Chapter P.4, Problem 96E

Flow Speed in a Channel The speed of water flowing in a channel, such as a canal or river bed, is governed by the Manning Equation,
$V=1.486\frac{A^{2/3}{S}^{1/2}}{p^{2/3}n}$
Here V is the velocity of the flow in ft. /s; A is the cross-sectional area of the channel in square feet: S is the downward slope of the channel; p is the wetted perimeter in feet (the distance from the top of one bank, down the side of the channel, across the bottom, and up to the top of the other bank); and n is the roughness coefficient (a measure of the roughness of the channel bottom). This equation is used to predict the capacity of flood channels to handle runoff from heavy rainfalls. For the canal shown in the figure, $A=75{\text{ft}}^2$ , $S=0.050$ , $p=24.1\text{ft}$ and $n=0.040$ .
(a) Find the speed at which water flows through the canal.
(b) How many cubic feet of water can the canal discharge per second? [Hint: Multiply V by A to get the volume of the flow per second.].