Question

A water jet discharging from a 4 cm diameter orifice has a diameter of 3.5 cm at its vena contracta. The coefficient of velocity is defined as the ratio of the actual velocity of the jet at vena contracta to the theoretical velocity of the jet. If the coefficient of velocity is 0.98, the coefficient of discharge for the orifice will be _______ (rounded off to two decimal places).

Hint:

The coefficient of discharge is calculated using the coefficient of velocity and the ratio of the diameters of the vena contracta and the orifice.

Answer 1

Correct Answer: 0.74

The coefficient of discharge is related to the coefficient of velocity and the diameter at the vena contracta. The formula for the coefficient of discharge \( C_d \) is: \[ C_d = C_v \times \left( \frac{d_{\text{vena contracta}}}{d_{\text{orifice}}} \right)^2. \] Substituting the given values: \[ C_d = 0.98 \times \left( \frac{3.5}{4} \right)^2 = 0.98 \times (0.875)^2 = 0.76. \] Thus, the coefficient of discharge is \( 0.76 \).