Q (ft3/min) : 3.9, 7.9, 11.8, 15.7, 19.6, 23.6, 27.5, 31.4, 35.3, 39.3

Delta P (psi): 0.13, 0.52, 1.18, 2.09, 3.27, 4.71, 6.41, 8.37, 10.59, 13.08
My professor gave the information above and wants us to come up with a linear equation that relates Q and square root of delta P. He also said that the pressure drop (delta P) is proportional to the flow rate squared (Q^2).
I have no idea how to come up with this equation please help or point me in the right direction.

3 answers

He wants a linear equation like

q = k√p + n

where q = Q and p = psi

In fact, when he says that p is proportional to Q^2 it means that

p = q^2/k, so n=0

If you tabulate √p/.36 you will have

√p/.36 Q
1 3.9
2 7.9
3 11.8
4 15.7
5 19.6
6 23.6
7 27.5
8 31.4
9 35.3
10 39.3

Taking rounding into account, it looks like

Q = 3√p/.36
Q = 25/3 √p

or,

p = .36 q^2
Thank you so much.
When I tried your equations I did not receive the right values.
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