A fluid jet discharging from a 4 cm diameter orifice has a diameter of 3 cm at its venacontracta. If coefficient of velocity is 0.98, then the coefficient of discharge of the orifice will be
- A0.98 × (0.75)²Correct
- B(0.75)² / 0.98
- C0.98 × (1.33)²
- D0.98 / (1.33)²
Solution
Concept
Cd = Cv × Cc
Formula
Cd = Cv × Cc, Cc = ac / ao = (dc / do)²
Step-by-step solution
1. Cc = (3/4)² = (0.75)². 2. Cd = Cv × Cc = 0.98 × (0.75)².
Explanation
The coefficient of discharge is the product of coefficient of velocity and coefficient of contraction. The contraction coefficient is the area ratio, so it is the square of the diameter ratio (3/4 = 0.75).
Shortcut
Cd = Cv × Cc; Cc is always less than 1.
Common mistake
Using the diameter ratio instead of the area ratio, or inverting it.
Correct answer: A) 0.98 × (0.75)²