§ 16

Hydraulic pump: flow and power requirement

How much oil does the pump deliver, and how many kW does it require?

Answer: A gear or piston pump delivers a flow that is the displacement per revolution times the revolution rate, minus the internal leakage (the volumetric efficiency). The hydraulic power is pressure times flow. The motor must deliver more than that because the pump also has mechanical losses. The calculator is used when you troubleshoot slow hydraulics, check a new pump or assess whether the tractor's engine can pull a hydraulic implement.

Formula

Flow Q [l/min] = V [cm³/omdr] × n [o/min] × ηv ÷ 1000

Hydraulisk effekt P [kW] = p [bar] × Q [l/min] ÷ 600

Optaget effekt = hydraulisk effekt ÷ ηt (samlet virkningsgrad = volumetrisk × mekanisk-hydraulisk)

Moment M [Nm] = 9549,3 × P [kW] ÷ n [o/min]

Symbols and units in the formula
Symbol	Meaning	Unit
fortraengning	Pump's displacement (geometric volume)	cm³/omdr
omdr	Pump's rev number	o/min
eta_vol	Volumetric efficiency (data sheet, worn pump lower)	%
tryk	Working pressure	bar
eta_total	Total efficiency	%
=	Flow from pump	l/min
=	Hydraulic power	kW
=	Power the pump draws from the motor	kW
=	Moment on the pump shaft	Nm

Validity and source

Source: Hydraulikkens grundformler (Q = V·n·ηv ÷ 1000, P = p·Q ÷ 600), jf. Bosch Rexroth og Danfoss

Does not apply when

Efficiencies are in the pump's data sheet. If you measure a flow that is much lower than calculated at the same revolutions and pressure, the pump or a valve is leaking. Check with flow meter under load.

Worked example

The calculator's own default values inserted. The figures are calculated with exactly the formula the tool uses.

Substituted

Pump's displacement (geometric volume)45 cm³/omdr
Pump's rev number2,000 o/min
Volumetric efficiency (data sheet, worn pump lower)95 %
Working pressure200 bar
Total efficiency85 %

Giver

Flow from pump85.5 l/min
Hydraulic power28.5 kW
Power the pump draws from the motor33.5 kW
Moment on the pump shaft160.1 Nm

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Sådan bruger du den

Klager kunden over, at frontlæsseren er langsom, eller at et hydraulisk redskab mangler kraft, skal du vide, hvad pumpen burde levere. Beregneren regner flowet ud fra pumpens fortrængning og omdrejninger, den hydrauliske effekt og hvor mange kW pumpen trækker fra motoren. Sammenlign med en flowmåling under tryk.

Step by step

Find pumpens fortrængning.
Mål omdrejningstallet.
Vælg virkningsgrader fra databladet.
Aflæs flow, effekt og moment, og sammenlign med en flowmåling.

Typical errors

At måle flow uden tryk.
At bruge motoromdrejningstal i stedet for pumpens.
At glemme virkningsgraden.

Examples from everyday life

Ny pumpe på en traktor

En traktors hydraulikpumpe har 45 cm³/omdr og kører 2.000 o/min. Arbejdstrykket er 200 bar, og databladet giver 95 % volumetrisk og 85 % samlet virkningsgrad.

Pump's displacement (geometric volume): 45 cm³/omdr
Pump's rev number: 2,000 rpm
Volumetric efficiency (data sheet, worn pump lower): 95 %
Working pressure: 200 bar
Total efficiency: 85 %

It means: Pumpen leverer 85.5 l/min. Den hydrauliske effekt er 28.5 kW, og den trækker 33.5 kW fra motoren, svarende til 160.1 Nm på akslen.

Slidt pumpe

Frontlæsseren er blevet langsom. En flowmåling under 200 bar ved 2.000 o/min viser kun 72 l/min. Du prøver at regne med 80 % volumetrisk virkningsgrad.

Pump's displacement (geometric volume): 45 cm³/omdr
Pump's rev number: 2,000 rpm
Volumetric efficiency (data sheet, worn pump lower): 80 %
Working pressure: 200 bar
Total efficiency: 70 %

It means: Med 80 % volumetrisk virkningsgrad giver pumpen 72 l/min, som passer med målingen. Pumpen er slidt.

Rule of thumb

100 l/min ved 200 bar er ca. 33 kW.

How to check the answer

Hydraulisk effekt × 600 ÷ tryk skal give flowet.