A pipe is connected in series to another pipe whose diameter is twice and the length is 32 times that of the first. The ratio of the frictional head losses for the first pipe to that of the second pipe by assuming both the pipes to have same frictional coefficient f is
- A8
- B4
- C2
- D1Correct
Solution
Concept
Head loss in series pipes
Formula
hf = 4 f L Q²/(π² g D⁵ ...) ∝ L/D⁵
Step-by-step solution
1. Same Q: hf ∝ L/D⁵. 2. Pipe 2: L2 = 32 L1, D2 = 2 D1 ⇒ L2/D2⁵ = 32 L1/(32 D1⁵) = L1/D1⁵. 3. Ratio hf1/hf2 = 1.
Explanation
The length factor 32 is exactly cancelled by D⁵ = 32.
Why the other options are wrong
8, 4 and 2 do not equal 1.
Shortcut
hf ∝ L/D⁵.
Common mistake
Using hf ∝ L/D².
Correct answer: D) 1