Chapter 7.3, Problem 16CYU

To determine

To find the water height of the weir.

Answer to Problem 16CYU

4 feet

Explanation of Solution

Given:

L − Length of the weir is 3 feet

H − Height of the weir.

Flow of water $Q=1.6L{H}^{\frac{3}{2}}$ = 38.4 cubic feet per second.

Calculation:

Given that the flow of water is given by,

  $Q=1.6L{H}^{\frac{3}{2}}$

Substituting the values of H and Q,

  $\begin{array}{l}\Rightarrow Q=1.6L{H}^{\frac{3}{2}}\\ \Rightarrow 38.4=1.6(3)H^{\frac{3}{2}}\\ \Rightarrow 38.4=4.8H^{\frac{3}{2}}\\ \Rightarrow \frac{38.4}{4.8}=H^{\frac{3}{2}}\\ \Rightarrow 8=\sqrt{H^3}\end{array}$

Now, 8 can be written as $2^3.$

  $\begin{array}{l}\Rightarrow 2^3=\sqrt{H^3}\\ \Rightarrow 2^3=\sqrt{H^3}\\ \Rightarrow 64=H^3\\ \Rightarrow H=4\end{array}$

Conclusion:

Therefore, the height of the weir is 4 feet.