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Pump Design Modules

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CALCULATOR MODULE : Pump Delta Pressure Versus Flowrate Curve   ±

Calculate pump curve (pressure versus flowrate) for viscous and non viscous flow. Viscous flow is recommended if the kinematic viscosity is greater than 20 cSt.

The pump curve is calculated using a three term quadratic curve (ΔP = ΔPo - A Q - B Q^2) calculated from the shut-in delta pressure (zero flow), the maximum flowrate, and the best efficiency point (BEP).

Note : The delta stagnation pressure is required for the calculation. Some pump curves show delta static pressure (the pressure equals zero at maximum flow) instead of delta stagnation pressure (the pressure equals the dynamic pressure at maximum flow). Use the pump pressure and head conversion calculator to convert delta static pressure to delta stagnation pressure.

The pump flowrate, delta pressure, inside diameter and efficiency can be scaled for a geometrically similar pump using the affinity or similarity laws. For geometric similarity the pump inside diameter should be proportional to the impeller diameter. In practice the pump inside diameter is usually limited to pipe sizes (eg 10 inch, 12 inch etc). The impeller diameter is also normally limited to fixed sizes. It is often more practical to select an available 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).

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

Change Module :

CALCULATOR MODULE : Pump Specific Speed   ±

Calculate pump specific speed from pump rotational speed, flowrate and delta pressure.

The pump specific speed is calculated at the best efficiency point (BEP), the point on the pump curve with the greatest efficiency.

`Ns = n Q^(1/2) (ρ/(ΔP))^(3/4) = n (Q^(1/2)) / (g.ΔH)^(3/4) `

where :

Ns = pump specific speed
n = pump rotational speed
Q = flow rate at BEP
ρ = fluid density
ΔP = delta pressure at BEP
ΔH = delta head at BEP
g = gravity constant
BEP = best efficiency point

The pump specific speed can be used to determine the type of pump which should be used (multi stage, centrifugal, mixed flow or axial). The pump size and speed can then be determined from the pump coefficients using the affinity or similarity laws. Usually, a known pump is scaled to operate at the BEP with the required design flow rate and delta pressure.

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

Change Module :

CALCULATOR MODULE : 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 :

CALCULATOR MODULE : Pump Cavitation And NPSH   ±

Calculate pump cavitation number (Ca), nett positive suction pressure (NPSP), and suction specific speed (Nss).

`Nss = n* Q*^1/2 (ρ/NPSP*)^3/4 `
`NPSP* = Ps + 1/2 ρ V^2 - Pv = Ps + Pd - Pv = Pg - Pv `
`Ca = (Ps - Pv) / Pd `

where :

Nss = pump suction specific speed at BEP `
`NPSP* = nett positive suction pressure at BEP `
`Ca = cavitation number `
`n* = pump rotational speed at BEP `
`Q* = flowrate at BEP `
`Ps = static pressure at inlet `
`Pg = stagnation pressure at inlet `
`Pd = dynamic pressure at inlet `
`Pv = vapour pressure `
`V = fluid velocity at inlet `
`ρ = fluid density

The pump suction specific speed and nett positive suction pressure are calculated at the best efficiency point (BEP), the point on the pump curve with the greatest efficiency. The pump suction specific speed, nett positive suction pressure and cavitation number can be used to determine the onset of cavitation. The minimum recommended values are dependent on the pump geometry and operating conditions, and should be obtained from the manufacturer.

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

Change Module :

CALCULATOR MODULE : 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.

Change Module :

CALCULATOR MODULE : Pump Hydraulic And Input Power   ±

Calculate pump hydraulic power and input power or motive power from flowrate and delta pressure.

`Wh = Q ΔP `
`Wi = (Wh) / E `

where :

Wh = hydraulic power
Wi = input power or motive power
Q = volume flowrate
ΔP = delta stagnation pressure
E = efficiency factor

The pump efficiency accounts for energy losses in the pump such as friction etc. The input power is the motive power required to drive the pump (the size of motor). To calculate the energy required (eg electrical energy) the efficiency factor should equal the pump efficiency times the motor efficiency.

`E = Ep.Ee `

where :

Ep = pump efficiency factor
Ee = electric motor efficiency factor

Pump efficiency varies with flowrate. The flowrate with maximum efficiency is referred to as the best efficiency point (BEP).

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

Change Module :

CALCULATOR MODULE : Pump Flowrate Pressure And Power Coefficient   ±

Calculate pump flow coefficient (Cq), pressure coefficient (Cp), power coefficient (Cw) and pump specific speed from flowrate, delta pressure, pump speed and impeller diameter. The pump coefficients are calculated at the best efficiency point (BEP).

