Question

QUESTION 8 You are told to visit a job site and measure a tank that will hold water to be pumped for irrigation. The tank measures 40 feet tall with a diameter of 20 feet. The boss said on your way back to the shop, to stop and pick up four pumps that are capable of pumping half the volume of tank in one hour when the tank is full. What is the minimum gallon per hour (GPH) of each pump, when working together, that can get the job done?

Answer 1

Let's begin by listing out the information given to us:

Height (h) = 40 ft, diameter (d) = 20 ft, radius (r) = 20/2 = 10 ft

The volume of the tank is given by:

$\begin{gathered} V=\pi r^2h \\ V=3.14(10^2\cdot40) \\ V=12,560ft^3 \end{gathered}$

The volume of the tank is given by the product of pi, radius square & the height of the tank

Volume = 3.14 * 10² * 40 = 12,560 ft³

You pick up 4 pumps that can pump half the volume of the tank in 1 hour = 12560/2 ft³/h = 6280 ft³/h

Each pump supplies this amount of water:

$\Rightarrow\frac{6280}{4}=1570ft^{3}/h$

Each pump supplies 1,570 ft³/h of water. If it takes 1 hour to fill half the tank, then it will take 2 hours to fill the tank.

Convering 1570 ft³/h to gal/h, we have:

$\begin{gathered} 1ft=7.48gal\Rightarrow1ft^3/h=7.48gal/h \\ 1ft^3/h=7.48gal/h \\ 1570ft^3/h=x \\ \text{Cross multiply, we have:} \\ x=7.48(1570)=11743.6 \\ x=11744gal/h \end{gathered}$

Therefore, each pump supplies 11,744 gallons per hour