Chapter 8.5, Problem 18E

To determine

To find the work done it take to pump the kerosene weighing to the level of the top of the tank.

Answer to Problem 18E

7238229 ft-lbs work does it take to pump the kerosene weighing to the level of the top of the tank.

Explanation of Solution

Given information: A vertical right cylindrical tank measures 30ft high and 20ft in diameter. It is full of kerosene weighting $51.2lb/f{t}^3$ .

Calculation:

Volume of the small section of the cylindrical tank where the radius is 10 and the height is represented by a small change in y.

  $\begin{array}{l}dv=\pi {\left(10\right)}^{2}dy\\ =100\pi dy\end{array}$

Multiply the volume of the small section by the weight density for kerosene tp get the force in lbs.

  $dF=\left(51.2\right)\left(100\pi \right)dy$

By multiplying the force by the distance of (300-y) you get the work required to pump a small section of kerosene to the top of the tank.

  $dW=\left(30-y\right)\left(51.2\right)\left(100\pi \right)dy$

Take the definite integral to dW,

  $\begin{array}{l}{\displaystyle {\int }_0^{30}\left(30-y\right)\left(51.2\right)\left(100\pi \right)dy}\\ =7238229\end{array}$

Hence, 7238229 ft-lbs work does it take to pump the kerosene weighing to the level of the top of the tank.