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GATE 2021 CH – Question 38

Fluid Mechanics and Mechanical Operations · Flow through pipes, friction factors, flow meters and pumps · 2 marks · Multiple choice

Water of density $1000\ \mathrm{kg\,m^{-3}}$ flows in a horizontal pipe of 10 cm diameter at an average velocity of $0.5\ \mathrm{m\,s^{-1}}$. The plot shows the pressure measured at various distances from the pipe entrance. Using the data shown in the figure, the Fanning friction factor in the pipe when the flow is FULLY DEVELOPED is

pressures at distances 1, 2, 3, 4, 5 and 6 m are 1205, 1152, 1112, 1074, 1037 and 1000 Pa, respectively.
  1. 0.0012
  2. 0.0074
  3. 0.0082
  4. 0.0106

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Correct answer: (B) 0.0074

Explanation

Use the downstream region where the pressure gradient becomes constant. Between 4 and 6 m the pressure falls from 1074 to 1000 Pa, giving $\Delta P/L=74/2=37$ Pa/m. The last two one-metre drops are both 37 Pa.

For the **Fanning** friction factor, $\Delta P/L=2f_F\rho\bar V^2/D$. Therefore
$$f_F=\frac{37(0.10)}{2(1000)(0.5)^2}=\mathbf{0.0074}.$$

**Answer: B.** Using entrance-region data or the Darcy factor would give a different result.