Question

How does the head loss in turbulent flow in a pipe vary?

• A. \(\text{directly as the velocity}\)
• B. \(\text{inversely as the square of the velocity}\)
• C. \(\text{approximately as the square of the velocity}\)
• D. \(\text{inversely as the square of the diameter}\)

Hint:

In turbulent flow, head loss varies as \( v^2 \) and inversely with pipe diameter \( d \).

Answer 1

The Correct Option is C

Step 1: Understanding head loss in turbulent flow.
- According to the Darcy-Weisbach equation, the head loss (\( h_f \)) due to friction in turbulent flow is: \[ h_f \propto \frac{v^2}{d} \] where \( v \) is velocity and \( d \) is pipe diameter.
Step 2: Explanation of incorrect options.
- (A) Directly as velocity: Incorrect, as head loss follows a square relationship with velocity.
- (B) Inversely as square of velocity: Incorrect, as increasing velocity increases head loss.
- (D) Inversely as square of diameter: Partially correct but does not fully describe velocity dependence.
Step 3: Selecting the correct option. Since head loss is approximately proportional to the square of velocity, the correct answer is (C) approximately as the square of the velocity.