Centrifugal/Reciprocating Pump Efficiency

[Mingsliced]

Homework Statement

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.

Homework Equations

P_o = Q_vρGH_P

η_p = P_o/P_I
η_m = P_I/P_e
η_o = P_o/P_e

The Attempt at a Solution

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Data Collection

ρ = 1100 kg m^–3
G = 9.81 m/s^-1
H_p = 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:

P_o = Q_vρGH_P

P_o = 0.033 * 1100 * 9.81 * 10

P_o = 3561.03 Watts

Calculate centrifugal pump efficiency:

η_p = P_o/P_I * 100

η_p = 3561.03/5000 * 100

η_p = 0.712 * 100

η_p = 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, P_e or even the motor efficiency. Should I assume that the motor is running at 100% efficiency and that the electrical input power P_e is the same as the input power to pump P_I?

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

Cheers!

 

[Ronie Bayron]

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, P_e or even the motor efficiency. Should I assume that the motor is running at 100% efficiency and that the electrical input power P_e is the same as the input power to pump P_I?

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

Cheers!

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.

 

[256bits]

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?

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.