A rectangular orifice of 1.5 m wide and 1.2 m deep is fitted in one side of a large tank. The water level on one side of the orifice is 2 m above the top edge of the orifice, while on the other side the water level is 0.4 m below its top edge. Calculate the discharge through the orifice if Cd = 0.62.

Discharge Analysis of a Partially Submerged Rectangular Orifice

Problem Statement

A rectangular orifice of 1.5 m wide and 1.2 m deep is fitted in one side of a large tank. The water level on one side of the orifice is 2 m above the top edge of the orifice, while on the other side the water level is 0.4 m below its top edge. Calculate the discharge through the orifice if C_d = 0.62.

Given Data

Width of orifice (b)	1.5 m
Depth of orifice (d)	1.2 m
Height of water above top edge (H₁)	2.0 m
Difference in water level on both sides (H)	2.0 + 0.4 = 2.4 m
Height of water from bottom edge (H₂)	H₁ + d = 2.0 + 1.2 = 3.2 m
Coefficient of Discharge (C_d)	0.62

Calculations

Step 1: Discharge through Partially Submerged Orifice

The discharge (Q) through a partially submerged orifice is given by:

Q = (2/3) × C_d × b × √(2g) × (H^3/2 – H₁^3/2) + C_d × b × (H₂ – H) × √(2gH)

Substituting the given values (using g = 9.81 m/s²):

Q = (2/3) × 0.62 × 1.5 × √(2×9.81) × (2.4^3/2 – 2.0^3/2) + 0.62 × 1.5 × (3.2 – 2.4) × √(2×9.81×2.4)

Evaluating the expression yields:

Q ≈ 7.55 m³/s

Conclusion

The discharge through the partially submerged rectangular orifice is approximately 7.55 m³/s.