Pump Laws: When Do They Apply?

I can’t get the pump laws to work for me! It’s supposed to be that head decreases as flow increases for a centrifugal pump. But, Cameron Handbook states Q1/Q2 = H1^(0.5)/H2^(0.5). If you play with this, you’ll find that head decreases as flow decreases. Also, there is no accounting for impeller size.

Also, a college fluids mechanics book states Q1/Q2 = wD1^2/wD2^2 where w is rpm, but we can assume rpm is constant. I can’t get this equation to work, either. In my case, Q1 = Q2, yet the impeller diameters are different, so the feet of head (H) must be different.

In short, I have this:
A 10" impeller delivers 176 gpm @ 350 ft. It was trimmed to some smaller diameter where it now delivers 176 gpm @ 257 ft. Ultimately, I need to know how much feet of head will this new impeller size deliver at 75 gpm based on the info here. I can add that the original 10" impeller woudl deliver 75 gpm @ 372.5 ft of head.

Can anyone help me figure this out?
Thanks,
Jinx

Correction: The above equation should read:
Q1/ (w1*D1^3) = Q2/ (w2 * D2^3)

  • Jinx