The loss of head in a pipe carrying turbulent flow varies i. directly as square of the velocity of flow ii. directly as length of flow iii. inversely as square of the velocity of flow iv. inversely as length of flow
- AOnly (i)
- BOnly (i) and (ii)Correct
- COnly (i) and (iv)
- DOnly (ii) and (iii)
Solution
Concept
Head loss in turbulent pipe flow
Formula
hf = (f × L × v2) / (2 × g × d)
Step-by-step solution
1. According to the Darcy-Weisbach equation, friction head loss in turbulent pipe flow is given by hf = (f × L × v2) / (2 × g × D). 2. Head loss varies directly as the length of flow and directly as the square of the flow velocity. Answer: B
Explanation
According to the Darcy-Weisbach equation, frictional head loss in turbulent pipe flow is directly proportional to pipe length and the square of the flow velocity. It is also inversely proportional to pipe diameter rather than velocity or length. Thus, statements i and ii are true, making option B the correct choice.
Why the other options are wrong
A) Statement (i) alone is incomplete as statement (iv) is also true. D) Statement (iii) is incorrect as head loss varies directly as square of velocity.
Shortcut
Darcy-Weisbach equation (hf proportional to L·V2): Head loss varies directly with length and velocity squared.
Common mistake
Confusing turbulent flow head loss relationship (proportional to velocity squared) with laminar flow head loss (proportional to velocity).
Correct answer: B) Only (i) and (ii)