Civil Engineering > GATE 2026 SET-1 > Pipe Flow
In a laminar flow of a Newtonian fluid through a circular pipe of radius 5 cm, the maximum velocity is found to be 2 m/s. The velocity (in m/s) at a radial distance of 2.50 cm from the axis of the pipe is
Correct : c
For laminar (Hagen-Poiseuille) flow in a circular pipe, the velocity distribution is parabolic and given by u(r) = umax × [1 − (r/R)²], where umax is the maximum velocity at the centre (r = 0), R is the pipe radius, and r is the radial distance from the axis.
Given umax = 2 m/s, R = 5 cm, and r = 2.5 cm:
u(2.5) = 2 × [1 − (2.5/5)²] = 2 × [1 − 0.25] = 2 × 0.75 = 1.50 m/s
At exactly half the radius, the velocity is 75% of the maximum, which is a direct consequence of the parabolic profile — each halving of the radius fraction removes only (r/R)² of the maximum, not half of it.
Correct answer: C — 1.50 m/s ✓
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