Question

The discharge over a broad crested weir is maximum when the depth of flow is

• A. $\frac{H}{3}$
• B. $\frac{2H}{3}$
• C. $\frac{H}{2}$
• D. $\frac{2H}{5}$

Answer 1

The correct option is B $\frac{2H}{3}$

Broad crested weir supports nappe so that pressure variation is hydrostatic at section (2).

Applying Bernoulli's equation between (1) and (2)

$0+0+H=(h-z)+\frac{V_2^2}{2g}+z$

$\Rightarrow \frac{V_2^2}{2g}=H-h$

$V_2=\sqrt{2g(H-h)}$

Thus, the velocity across cross section 2-2 is constant.

$Q_{th}=L\times h\times \sqrt{2g(H-h)}$

$Q_{\text{actual}}=C_{d}L\times h\times \sqrt{2g(H-h)}$

In broad crested weir, flow adjusts itself to have maximum discharge for the available head H, the critical depth is achieved by itself.

$\frac{dQ}{dh}=0$

$\Rightarrow h=\frac{2}{3}H,\text{for maximum discharge}$

$h=\frac{2}{3}H=\text{Critical depth}$

$\text{By putting}h=\frac{2}{3}H\text{, in equation,}$

$Q_{\text{actual}}=1.7C_{d}L{H}^{\frac{3}{2}}$