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Maximum efficiency for power transmission through a pipe For power transmitted hydraulically through a pipeline with frictional head loss, what is the maximum possible transmission efficiency (at the condition for maximum power at the outlet)? Choose the correct percentage value.

Difficulty: Easy

50%
56.7%
66.67%
76.66%

Correct Answer: 66.67%

Explanation:

Given data
Power transmitted through a pipe with head loss due to friction.

Concept/Approach
For a pipeline delivering power, the power at the outlet is P ∝ Q (H − h_f), with head loss h_f ∝ Q^2. Differentiating w.r.t. flow rate shows maximum power occurs when h_f = H/3. The corresponding efficiency is η = (H − h_f)/H = (H − H/3)/H = 2/3 = 66.67%.

Final Answer
66.67%

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