## Chapter 15

## Q. 15.19

_{1 }− y_{W} = 0.65 m, and the weir is 10 m wide, ﬁnd the volume ﬂowrate crossing the weir and the critical water depth, y_{C}.

## Step-by-Step

## Verified Solution

_{1} − y_{W})^{3/2} = 10 m\sqrt{9.81\ m/s^2} \left(\frac{2}{3}\right)^{3/2} × ( 0.65 m)^{3/2 }= 8.9 m^{3}/s. To ﬁnd the crtical water depth, we note that y_{C} ≈ \frac{2}{3}(y_{1} − y_{W}). Since we know y_{1} − y_{W} = 0.65 m, we obtain y_{C} ≈ \frac{2}{3}(y_{1} − y_{W}) = \frac{2}{3}(0.65 m) = 0.43 m.