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GATE 2021 MT – Question 44

Transport Phenomena and Rate Processes · Fluid flow and momentum transfer · 2 marks · Multiple choice

Fully developed one-dimensional Newtonian flow in a horizontal pipe of radius $R$ has $v_z=(\Delta P/L)(R^2-r^2)/(4\mu)$. Here $\Delta P=P_1-P_2$, viscosity is $\mu$, radial coordinate is $r$, and tube length is $L$. The fluid’s wall shear stress is ______.

Diagram for GATE 2021 MT question 44
  1. $\Delta PR/(2L)$
  2. $\Delta PR/L$
  3. $3\Delta PR/(2L)$
  4. $2\Delta PR/L$

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Correct answer: (A) $\Delta PR/(2L)$

Explanation

Differentiate Poiseuille velocity: dv/dr=−ΔPr/(2μL). Newtonian shear magnitude at r=R is μ|dv/dr|=**ΔPR/(2L), A**. The fluid exerts a downstream traction on the wall of that magnitude.