# Homework Help: Centrifugal/Reciprocating Pump Efficiency

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1. Mar 14, 2016

### Mingsliced

1. The problem statement, all variables and given/known data

It is proposed to pump 1500 m3 of a liquid (density 1100 kg m–3) each day through a total head of 10 m (including all losses) by using either a centrifugal pump or a reciprocating pump.

The centrifugal pump discharges 2.0 m3 min–1 when driven by an electric motor supplying a power of 5 kW.

The reciprocating pump has a discharge rate of 1.75 m3 min–1 when driven by an electric motor supplying 3.5 kW.

1) Calculate the efficiency of the pumps.

2. Relevant equations

Po = QvρGHP

ηp = Po/PI
ηm = PI/Pe
ηo = Po/Pe

3. The attempt at a solution

Data Collection

ρ = 1100 kg m–3
G = 9.81 m/s-1
Hp = 10m

Convert flowrate from m3/min-1 to m3/sec-1:

2/60 = 0.033m3/sec-1 for the centrifugal pump.

1.75/60 = 2/60 = 0.029m3/sec-1 for the reciprocating pump.

Calculate output power of the centrifugal pump:

Po = QvρGHP

Po = 0.033 * 1100 * 9.81 * 10

Po = 3561.03 Watts

Calculate centrifugal pump efficiency:

ηp = Po/PI * 100

ηp = 3561.03/5000 * 100

ηp = 0.712 * 100

ηp = 71.2% efficiency

I'm a little bit stumped from this point on as I cannot calculate the overall efficiency of each pump without knowing the electrical input power, Pe or even the motor efficiency. Should I assume that the motor is running at 100% efficiency and that the electrical input power Pe is the same as the input power to pump PI?

If not, is there a way that I can calculate Pe without knowing the overall/motor efficiency?

Cheers!

2. Mar 14, 2016

### Ronie Bayron

In the real world, we consult the manufacturer. They have this pump curve which are based on the actual test of the size and other essential parameters of pumps and you have corresponding plots for hydraulic efficiency, might as well the minimum electrical power or motor match with the corresponding pump. I hope this helps.

3. Mar 16, 2016

### 256bits

Are you being asked to calculate the efficiency of the pump, or the motor-pump unit?
For both cases, the power delivered to the pump by the motor is given.