## Related questions with answers

A plane gate of uniform thickness holds back a depth of water as shown. Find the minimum weight needed to keep the gate closed.

Solutions

VerifiedThe hydrostatic force acting on the gate by

$\begin{equation} F=\rho g A \bar{x} \end{equation}$

where $\rho$ is the water density, $g$ is the gravity acceleration, $A$ is the gate area, $\bar{x}$ is the vertical distance between centroid of the gate from the free surface. The gate area can be calculated as

$\begin{equation} A=L \times w \end{equation}$

where $L$ is the length of the plate and $w$ is the plate width. We substitute $3 \mathrm{~m}$ for $L$ and $2 \mathrm{~m}$ for $w$, so

$\begin{equation} \begin{aligned} A &=3 \times 2 \\ &=6 \mathrm{~m}^{2} \end{aligned} \end{equation}$

The centroid of the plate from the free surface can be calculated with

$\begin{equation} \bar{x}=\frac{L}{2} \sin \theta \end{equation}$

and by replacing $3 \mathrm{~m}$ for $L$ and $30^{\circ}$ for $\theta$, we have

$\begin{equation} \begin{aligned} \bar{x} &=\frac{3}{2} \times \sin 30^{\circ} \\ &=0.75 \mathrm{~m} \end{aligned} \end{equation}$

**Given:**

$\begin{aligned} L&=3\text{ m}\\ w&=2\text{ m}\\ \rho_{water}&=1000\:\frac{\text{ kg}}{\text{ m}^3}\\ g&=9.81\:\frac{\text{ m}}{\text{ s}^2}\\ \theta&=30\degree \end{aligned}$

## Create a free account to view solutions

## Create a free account to view solutions

## Recommended textbook solutions

#### Fundamentals of Electric Circuits

6th Edition•ISBN: 9780078028229 (2 more)Charles Alexander, Matthew Sadiku#### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

4th Edition•ISBN: 9780133942651 (8 more)Randall D. Knight#### Advanced Engineering Mathematics

10th Edition•ISBN: 9780470458365 (2 more)Erwin Kreyszig#### Fox and McDonald's Introduction to Fluid Mechanics

9th Edition•ISBN: 9781118912652 (3 more)Alan T. McDonald, John C Leylegian, John W Mitchell, Philip J. Pritchard, Rajesh Bhaskaran, Robert W Fox## More related questions

1/4

1/7