October 30

Exam Question 29 Pump Horsepower

What is the minimum size of motor needed for a 2 x 1 pump to deliver 100 gallons per minute (gpm) of water to a water skimmer that is located 50 feet above the pump and has an operating pressure of 35 psig. The water pressure on the suction side of the pump is 5 in Hg vacuum. Assume standard wall thickness.
A) 100
B) 75
C) 25
D) 50


This fluids practice question show you how to solve for horsepower when you have pressure and flow rate in forms other than the units that are standard in Bernoulli’s equation.

Converting units

Converting flow rate from gallons per minute to cubic feet per second

1\ ft^3 = 7.48\ gal
\dot {Q} = (\frac {1\ minute}{60\ seconds})(100\ gpm)(\frac {1\ ft^3}{7.48\ gallons}) = 0.228 \frac {ft^3}{s}

Converting pounds per square inch (PSI) to pounds per square feet (psf)

P_2 = (\frac {35\ pounds}{in^2})(\frac {144\ in^2}{ft^2}) = 5040\ psf

Converting inches of vacuum in mercury to feet of head in water

Specific Gravity of Mercury = 13.6

ft\ of\ head\ =\ (\frac {5\ inches}{12\ inches/foot})(13.6\ S.G.) = 5.7\ ft\ H_2O

Finding velocities

Q\ =\ AV
V\ =\ \frac{Q}{A}

Discharge Side

Internal area of 1″ Sch 40 pipe 0.006 ft2
V\ =\ 0.2228 \frac {ft^3}{s}(\frac {1}{0.006\ ft^2})\ =\ 37.14 \frac {ft}{s}

Suction Side

Internal area of 2″ Sch 40 pipe 0.02338 ft2
V\ =\ 0.2228 \frac {ft^3}{s}(\frac {1}{0.02330\ ft^2})\ =\ 9.56 \frac {ft}{s}

Calculate the amount of head needed using Bernoulli’s Equation

\frac {P_1}{\gamma} + \frac {V_1^2}{2g} + Z_1 + H_p = \frac {P_2}{\gamma} + \frac {V_2^2}{2g} + Z_2

-5.7\ ft\ hd\ + \frac {9.56^2}{2 * 32.2} + 0 + H_p = \frac {5040}{62.4} + \frac {37.14^2}{2*32.2} + 50\ ft
H_p\ =\ 156.4\ fet\ of\ head

There are 3 different equations that can be used to find the horspower needed based on the flow rate so you may have used a different one

Hp\ =\ \frac {(ft\ hd)(gpm)(Specific\ Gravity)}{3956}
Hp\ =\ \frac {(156.5)(100)(1.0)}{3956}\ =\ 3.95

The next size motor up is 5 hp
The correct answer is D


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Posted October 30, 2014 by Patrick Matherne in category "Fluid Mechanics", "Hydraulic and Fluid Equipment", "Qotd
  • JW

    Am I missing something? If I do the math for Hp using the numbers shown in the Bernoulli equation above I don’t get 1783 feet of head. I get 156 feet resulting in a pump motor under 10 horse power.