Question

If the coefficient of discharge and coefficient of velocity for an orifice are 0.63 and 0.75 respectively, then the coefficient of contraction is

• A. 0.47
• B. 0.75
• C. 0.84
• D. 1.19

Hint:

Remember the physical meaning and relationship of the orifice coefficients:
- $C_v = \frac{\text{Actual Velocity}}{\text{Theoretical Velocity}}$ (accounts for friction loss)
- $C_c = \frac{\text{Area of Vena Contracta}}{\text{Area of Orifice}}$ (accounts for streamline contraction)
- $C_d = \frac{\text{Actual Discharge}}{\text{Theoretical Discharge}} = C_c \times C_v$

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question asks to calculate the coefficient of contraction ($C_c$) for an orifice, given the coefficient of discharge ($C_d$) and the coefficient of velocity ($C_v$).

Step 2: Key Formula or Approach:
The orifice coefficients are related by the following fundamental formula:
The coefficient of discharge is the product of the coefficient of velocity and the coefficient of contraction.
\[ C_d = C_c \times C_v \]

Step 3: Detailed Explanation:
We are given:
- Coefficient of discharge ($C_d$) = 0.63
- Coefficient of velocity ($C_v$) = 0.75
We need to find the coefficient of contraction ($C_c$). Rearrange the formula:
\[ C_c = \frac{C_d}{C_v} \] Substitute the given values:
\[ C_c = \frac{0.63}{0.75} \] To solve this, we can multiply the numerator and denominator by 4:
\[ C_c = \frac{0.63 \times 4}{0.75 \times 4} = \frac{2.52}{3} \] \[ C_c = 0.84 \]

Step 4: Final Answer:
The coefficient of contraction is 0.84.