Water flows through a pipe of 200 mm in diameter 60 m long with a velocity of 2.5 m/s. What is the head loss due to friction using Darcy's formulae ? (Assume f = 0.005) 

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UPSC ESE (Prelims) Civil Engineering 19 Feb 2023 Official Paper
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  1. 1.52 m
  2. 1.79 m
  3. 1.85 m
  4. 1.91 m

Answer (Detailed Solution Below)

Option 4 : 1.91 m
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Detailed Solution

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Explanation:

Darcy-Weisbach Equation

\(h_{f}={fLv^2\over 2gD}\)

Where L = length of pipe 

D = Diameter of pipe

v = Mean velocity of flow

f = Friction factor 

\(h_{f}\) = Head loss due to friction

Calculation:

Given data:

Pipe diameter (D) = 200 mm

Length (L) = 60 m

The velocity of flow (v) = 2.5 m/s

Friction factor (f) = 0.005 × 4 

Head loss due to friction (hf) =?

\(h_{f}={0.005\times 4× 60× 2.5^2\over 2× 9.81× 0.2}\) = 1.91 m

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