Question

A tank in the shape of a right rectangular prism has a height of 5 feet, width of 3 feet, and length of 2 feet. It is full of a liquid weighing 50 pounds per cubic foot. How much work does it take to pump all of the liquid out of the top of the tank

Answer 1

Answer:

Step-by-step explanation:

Given

height of tank $h=5\ ft$

Width of tank $w=3\ ft$

length of tank $L=2\ ft$

suppose a layer of water at height h of thickness dh from bottom needed to be pump out

So distance moved by this layer to come out of tank is $\Delta h=5-h$

weight density of water $\rho =50\ pounds/ft$

Force required to hold this layer up $F_s=2\times 3\times \Delta h\times 50=300\Delta h$

Work done to remove the water

$W=\int_{0}^{5}300\Delta hdh$

$W=\int_{0}^{5}300\left ( 5-h\right )dh$

$W=3750\ Pound-ft$