Question

If H₁ is the height of the liquid surface above the orifice top, H₂ is the height of the liquid surface above the orifice bottom, b is the width of the orifice and C_d is the coefficient of discharge, what would be the expression to calculate the discharge denoted by Q?

1. \(Q = \frac{1}{2} \times 3{C_d}b\sqrt {2g} (H_2^{3/2} - H_1^{3/2})\)
2. \(Q = \frac{1}{2} \times 3{C_d}b\sqrt {2g} (H_1^{3/2} - H_2^{3/2})\)
3. \(Q = \frac{1}{3} \times 2{C_d}b\sqrt {2g} (H_1^{3/2} - H_2^{3/2})\)
4. \(Q = \frac{1}{3} \times 2{C_d}b\sqrt {2g} (H_2^{3/2} - H_1^{3/2})\)

Answer 1

Correct Answer - Option 4 : \(Q = \frac{1}{3} \times 2{C_d}b\sqrt {2g} (H_2^{3/2} - H_1^{3/2})\)

Concept:

For a large rectangular orifice, the expression to calculate discharge is given by:

\(Q = \frac{1}{3} \times 2{C_d}b\sqrt {2g} (H_2^{3/2} - H_1^{3/2})\)

where,

Q = Required Discharge 

C_d = Coefficient of discharge

H₁ = Height of the liquid surface above the orifice top

H₂ = Height of the liquid surface above the orifice bottom

b = Width of the orifice

These parameters are mentioned in the following figure:

Note:

If the head of liquid is less than five times the depth of orifice, it will be termed as large orifice