Discussion
If Cv , Cc , Cd and Cr are the hydraulic coefficients of an orifice , then :
Where, Cv= coefficient of velocity
Cc = Coefficient of contraction
Cd = coefficient of discharge
Cr = coefficient of retention
Answer: B
The correct relation is \(C_d = C_c \times C_v\).
Actual discharge is the actual area of the jet at the vena contracta times the actual velocity there. The area is \(C_c\) times the orifice area and the velocity \(C_v\) times the theoretical velocity, so
\[ \begin{aligned} Q_{act} &= (C_c a)(C_v \sqrt{2gH}) \\ C_d &= \frac{Q_{act}}{a\sqrt{2gH}} = C_c C_v \end{aligned} \]
The coefficients multiply, so a sum as in the first option is wrong, and \(C_c = C_v/C_d\) inverts the relation (it should be \(C_c = C_d/C_v\)). The relation offered for \(C_r\) is not a standard result.
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