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GATE 2025 CH – Question 43

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

For a steady state, fully developed laminar flow of a Newtonian fluid through a cylindrical pipe at a constant volumetric flow rate, which of the following statements regarding the pressure drop across the pipe ($\Delta P$) is/are TRUE?

  1. $\Delta P$ increases with fluid viscosity
  2. $\Delta P$ increases with pipe length
  3. $\Delta P$ increases with pipe diameter
  4. $\Delta P$ remains unchanged with fluid viscosity

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Show answer and explanation

Correct answer: (A) $\Delta P$ increases with fluid viscosity; (B) $\Delta P$ increases with pipe length

Explanation

By the Hagen-Poiseuille equation, $\Delta P = \frac{128\mu LQ}{\pi D^4}$. At constant $Q$, $\Delta P$ increases with viscosity $\mu$ and with length $L$, and it falls strongly (as $D^{-4}$) when the diameter increases. So A and B are true, and C and D are false.