Chapter 8, Problem 38RE

To determine

To find : the fluid force against the base and each side of the can when it is full.

Answer to Problem 38RE

The fluid force against the base is $6.6385$ lb and each side is $9.4835$ lb.

Explanation of Solution

Given information : A standard olive oil can measures $5.75$ inches by $3.5$ inches by $10$ inches.

Calculation :

The fluid against the base is:

  $\begin{array}{l}57\times \frac{10}{12}\times \frac{3.5}{12}\times \frac{5.75}{12}\\ \Rightarrow 6.6385\end{array}$

The fluid force against the front and back is:

  $\begin{array}{l}{\displaystyle \underset{0}{\overset{\raisebox{1ex}{$10$}\!\left/ \!\raisebox{-1ex}{$12$}\right.}{\int }}\frac{3.5}{12}\cdot 57\cdot xdx}\\ \Rightarrow 5.7726\end{array}$

The fluid forces against the sides are:

  $\begin{array}{l}{\displaystyle \underset{0}{\overset{\raisebox{1ex}{$10$}\!\left/ \!\raisebox{-1ex}{$12$}\right.}{\int }}\frac{5.75}{12}\cdot 57\cdot xdx}\\ \Rightarrow 9.4835\end{array}$