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