Solving Fluid Dynamics Questions: Pump Similarity Laws and Efficiency Comparison

[datf]

Hi guys, please help me with these questions. I've been racking my brain for days but I'm not sure of the answers.

1) (Assume that pump similarity laws are valid and that the effects of Reynolds number (Re) are small.)
A centrifugal pump operating at speed N is combined in series with an identical centrifugal pump operating at speed 2N. The head rise across the pump operating at the lower speed is H, which is below its maximum head. Which of the following statements is/are valid?
I. Under steady state conditions, the flowrate through both pumps is identical.
II. Under steady state conditions, the head rise across the pump operating at the higher speed is 4H.a. None of the other options is valid.
b. I only.
c. II only.
d. I and II.

I'm thinking it's I and II.


2) The efficiency n of a centrifugal pump with impeller diameter D operating at a specified speed is given by n = 16(Q – 10Q^2), where Q is the volume flow rate in m^3/s. Ignoring the effects of Reynolds number, the efficiency of a homologous centrifugal pump of impeller diameter 2D is given by

a. n = 128(Q – 10Q^2)
b. n = 16(Q – 10Q^2)
c. None of the other options is valid.
d. n = 2Q – 2.5Q^2

I'm thinking it's n = 2Q – 2.5Q^2

 

[BvU]

Hello datf,

This looks a lot like homework; please read the guidelines to help us help you ! PF will help, but we're not for doing your work -- it wouldn't help you.

 

[datf]

for the first question, if we equate the original and final head coefficient Ch1 = Ch2 --> gH1/(N^2 D^2) = gH2/((2N)^ 2 D^2) --> H2 = 4H1. but is it fine if i simply equate the two original and final head coefficient? I'm quite sure the flow rate is the same for both pumps (statement I)

for the second question, can we assume the flow coefficient Cq remains unchanged. Does homologous pump mean that the Cq would be the same too? Cause if it is true, then I can equate the original and final Cq and get Q2 = 8Q1, which will give me option d.