Question 15.19: A broad crested weir rises 0.3 m high above the bottom of a ...

Introduction to Fluid Mechanics

A broad crested weir rises 0.3 m high above the bottom of a stream channel. If the measured weir head is y₁− 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.

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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 − 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 m³/s. To ﬁnd the crtical water depth, we note that y_C ≈ $\frac{2}{3}$ (y₁ − y_W). Since we know y₁ − y_W = 0.65 m, we obtain y_C ≈ $\frac{2}{3}$ (y₁ − y_W) = $\frac{2}{3}$ (0.65 m) = 0.43 m.

15.50

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