A pipe carrying 0.05 m3/s of water suddenly contracts from 30 cm to 15 cm in diameter. Then the coefficient of contraction is _________ when the loss of head is 0.5 m. 

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JKPSC Lecturer Paper I Civil 2022 Official Paper
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  1. 0.89
  2. 0.23
  3. 0.47
  4. 0.65

Answer (Detailed Solution Below)

Option 3 : 0.47
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Detailed Solution

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Explanation:

Loss of head due to sudden contraction:

h = \(KV^2\over 2g\)

h = \((V_c - V_2)^2\over 2g\) = \({V^2\over 2g}({1\over C_c} -1)^2\)

K = \(({1\over C_c} -1)^2\)

where

Cc = Coefficient of contraction

Vc = Velocity at the contracted portion

V2 = velocity after contraction

Calculation:

Q = 0.05 m3/s

h = 0.5 m

A =  (π/4)× 0.152 = 0.01767

V = Q/A = 0.05/0.01767 = 2.8296 m/sec

K = h(2g)/V2 = (0.5× 2× 9.81)/(2.8296)2 = 1.2252

Now

K = \(({1\over C_c} -1)^2\)

\(({1\over C_c} -1)^2\) = K

\(({1\over C_c} -1)^2\) = 1.2252

\(({1\over C_c} -1)\) = 1.10688

CC = 0.474

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