What is the calculation of pump efficiency

Pump technology



Selection of positive displacement pumps

The details are only reference values ​​for the pump selection.


Pump designationWay of workingPulsationpMax (bar)Efficiency ηMax
In-line piston (1-cyl.)oscillatingvery largeup to 50000,92
Axial pistonoscillatingmediumup to 4000,95
Radial pistonoscillatingmediumup to 3500,90
Vane cellsrotatinguniformto 1200,80
gearrotatingweakup to 2500,92
Screw spindle HDrotatinguniformup to 1800,85
Screw spindle NDrotatinguniformuntil 250,70

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Volume flow of displacement pumps

Reciprocating piston pump - single-acting



V  = Volume flow (m3/ s)
z  = Number of cylinders (-)
d  = Piston diameter (m)
H  = Piston stroke (m)
n  = Speed ​​(1 / s)
V  = Volume flow (m3/ s)
z  = Number of cylinders (-)
d  = Piston diameter (m)
H  = Piston stroke (m)
n  = Speed ​​(1 / s)
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Volume flow of an external gear pump - two-wheel, same number of teeth



V  = Volume flow (m3/ s)
d  = Pitch circle diameter (m)
m  = Module
b  = Gear width (m)
n  = Speed ​​(1 / s)
V  = Volume flow (m3/ s)
d  = Pitch circle diameter (m)
m  = Module
b  = Gear wheel width (m)
n  = Speed ​​(1 / s)
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Volume flow of a screw spindle pump - two-spindle



V  = Volume flow (m3/ s)
d  = Pitch diameter (m)
b  = Thread depth (m)
P.  = Thread pitch (m)
n  = Speed ​​(1 / s)
V  = Volume flow (m3/ s)
d  = Pitch diameter (m)
b  = Thread depth (m)
P.  = Thread pitch (m)
n  = Speed ​​(1 / s)
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Volume flow of a vane pump



V  = Volume flow (m3/ s)
ΔV  = Change in volume of a cell (m3)
z  = Number of cells (-)
n  = Speed ​​(1 / s)
V  = Volume flow (m3/ s)
ΔV  = Change in volume of a cell (m3)
z  = Number of cells (-)
n  = Speed ​​(1 / s)

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Delivery head of the pump

The delivery head H is the usable mechanical work transferred from the pump to the delivery liquid, based on the weight force in m. It is independent of the density of the delivery liquid, i.e. a centrifugal pump delivers different delivery media with the same delivery flow Q to the same delivery head H, whereby here the power requirement changes linearly with the density.



H P. = Pump delivery head (m)
z 1 = Height of pump inlet (m)
z 2 = Height of pump outlet (m)
p 1 = Pump inlet pressure (Pa)
p 2 = Pump outlet pressure (Pa)
v 1 = Speed ​​of pump inlet (m / s)
v 2 = Speed ​​of pump outlet (m / s)
ρ = density of the conveyed medium (kg / m³) 
g = acceleration due to gravity 9.81 (m / s²) 
H P. = Pump delivery head (m)
z 1 = Height of pump inlet (m)
z 2 = Height of pump outlet (m)
p 1 = Pump inlet pressure (Pa)
p 2 = Pump outlet pressure (Pa)
v 1 = Speed ​​of pump inlet (m / s)
v 2 = Speed ​​of pump outlet (m / s)
ρ = density of the conveyed medium (kg / m³) 
g = acceleration due to gravity 9.81 (m / s²) 

The density therefore only determines the pressure p generated in the pump.


p = pump pressure (Pa)  
ρ = density of the conveyed medium (kg / m³) 
g = acceleration due to gravity 9.81 (m / s²) 
HP. = Pump delivery head (m)
p = pump pressure (Pa)  
ρ = density of the conveyed medium (kg / m³) 
g = acceleration due to gravity 9.81 (m / s²) 
HP. = Pump delivery head (m)

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Head of the system

The head HA. the system consists of the following parts:
Geodetic head is the difference in height between the liquid level on the suction and pressure side. If the pressure line opens above the liquid level, the center of the outflow cross-section is referred to. 
Manometric pressure difference is the difference between the pressure levels above the liquid level on the suction and pressure side for at least one closed container. 
Difference in speed level is the difference in speeds in the containers. Can be neglected in practice. 
Head losses are the sum of the flow resistances in pipes, fittings, fittings, etc. in the suction and pressure lines as well as the inlet and outlet losses, which in practice are referred to as pressure losses in the system. 
The delivery head H results from all four componentsA. the plant



H A. = System delivery head (m)
H geo = geodetic height difference between
Outlet and inlet cross-section (m) 
p e = Pressure in the tank on the suction side (Pa)
p a = Pressure in the pressure-side container (Pa)
v e = Speed ​​in the tank on the suction side (m / s)
v a = Speed ​​in the pressure-side container (m / s)
ρ = density of the conveyed medium (kg / m³) 
g = acceleration due to gravity 9.81 (m / s²) 
H v = Pressure head loss due to flow losses
and pipeline components (m) 
p v = System pressure loss according to Hv (Pa)

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Geodetic height difference


Calculation program: pressure loss and delivery head calculation

Calculation of pressure loss for various pipe components.
Calculation of the delivery head and pump output for the design of the pump.
Diagram showing the system and pump characteristics.
When entering the pump characteristic, the specified and actual operating point is calculated and displayed in a diagram.
The medium data volume flow, density and viscosity can be changed later.

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Power requirement on the pump shaft

The power requirement of a pump is the mechanical power absorbed on the pump shaft or coupling.
The pump efficiency is mainly dependent on the pump size, the pumped medium and the pump type.
The efficiency can be found in the manufacturer's information.


P. pump = Pump output (W = kg * m² / s³)
P. wave = Wave power (W = kg * m² / s³)
ρ = density of the conveyed medium (kg / m³) 
g = acceleration due to gravity 9.81 (m / s²) 
Q = flow rate (m³ / s) 
H A. = System delivery head (m)
η pump = Pump efficiency (-)  
P. pump = Pump output (W = kg * m² / s³)
P. wave = Wave power (W = kg * m² / s³)
ρ = density of the conveyed medium (kg / m³) 
g = acceleration due to gravity 9.81 (m / s²) 
Q = flow rate (m³ / s) 
H A. = System delivery head (m)
η pump = Pump efficiency (-)  
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Electric motor power

The electrical motor power is calculated from the shaft power and the motor efficiency.
Depending on the motor power, the efficiency for electric motors is defined according to IEC 60034-30. For design values, see below.


P. Mot = electr. Motor power (W)
P. wave = Shaft power (W)
η Mot = Motor efficiency (-)  
P. Mot = Motor power (W)
P. wave = Shaft power (W)
η Mot = Motor efficiency (-)  

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E-motor efficiency

The IEC 60034-30 standard defines the standard for the efficiency of IE1, IE2, IE3 and IE4 motors.
The efficiency of the electric motors at nominal power is divided into four efficiency classes:
- IE1 standard efficiency (formerly Eff2)
- IE2 high efficiency (formerly Eff1)
- IE3 premium efficiency
- IE4 super premium efficiency


Coefficients for electric motors 50 Hz - 4 poles

A.B.C.D.
IE10,5234-5,049917,418074,3171
IE20,0278-1,924710,439580,9761
IE30,0773-1,89519,298483,7025
IE4

η N = Motor efficiency (-)
P. N = Nominal motor power (kW)
A, B, C, D =  Coefficients (-)
η N = Motor efficiency (-)
P. N = Nominal motor power (kW)
A, B, C, D =  Coefficients (-)
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