Chemegate

GATE 2024 Chemical Engineering, Q33 · Fluid Mechanics

The correct answer is 0.019 to 0.021.

Question

Consider the steady, uni-directional, fully-developed, pressure-driven laminar flow of an incompressible Newtonian fluid through a circular pipe of inner radius 5.0 cm. The magnitude of shear stress at the inner wall of the pipe is 0.1N/m2.0.1 N/m². At a radial distance of 1.0 cm from the pipe axis, the magnitude of the shear stress, in N/m2,N/m², rounded off to 3 decimal places, is ______

Official answer: 0.019 to 0.021

Why

GATE 2024 official key: 0.019 to 0.021. For laminar pipe flow, shear stress varies linearly with radius: τ(r)=τwall(r/R)=0.1×(1/5)=0.02N/m2.τ(r) = τ_{wall}\cdot (r/R) = 0.1 \times (1/5) = 0.02 N/m².

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