Pump HP: 2005 #3 (similar)

Calculating drilling pump horsepower? Total pressure drop is needed (pipe, bit, annulus, surface).
We will assume annulus & surface pressure drop is 0.
All 5 equations needed are on a single Guidebook page, 3 HYD 1.

1) For pipe pressure drop (say MW=10ppg, PV=40cp, V=14 fps, 500 gpm, 10M ft):
 dP/dL= (ρ^0.75 V^1.75 μ^0.25)/1,800 d^1.25
dPd/10,000 = (10^0.75 14^1.75 40^0.25)/1,800*3.8^1.25
dPd = 1,500 psi.

2) Not given pipe ID? Merely back-calculate ID from your 14 fps & 500 gpm:
d=[q/2.448V]^1/2 = 500/[2.448*14)] = 3.8 in.

3) For bit pressure loss (given nozzle area = 0.39 si):
dPb = 8.311E-5 MW q²/[C_D² A_t²] dPb = 8.311E-5(10)500²/[0.95² 0.39²d
Pb = 1,500 psi.

4) So total pressure drop over the pumping system is 1,500 + 1,500 = 3,000 psi.

5) Enter this into the standard HP equation:
[dP q]/1,714 = 3,000*500/1714 = 875 HP.

This is a tricky problem; step 2 is especially mean. Yet the equations do logically progress on a single Guidebook page, making it easier.