Civil Engineering - UPSC Civil Service Exam Questions - Discussion


At the same mean velocity, what is the ratio of head loss per unit length for a sewer pipe flowing full to that for the same pipe flowing half full ?

[A]. 2.0
[B]. 1.7
[C]. 1.0
[D]. 0.6

Answer: Option A


No answer description available for this question.

Sadashiva said: (Aug 23, 2018)  
Head loss due to friction/unit length of pipe is proportional to mean velocity square V^2 and inversely proportional to the diameter D of the pipe.

V = volumetric flow rate remains same.

So, the head loss due to friction: ratio when flowing full / when flowing half full = 1.

Siddesh G M said: (Dec 12, 2018)  
Why not C?

Jinish said: (Jan 21, 2020)  
Head loss = v^2/2g and v= q/a and a=3.14xd^2/4.

So, for full flow D=d and half flow = d/2 now substitute value in head loss then ratio. So, it Will be 2.

Aditya Kumar said: (Jul 24, 2020)  
Use the formula:

Hf= flQ^2/12d^5.
Since all other values will be same other than "d"
For 1st condition - headloss =Q^2/d^5 = (A*V)^2/d^5.
For 2nd condition- headloss = (A*v)^2/d^5, where d = d/2.
divide 1 and 2.
So, the answer is 2.

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