Section 4: Soil and Water Conservation Engineering
Fluid Mechanics
Subtopic: Flow through orifices, weirs and notches
Question Statement:
For flow issuing through a sharp-crested circular orifice under a constant hydraulic head, the coefficient of discharge ($C_d$) is related to the coefficient of velocity ($C_v$) and coefficient of contraction ($C_c$) by which fundamental relationship?
Options:
(A) $C_d = C_c \times C_v$
(B) $C_d = \frac{C_c}{C_v}$
(C) $C_d = C_c + C_v - 1$
(D) $C_d = \sqrt{C_c^2 + C_v^2}$
Answer Key:
A
Step-by-Step Solution & Explanation
Actual discharge $Q_{act} = A_{act} \times V_{act}$.
Theoretical discharge $Q_{th} = A_{th} \times V_{th}$.
By definition:
$C_c = \frac{A_{act}}{A_{th}} \quad \text{and} \quad C_v = \frac{V_{act}}{V_{th}}$
$C_d = \frac{Q_{act}}{Q_{th}} = \frac{A_{act} V_{act}}{A_{th} V_{th}} = C_c \times C_v$
Option A is correct.