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## Q. 15.19

A broad crested weir rises 0.3 m high above the bottom of a stream channel. If the measured weir head is y1 − yW = 0.65 m, and the weir is 10 m wide, ﬁnd the volume ﬂowrate crossing the weir and the critical water depth, yC.

## Verified Solution

Figure 15.50 can serve as a sketch. To ﬁnd the volume ﬂowrate, we insert the data into Eq. 15.65, obtaining Q = w$\sqrt{g}$$\left(\frac{2}{3}\right)^{3/2}$(y1 − yW)3/2 = 10 m$\sqrt{9.81\ m/s^2}$ $\left(\frac{2}{3}\right)^{3/2}$ × ( 0.65 m)3/2 = 8.9 m3/s. To ﬁnd the crtical water depth, we note that yC$\frac{2}{3}$(y1 − yW). Since we know y1 − yW = 0.65 m, we obtain yC$\frac{2}{3}$(y1 − yW) = $\frac{2}{3}$(0.65 m) = 0.43 m. 