Question

Coefficient of resistance is the ratio of

• A. actual velocity of jet at vena contracta to the theoretical velocity
• B. area of jet at vena contracta to the area of orifice
• C. loss of head in the orifice to the head of water available at the exit of the orifice
• D. actual discharge through an orifice to the theoretical discharge

Hint:

Remember the relationship between the coefficient of resistance ($C_r$) and the coefficient of velocity ($C_v$):
\[ C_r = \frac{1}{C_v^2} - 1 \] This equation makes it easy to calculate one coefficient if the other is known.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question asks for the definition of the coefficient of resistance ($C_r$), which is a hydraulic coefficient used to quantify the frictional and turbulent energy losses occurring in fluid flow through an orifice.

Step 2: Key Formula or Approach:

• The fluid flow through an orifice is characterized by four major hydraulic coefficients:
1. Coefficient of Velocity ($C_v$): Ratio of actual velocity to theoretical velocity.
2. Coefficient of Contraction ($C_c$): Ratio of area of jet at vena contracta to area of orifice.
3. Coefficient of Discharge ($C_d$): Ratio of actual discharge to theoretical discharge ($C_d = C_v \times C_c$).
4. Coefficient of Resistance ($C_r$): Measures head loss in terms of kinetic energy head.

Step 3: Detailed Explanation:

• The coefficient of resistance ($C_r$) is defined mathematically as: \[ C_r = \frac{\text{Loss of head in the orifice}}{\text{Head of water available at the exit of the orifice}} \] \[ C_r = \frac{h_L}{\left(\frac{v^2}{2g}\right)} = \left(\frac{1}{C_v^2} - 1\right) \] where $h_L$ is the head loss and $v$ is the actual velocity of flow at the vena contracta.

• Let us evaluate the options:
- Option (A) defines the Coefficient of Velocity ($C_v$).
- Option (B) defines the Coefficient of Contraction ($C_c$).
- Option (D) defines the Coefficient of Discharge ($C_d$).
- Option (C) matches the mathematical definition of the Coefficient of Resistance ($C_r$).

Step 4: Final Answer:
The coefficient of resistance is the ratio of the loss of head in the orifice to the head of water available at the exit of the orifice.