Pump BEP Scaling Calculators

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Demo

Pump Best Efficiency Point (BEP) Scaling

Calculate pump speed, impeller diameter and inside diameter to operate a known pump at the design delta pressure and flowrate, and at the best efficiency point (BEP).

The reference pump specific speed can be calculated by:

`Ns = nr.Qr^(1/2) ((ρr)/(ΔPr))^(3/4) `

where :

Ns = reference pump specific speed at BEP
nr = reference pump rotational speed at BEP
Qr = reference flow rate at BEP
ρr = reference fluid density
ΔPr = reference delta pressure at BEP

The flowrate and delta pressure can be calculated from the pump specific speed, and design flowrate and delta pressure using the affinity or similarity laws. For geometric similarity the pump inside diameter should be proportional to the impeller diameter.

`np = (Ns) / (Qd^(1/2)) ((ΔPd) / (ρd))^(3/4) `
`dp = dr √((ΔPd) / (ΔPr) (ρr) / (ρd)) (nr) / (np) `
`Dp = ((dp) / (dr)) Dr `

where :

np = scaled pump rotational speed
dp = scaled impeller diameter
dr = reference impeller diameter
ρd = design fluid density
Qd = design flow rate
ΔPd = design delta pressure
ΔPr = reference delta pressure at BEP
Dp = scaled pump inside diameter
Dr = reference pump inside diameter

For this case the scaled pump matches the design delta pressure and flowrate at BEP. In practice the pump inside diameter is usually limited to pipe sizes (eg 10 inch, 12 inch etc). Similarly, the impeller diameter is also normally limited to fixed sizes. It is therefore often more practical to select an available pump inside diameter and impeller diameter, and vary the pump speed. This means that it is possible to match either the design delta pressure or the design flowrate, but not both. For example to calculate the pump speed to match the design flowrate at BEP:

`np = nr ((Qd) / (Qr)) ((dr) / (dp)) ((Dr) / (Dp))^2 `

To calculate the pump speed to match the design delta pressure at BEP:

`np = nr √( (ΔPd) / (ΔPr) (ρr) / (ρd) ((dr) / (dp))^2 ) `

Usually a pump speed is selected so that the scaled delta pressure and flowrate are greater than or equal to the design delta pressure and flowrate. Check that ΔPp-ΔPd and Qp-Qd are both greater than or equal to zero.

The design pump specific speed can be calculated from the design pump speed, delta pressure and flowrate, and can be used to determine the type of pump which should be used (multi stage, centrifugal, mixed flow or axial).

PLEASE NOTE : The pump calculators are currently being updated. Apologies for any inconvenience.

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

Pump Best Efficiency Point (BEP) Scaling

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Tool Input

Tool Output