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GATE 2025 Chemical Engineering, Q43 · Fluid Mechanics

The correct answers are A. ΔP increases with fluid viscosity; B. ΔP increases with pipe length.

Question

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 (ΔP)(\Delta P) is/are TRUE?

  • A. ΔP\Delta P increases with fluid viscosity
  • B. ΔP\Delta P increases with pipe length
  • C. ΔP\Delta P increases with pipe diameter
  • D. ΔP\Delta P remains unchanged with fluid viscosity

Official answer: A. ΔP\Delta P increases with fluid viscosity; B. ΔP\Delta P increases with pipe length

Why

GATE 2025 official key: (A, B). By the Hagen-Poiseuille equation, ΔP=8μLQ/(πR4):ΔP\Delta P = 8μLQ/(πR⁴): \Delta P increases with viscosity μμ (A) and length L (B), and decreases (not increases) with pipe diameter, so (C) and (D) are false.

Explanation cross-checked for consistency. Final answer matches the official IIT answer key.

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