Chapter 8.5, Problem 25E

a.

To determine

To find the fluid force against each end of the tank.

Answer to Problem 25E

209.73 lb fluid force against each end of the tank.

Explanation of Solution

Given information: A rectangular freshwater fish tank with base $2\times 4$ ft and height 2 ft is filled to within 2 in. of the top.

Calculation:

As per the given problem,

Assume that the weight density of water is $62.4lb/f{t}^3$ . The end of the tank , refers to the $2\times 2$ side of the tank. The fluid force on each of these ends is given by the integral.

  $\begin{array}{l}{\displaystyle {\int }_0^{22/12}2\cdot 62.4hdh}\\ =209.73\end{array}$

Hence, 209.73 lb fluid force against each end of the tank.

b.

To determine

To find work done to fluid forces on the rectangular sides.

Answer to Problem 25E

The required solution is 838.93 lb.

Explanation of Solution

Given information: A rectangular freshwater fish tank with base $2\times 4$ ft and height 2 ft is filled to within 2 in. of the top.

Calculation:

As per the given problem,

To find the fluid force on the rectangular sides, first note that the height of the water is now 11/3 feet. The fluid force is then given by the integral.

  $\begin{array}{l}{\displaystyle {\int }_0^{11/3}2\cdot 62.4hdh}\\ =838.93\end{array}$

Hence, the required solution is 838.93 lb.