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Chapter 15

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.

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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.

15.50