Calculate the work required to pump water into the tank shown below, through a hole at the base of the tank. The water source is at ground level.
Hint: Density of water $= 62.4 lb / {ft}^{3}$ .
Round your answer to the nearest whole number.
Enter

Answer

Expert–verified

Hide Steps

Answer

$W = 62.4 \int_{0}^{h} (h - y) \frac{y^{2}}{h^{2}} π d y$

Steps

Step 1 ： $V = \frac{1}{3} π h r^{2}$

Step 2 ： $W = ρ \int_{0}^{h} (h - y) A (y) d y$

Step 3 ： $W = 62.4 \int_{0}^{h} (h - y) \frac{y^{2}}{h^{2}} π d y$