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GATE 2026 Chemical Engineering, Q65 · Fluid Mechanics

The correct answer is 5.

Question

The velocity profile for fully developed laminar flow of an incompressible Newtonian fluid through a horizontal infinitely wide slit of gap 0.01 m is u(y) =7.5−3×105y2,= 7.5 − 3 \times 10⁵y², where y is measured from the center of the slit. The average velocity of the fluid (in m s−1)s⁻¹) is ____________ (rounded off to the nearest integer).

Official answer: 5

Why

GATE 2026 official key: 5. Averaging u(y) over y ∈ [−0.005, 0.005]: uavg=(1/0.01)×[7.5×0.01−3×105×(2×0.0053/3)]=0.05/0.01=5u_{avg} = (1/0.01) \times [7.5 \times 0.01 − 3 \times 10⁵ \times (2 \times 0.005³/3)] = 0.05/0.01 = 5 m/s.

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

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