`Cq = Q / (n d^3) `
`Cp = (ΔP) / (ρ n^2 d^2) = (gΔH) / (n^2 d^2) `
`Cw = Cq. Cp = (Q ΔP) / (ρ n^3 d^5) `
`Ns = (Cq^(1/2)) / (Cp^(3/4)) = nQ^(1/2) (ΔP^(3/4)) / ρ `

where :

Cq = flowrate coefficient at BEP
Cp = pressure coefficient at BEP
Cw = power coefficient at BEP
Ns = pump specific speed at BEP
n = pump rotational speed at BEP
d = impeller diameter at BEP
Q = flow rate at BEP
ΔP = delta pressure at BEP
ΔH = delta head at BEP
ρ = fluid density
g = gravity constant

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

Change Module :

CALCULATOR MODULE : Pump Liquid Vapour Pressure Viscosity And Density   ±
CALCULATOR MODULE : Pump Viscosity Correction   ±
CALCULATOR MODULE : Pump Variable Frequency Drive (VFD) Design Speed   ±

Calculate pump variable frequency drive (VFD) speed to match pump design pressure and design flowrate for viscous and non viscous fluids.

The design pump speed is calculated using the affinity or similarity laws.

`(ΔP2)/(ΔP1) = (ρ2)/(ρ1) (n2)/(n1)^2 `
`(Q2)/(Q1) = (n2)/(n1) `

where :

ΔP1 and ΔP2 = the delta pressure 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
ρ1 and ρ2 = the fluid density for pump 1 and 2

The pump curve is calculated using a three term quadratic curve:

`ΔP = ΔPo (1 - A Q - B Q^2 ) `

where :

ΔPo = the shut in delta pressure
A and B are constants

The design pump speed can be calculated by solving the quadratic equation for the design delta pressure and flowrate. For fluids with a kinematic viscosity ν > 20 cSt, the viscous calculation is recommended.

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

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CALCULATOR MODULE : Pump And Piping System Curve   ±

Calculate pump and piping combined system curve (pressure versus flowrate) for viscous and non viscous flow.

For a combined pump and piping system, the flowrate reaches an equilibrium so that the pump delta pressure equals the piping delta pressure. If the pump shutin delta pressure is less than or equal to the piping shutin delta pressure, the flowrate is zero.

The piping delta pressure is calculated from the change in elevation, and piping friction losses calculated from the Moody diagram. The inlet conditions can be calculated for either the liquid depth at the inlet in a tank or reservoir, or the stagnation pressure at the inlet. The outlet conditins can be calculated for either an exit to atmosphere, the liquid depth at the outlet in a tank or reservoir, or the stagnation pressure at the outlet.

Viscous flow is recommended if the kinematic viscosity is greater than 20 cSt. Pump performance is normally measured using water (density is assumed to be 1000 kg/m^3).

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

Change Module :

CALCULATOR MODULE : Pump Delta Temperature   ±

Calculate pump power loss and temperature rise due to pump inefficiency.

The delta temperature across the pump can be calculated by:

`Wh = ΔP Q `
`Wi = (Wh) / E `
`Wp = Wi - Wh `
`ΔTp = (Wp) / (ρ.Q.cp) = (1/E-1 ) (ΔP Q) / (ρ.Q.cp) `

where :

Q = flowrate
ΔP = delta pressure
Wh = hydraulic power
Wi = pump input power
Wp = pump power lost to inefficiency
ΔTp = delta temperature across pump
ρ = fluid density
cp = fluid specific heat
E = pump efficiency factor

The hydraulic power is the energy added to the fluid by the pump. The input power is the power required to drive the pump, including pump inefficiencies. The power loss is equal to the difference between the input power and the hydraulic power. The pump efficiency 0 ≤ E ≤ 1.

For closed system piping where the entire pump power is lost as system friction losses, the system fluid temperature rise can be calculated by

`ΔTs = (Wi) / (ρ.Q.cp). `

where :

ΔTs = system delta temperature

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

Change Module :

CALCULATOR MODULE : Pump Efficiency Curve   ±

Calculate pump efficiency curves for viscous and non viscous flow. Viscous flow is recommended if the kinematic viscosity is greater than 20 cSt.

The efficiency curve is calculated using a three term cubic equation calculated from the best efficiency point, and the maximum flowrate:

`E = A Q + B Q^2 + C Q^3 `

where :

Q = the flowrate
A, B and C are constants

The efficiency is assumed to be zero at shut-in. The maximum efficiency occurs at the best efficiency point.

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

Change Module :

CALCULATOR MODULE : IAPWS R7-97 Steam Boiler Feed Pump Power   ±

Calculate IAPWS R7-97 boiler feed pump power from pressure and mass flow rate.

Changes of elevation and velocity are ignored.

Note : There is an anomaly in the steam calculation for region 3 between the saturated vapour line, the region 2/3 boundary, and the critical pressure. Refer to the region 3 anomaly help page for more details (click the utility button on the data bar). IAPWS R7-97 is intended for industrial use, and is a simplified version of IAPWS R6-95 for scientific use. IAPWS R7-97 was developed as an improvement of the IFC-67 model.

Reference : IAPWS R7-97 Industrial Formulation for thermodynamic Properties of Water and Steam

Change Module :

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