Chapter 3, Problem 3.6.1P

To determine

The magnitude and location of the hydrostatic force on the vertical rectangular plate.

Answer to Problem 3.6.1P

$469.92kN$ and $6.056m$

Explanation of Solution

Given:

Length of the rectangular plate = 4 m

Width of the rectangular plate = 2 m

Formula used:

$F=\gamma h_{c}A$

where, F is the hydrostatic force

$\gamma$ is a constant

$h_c$ is the vertical distance to the centroid

A is the surface area

Calculation:

The given figure is shown below:

The vertical distance to the centroid is calculated as:

$h_c=5+\frac{2}{2}=6m$

The hydrostatic force is calculated as:

$\begin{array}{l}F=\gamma h_{c}A\\ F=9.79\times 6\times \left(4\times 2\right)\\ F=469.92kN\end{array}$

The location of the hydrostatic force is calculated as:

$\begin{array}{l}y=y_c+\frac{I}{y_{c}A}\\ y=6+\frac{\frac{4\times 2^3}{12}}{6\times \left(4\times 2\right)}\\ y=6+\frac{2.67}{48}\\ y=6+0.056\\ y=6.056m\end{array}$

Conclusion:

The magnitude and location of the hydrostatic force on the vertical rectangular plate are $469.92kN$ and $6.056m$.