Question

# While using Darcy-Wesibach equation for estimating head loss in a pipe flow, the friction factor was misjudged by +20% for this case, the error in estimating discharge is

A
+ 10%
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B
+ 40%
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C
- 40%
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D
- 10%
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Solution

## The correct option is D - 10%The head loss through the pipe is given by hL=fLQ212.1D5 If all the parameters remain same other than friction factor and discharge then fQ2=constant Let this constant be C, then fQ2=C ⇒ Q2=Cf ....(i) Differentiating Q w.r.t f, we get 2QdQ=C×(−1f2)df......(ii) Dividing (ii) by (i), we get 2QdQQ2=C×(−1f2)dfCf ⇒ 2dQQ=−dff ⇒ dQQ=12×dff ⇒ dQ=−Q2×dff ⇒ dQ=−1002×20100 ⇒ dQ=−10%

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