Fresh features from the #1 AI-enhanced learning platform.Try it free
Fresh features from the #1 AI-enhanced learning platformCrush your year with the magic of personalized studying.Try it free
Question

# Water flows through a sluice gate with a 1.1-ft- high opening and is discharged with free outflow. If the upstream flow depth is 5 ft, determine the flow rate per unit width and the Froude number downstream the gate.

Solution

Verified
Step 1
1 of 3

The rate of discharge is given by Eq.(13-77):

$\begin{equation*} \dot V=C_d b a \sqrt{2gy_1} \end{equation*}$

where $C_d$ is discharge coefficient, $b$ is width of the gate, $a$ is the height of the gate opening, $g$ is gravitational acceleration and $y_1$ is reservoir depth before the gate.

The flow rate per unit width is:

$\begin{equation*} \frac{ \dot V}{b}=C_d a \sqrt{2gy_1} \end{equation*}$

The depth ratio is:

$\begin{equation*} \frac{y_1}{a}=\frac{5\:\text{ft}}{1.1\:\text{ft}}=4.545 \end{equation*}$

The corresponding discharge coefficient is determined from Fig. 13–46 (according to $y_1/a$ and free outflow ) to be : $C_d=0.58$.

With $C_d=0.58$, $a=1.1$ ft, $g=32.2$ ft/s$^2$ and $y_1=5$ ft, the rate of discharge per unit width is:

$\begin{equation*} \frac{\dot V}{b}=0.58\cdot1.1\:\text{ft} \sqrt{2\cdot32.2\:\frac{\text{ft}}{\text{s}^2}\cdot5\:\text{ft}} \end{equation*}$

$\begin{equation*} \fbox{ \frac{\dot V}{b}=11.45\:\frac{\text{ft}^3}{\text{s}\cdot\text{ft}}} \end{equation*}$

## Recommended textbook solutions

#### Fundamentals of Electric Circuits

6th EditionISBN: 9780078028229 (12 more)Charles Alexander, Matthew Sadiku
2,120 solutions

#### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

4th EditionISBN: 9780133942651 (4 more)Randall D. Knight
3,508 solutions