Similarity Laws-Centrifugal pump

[serfinos]

Homework Statement

Right people, I had an experiment the other day on the lab. I measured flow rate, delivery, power, Head, at certain speeds in a centrifugal pump. I put values of Head vs. Delivery on Excel and I got graph showing a curve . How can I predict this curve by calculation of the similarity laws ? does anyone know??

Homework Equations

So I plot, ΔΗ vs. V , Pf vs V, and η vs V.
Where ΔΗ=head, V=flow rate, Pf=power fluid , η=electromechanical eficiency.

I got the readings put them on Excel and got the various graphs.

Now how can I predict these lines on the graphs by similarity laws?
V/N=constant delivery varies with speed
ΔΗ/N^2=constant, pump head varies with speed^2
P/N^3=constant, power varies with speed^3
Pf=ρgVΔΗ , power fluid
Pe=VI , electrical power
Electromechanical eficiency η=Pf/Pe



any idea?

The Attempt at a Solution

 

[Valkarie]

The similarity laws can be used to predict the curves on the graphs that you have plotted. For example, using the law V/N=constant, you can use this to predict the variation in delivery with speed. Similarly, using ΔΗ/N^2=constant, you can predict the variation in head with speed^2. Additionally, using P/N^3=constant, you can predict the variation in power with speed^3. You can also use the equations Pf=ρgVΔΗ and Pe=VI to calculate the power fluid and electrical power, and then use these values to calculate the electromechanical efficiency η=Pf/Pe. This will help you predict the variations in the electromechanical efficiency with speed.