Question

Flow depths across a sluice gate are 2.0 m and 0.5m. What is the discharge (per meter width)?

• A. $2.0m^2/s$
• B. $1.4m^2/s$
• C. $1.0m^2/s$
• D. $2.8m^2/s$

Answer 1

The correct option is D $2.8m^2/s$

If the loss of energy across the sluice gate is assumed to be negligible, then by energy equation, we have

$y_1+\frac{V_1^2}{2g}=y_2+\frac{V_2^2}{2g}$

But, discharge per unit width,

$q=V_1{y}_1=V_1{y}_2$

$\therefore y_1+\frac{q^2}{2g{y}_1^2}=y_2+\frac{q^2}{2g{y}_2^2}$

$\Rightarrow \frac{q^2}{g}=\frac{2y_1^2{y}_2^2}{y_1+y_2}$

$\Rightarrow \frac{q^2}{9.81}=\frac{2\times {\left(2\right)}^2\times {\left(0.5\right)}^2}{2+0.5}$

$\Rightarrow q^2=0.8\times 9.81$

$\Rightarrow q=2.8m^2/s$