The coefficient of discharge (Cd) in terms of the coefficient of velocity (Cv) and the coefficient of contraction (Cc) is:
- ACd = Cc / Cv
- BCd = Cv + Cc
- CCd = Cv × CcCorrect
- DCd = Cv / Cc
Solution
Concept
The coefficient of discharge is the product of the coefficient of velocity and the coefficient of contraction.
Formula
Cd = Cv × Cc
Step-by-step solution
1. Actual discharge Q = actual area × actual velocity. 2. Actual area = Cc × orifice area a. 3. Actual velocity = Cv × √(2gH). 4. So Q = Cc × Cv × a × √(2gH). 5. Theoretical discharge = a × √(2gH). 6. Cd = Qactual / Qtheoretical = Cv × Cc.
Explanation
Discharge is area multiplied by velocity. The jet area is reduced by Cc and the jet velocity is reduced by Cv. So the discharge is reduced by both, which gives Cd = Cv × Cc.
Why the other options are wrong
A and D: Division is wrong because discharge is a product of area and velocity, not a ratio. B: Adding them gives a value greater than 1, which is not possible for Cd.
Shortcut
Q = A × V, so Cd = Cc × Cv.
Common mistake
Adding the coefficients instead of multiplying them.
Correct answer: C) Cd = Cv × Cc