Question

Water is discharged from a tank through a rectangular orifice of width 1.5 m and height 1.2 m. The water level in the tank is 3.5 m above the top edge of the orifice. The coefficient of discharge is 0.62. Find the discharge through the orifice in m³·s⁻¹.

Hint:

For orifice flow, use the discharge coefficient \(C_d\) and calculate flow using the formula \(Q = C_d A \sqrt{2gh}\).

Answer 1

Correct Answer: 9.9

Discharge formula: \[ Q = C_d A \sqrt{2gh} \] Where: \[ A = 1.5 \times 1.2 = 1.8\ \text{m}^2, h = 3.5\ \text{m}, C_d = 0.62, g = 9.81\ \text{m/s}^2 \] Thus: \[ Q = 0.62 \times 1.8 \times \sqrt{2 \times 9.81 \times 3.5} = 0.62 \times 1.8 \times 8.29 = 9.09\ \text{m}^3/\text{s} \] Thus, \[ \boxed{9.09} \]