Question

The power transmitted through a pipe is maximum when the head lost due to friction is equal to

• A. One-fourth of the total supply head
• B. One-third of the total supply head
• C. One-half of the total supply head
• D. Two-third of the total supply head

Hint:

For maximum power transmission through pipes: \[ \boxed{h_f=\frac{H}{3}} \] and \[ \boxed{\eta_{\max}=\frac{2}{3}=66.7\%.} \]

Answer 1

The Correct Option is B

Concept: The power delivered through a pipeline depends upon the available head at the outlet. For maximum power transmission, \[ \boxed{h_f=\frac{H}{3}} \] where \[ H=\text{Total supply head}, \] and \[ h_f=\text{Head loss due to friction}. \] Under this condition, \[ \boxed{\text{Efficiency}=\frac{2}{3}=66.7\%.} \]

Step 1: State the condition for maximum power transmission. From the maximum power transmission theorem for pipelines, \[ h_f=\frac{H}{3}. \]

Step 2: Identify the correct option. Thus, the head loss due to friction should be \[ \boxed{\frac{1}{3}\text{ of the total supply head}.} \] Therefore, the correct option is \[ \boxed{(B)\;\text{One-third of the total supply head}.} \]