The spillway of a dam is (20.0 mathrm{ft}) wide and has a flow rate of (5000 mathrm{ft}^{3}
Question:
The spillway of a dam is \(20.0 \mathrm{ft}\) wide and has a flow rate of \(5000 \mathrm{ft}^{3} / \mathrm{s}\). The spillway makes an angle of \(30^{\circ}\) with the horizontal. Find the vertical water depth down the spillway. See Problem 10.72.
Problem 10.72
Consider the flow down a prismatic channel having a rectangular cross section of width \(b\). The channel bottom makes an angle \(\theta\) with the horizontal. Show that
\[ \frac{d y}{d x}=\frac{\tan \theta-\left(n^{2} Q^{2}\right) /\left(A^{2} R_{h}^{4 / 3} \kappa^{2}\right)}{1-Q^{2} /\left(A^{2} g y \cos ^{2} \theta\right)} \]
where \(y\) is the vertical fluid depth, \(A=b y \cos \theta\), and \(Q\) is the volume flow rate. Discuss the form of the equation for small values of \(\theta\left(\theta \sim 1^{\circ}\right)\)
Step by Step Answer:
Munson Young And Okiishi's Fundamentals Of Fluid Mechanics
ISBN: 9781119080701
8th Edition
Authors: Philip M. Gerhart, Andrew L. Gerhart, John I. Hochstein