Question

A fluid flows through an orifice of an area 0.4 m² with an actual discharge of 400 l/s. If the theoretical velocity of flow through the orifice is 2 m/s, what is the coefficient of discharge?
1. 0.71
2. 0.68
3. 0.50
4. 0.56

Answer 1

Correct Answer - Option 3 : 0.50

Concepts:

The coefficient of discharge (C_d) is the ratio of the actual discharge (Q_a) to theoretical discharge (Q_th) .

The actual discharge is the discharge obtained when all the looses through orifice or pipe flow are considered. While, theoretical discharge is the discharge obtained under ideal conditions i.e. no loss is considered.

The  theoretical discharge is given as:

Q_th = A × V_th

V_th is the theoretical velocity of flow

Calculations:

Given: V_th = 2 m/s; A = 0.4 m²

So, Q_th = 0.4 × 2 = 0.8 m³/s  or 800 l/s

∴ C_d = 400/800

C_d = 0.5

Other important Coefficients:

1. Coefficient of velocity is the ratio of theoretical velocity to actual velocity.

2. Coefficient of contraction is the ratio of cross-section area at vena-contracta to original cross- sectional area.