Chapter 8.5, Problem 17E

a.

To determine

To find: The work done to fill an empty tank by pumping the water back to the level ground once the tank is full.

Answer to Problem 17E

The work done is $1,497,600\text{ft-lb}$ .

Explanation of Solution

Given:

The weight of the water is $62.4{\text{lb/ft}}^{\text{3}}$ .

  

Calculation:

The work done can be calculated as,

  $\underset{0}{\overset{20}{{\displaystyle \int }}}62.4\cdot 120\left(120-y\right)dy=1,497,600\text{ft-lb}$

Therefore, the work done is $1,497,600\text{ft-lb}$ .

b.

To determine

To find: The time to fill an empty tank.

Answer to Problem 17E

The time to fill an empty tank is $\approx 100\min$ .

Explanation of Solution

Given:

Water is pumped to the ground level with a $\left(5/11\right)$ horsepower.

Calculation:

The time to fill an empty tank is,

  $\begin{array}{c}T=\frac{W}{250}\\ =\frac{1,497,600}{250}\\ =5990.4\sec \\ \approx 100\min \end{array}$

Therefore, the time to fill an empty tank is $\approx 100\min$ .

c.

To determine

To find: To show that the pump in part b will lower the water level during the first $25\min$ of pumping.

Answer to Problem 17E

Therefore, the pump in part b will lower the water level during the first $25\min$ of pumping is $\approx 10$ .

Explanation of Solution

Given:

The information is given above.

Calculation:

The tank started out with $1200\text{cubic}\text{feet}$ .

In twenty five minutes of pumping the work done by pump is $375,000\text{ft-lb}$ .

Hence on further solving,

  $\begin{array}{c}375,000=\underset{0}{\overset{h}{{\displaystyle \int }}}62.4\cdot 120\left(y\right)dy\\ 375,000=3744h^2\\ h\approx 10\end{array}$

Therefore, the height is $\approx 10$ .