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GATE 2016 ME (ME3) – Question 49

Fluid Mechanics · Flow through pipes, head losses, bends and fittings · 2 marks · Numerical answer

Consider a fully developed steady laminar flow of an incompressible fluid with viscosity µ through a circular pipe of radius R. Given that the velocity at a radial location of R/2 from the centerline of the pipe is U1, the shear stress at the wall is KµU1/R, where K is __________

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Correct answer: 2.6 to 2.7

Explanation

Laminar fully developed pipe flow has u(r)=u_max[1−(r/R)²]. Therefore U₁=u(R/2)=3u_max/4, giving u_max=4U₁/3. Wall-shear magnitude is μ|du/dr|_R=2μu_max/R=(8/3)μU₁/R. Hence **K=2.6667**.