affinity law for pumps

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Saad85

Well-known member
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Jun 24, 2016
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Hi all,

would you please provide the correct equations for affinity law for pumps with shaft speed hold constant ?

thanks 

 
Thanks for your feedback but dr tom classroom states different equations as below : Q2/Q1=(D2/D1)^3

H2/H1=(D2/D1)^2

P2/P1=(D2/D1)^5

so I am confused which one we should used in the exam?

 
Does page 110 of the FE Reference manual help you out?

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