dimensionless Dimensionless P Power horsepower kw P Pressure psi kpa or bar Q Flow gpm m 3 /h s Time seconds seconds U Specific heat btu/lbm- F kj/kg- C V Velocity ft/s m/s W Work ft m Z Elevation ft m NPSH Net positive suction head ft m SG Specific gravity Dimensionless Dimensionless η Efficiency Dimensionless Dimensionless ρ Density lbm/ft 3 Kg/m 3 τ Torque ft-lbf N-m ΔT Temperature change F C γ Specific weight lbf/ft 3 kn/m 3 9

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