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GATE 2025 MT – Question 31

Transport Phenomena and Rate Processes · Fluid flow and momentum transfer · 1 mark · Multiple select

Consider fully developed, steady, one-dimensional laminar flow of a Newtonian liquid through a pipe. Its maximum velocity is proportional to which quantities? Given: $\Delta P$ is the difference between outlet and inlet pressure; $\mu$ is dynamic viscosity; $R$ and $L$ are the pipe radius and length.

  1. $\Delta P$
  2. $1/R^2$
  3. $1/\mu$
  4. $1/L$

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Show answer and explanation

Correct answer: (A) $\Delta P$; (C) $1/\mu$; (D) $1/L$

Explanation

Hagen–Poiseuille flow gives vmax=(Pin−Pout)R²/(4μL). Its magnitude is linear in pressure difference and inverse in viscosity and length, while it grows as R² rather than 1/R². Thus **A,C,D**. With the stated outlet-minus-inlet convention, the signed expression includes a minus sign.