Q.23 If the pipes are connected in parallel, the total loss of head is:
- Athe same in each pipeCorrect
- Bequal to the reciprocal of the sum of head losses in each pipe
- Cequal to the sum of head losses in each pipe
- Dequal to the sum of the squares of head losses in each pipe
Solution
Concept
In parallel pipes, the head loss is the same in each branch. The total flow is the sum of the branch flows.
Formula
hf = hf1 = hf2 = hf3; Q = Q1 + Q2 + Q3
Step-by-step solution
1. In parallel pipes, all branches start at one common junction and end at another common junction. 2. The head difference between these two junctions is the same for every branch. 3. So the head loss in each pipe is equal to the total head loss. 4. The discharge divides among the pipes: Q = Q1 + Q2 + Q3. 5. Answer is (A).
Explanation
Parallel pipes join the same two points. The head difference between these two points is fixed, so every pipe has the same head loss. The flow is shared, but the loss is not added.
Why the other options are wrong
(B) There is no reciprocal rule for head loss. (C) Adding head losses is the rule for pipes in series, not parallel. (D) The sum of squares of head losses has no physical meaning here.
Shortcut
Series: losses add, flow same. Parallel: loss same, flows add.
Common mistake
Mixing up the series and parallel rules and choosing the sum of head losses.
Correct answer: A) the same in each pipe