Pump Affinity Or Similarity Law Scaling
Calculate pump scaling from pump speed and impeller diameter using the affinity or similarity laws for pumps and combined pump and piping systems. If the operating parameters of a pump are known (pump 1), the operating parameters for a geometrically similar pump (pump 2) which is operating with the same pump coefficients can be calculated from the pump speed and impeller diameter ratios using the affinity or similarity laws . `(P2)/(P1) = (ρ2)/(ρ1) ((n2)/(n1))^2 ((d2)/(d1))^2 `
`(Q2)/(Q1) = (n2)/(n1) ((d2)/(d1))^3 `
`(1-E2)/(1-E1) = ((d1)/(d2))^(1/4) ` where : P1 and P2 = the delta pressure (ΔP) for pump 1 and 2
Q1 and Q2 = the flowrate for pump 1 and 2
n1 and n2 = the rotation speed for pump 1 and 2
d1 and d2 = the impeller diameter for pump 1 and 2
ρ1 and ρ2 = the fluid density for pump 1 and 2
E1 and E2 = the pump efficiency at BEP for pump 1 and 2
BEP = Best Efficiency Point For geometric similarity the pump inside diameter should be proportional to the impeller diameter. In practice the pump inside diameter is usually limited to standard pipe sizes (eg 10 inch, 12 inch etc). The impeller diameter is also normally limited to fixed sizes. It is therefore often more practical to select an appropriate pump inside diameter and impeller diameter, and vary the pump speed. Pump efficiency scaling is based on an empirical formula. Pump efficiency scaling should be combined with flowrate scaling. Pump efficiency varies with flowrate. Pump performance is normally measured using water (density is assumed to be 1000 kg/m^3). For cases where the impeller size is varied (impeller trim) and the pump ID is constant, the flowrate can be calculated by: `(Q2)/(Q1) = (n2)/(n1) (d2)/(d1) ` For cases where both the impeller diameter and the pump ID vary, but not in proportion, the flowrate can be calculated by: `(Q2)/(Q1) = (n2)/(n1) (d2)/(d1) ( (ID2)/(ID1))^2 ` where : ID1 and ID2 = the pump ID for pump 1 and 2 A known pump can be scaled to operate at the best efficiency point (BEP) with a required design flow rate and delta pressure using the affinity laws. The pump curve is calculated using a three term quadratic equation `ΔP = ΔPo - A Q - B Q^2` . PLEASE NOTE : The pump calculators are currently being updated. Apologies for any inconvenience. Change Module :
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CALCULATOR : Pump Piping Diameter Schedule [FREE] ±
Calculate line pipe wall inside diameter and inside cross section area from pipe diameter and wall thickness. Select the pipe schedule type, diameter and wall thickness, or use the user defined option. Use the Result Table option to display a table of the inside diameter and cross section area versus either outside diameter or wall thickness. Tool Input- schdtype : Schedule Type
- diamtype : Diameter Type
- ODu : User Defined Outside Diameter
- IDu : User Defined Inside Diameter
- wtntype : Wall Thickness Type
- tnu : User Defined Wall Thickness
Tool Output- AX : Pipe Inside Cross Section Area
- ID : Nominal Inside Diameter
- OD : Nominal Outside Diameter
- OD/tn : Diameter Over Wall Thickness Ratio
- tn : Nominal Wall Thickness
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CALCULATOR : Pump Static Dynamic And Stagnation Pressure And Head Conversion [FREE] ±
Convert pump pressure and pump head (static and stagnation pressure / head). Pump head can be calculated from pump pressure by `H = (P) / (ρ g) ` where : H = head
P = pressure
ρ = fluid density
g = gravity constant The stagnation pressure is calculated by `Pg = Ps + Pd `
`Pd = 1/2 ρ V^2 `
`V = (4 Q) / (pi D^2) ` where : Ps = static pressure
Pg = stagnation pressure
Pd = dynamic pressure
V = fluid velocity
Q = volume flowrate
D = inside diameter Tool Input- schdtype : Pipe Schedule Type
- diamtype : Pipe Diameter Type
- ODu : User Defined Outside Diameter
- IDu : User Defined Inside Diameter
- wtntype : Wall Thickness Type
- tnu : User Defined Wall Thickness
- voltype : Fluid Flowrate Type
- Qu : User Defined Volume Flow Rate
- Mu : User Defined Mass Flow Rate
- Vu : User Defined Fluid Velocity
- presstype : Pressure Type
- Psu : User Defined Static Pressure
- Pgu : User Defined Stagnation Pressure
- Hsu : User Defined Static Head
- Hgu : User Defined Stagnation Head
- ρ : Fluid Density
Tool Output- Hd : Dynamic Head
- Hg : Stagnation Head
- Hs : Static Head
- ID : Inside Diameter
- M : Liquid Mass Flowrate
- Pd : Dynamic Pressure
- Pg : Stagnation Pressure
- Ps : Static Pressure
- Q : Liquid Volume Flowrate
- V : Fluid Velocity
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