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Question

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 _____
  1. 2.66

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Solution

The correct option is A 2.66

Shear stress at the wall,

τ0=τmax=KμU1R

We know that the velocity at any point for laminar flow through pipe,

u=14μ(px)(R2r2)

At r=R2,u=U1

U1=14μ(px)(R2R24)

=14μ(px)34R2

=316μ(px)R2

τo=KμR×316μ(px)R2

=316K(px)R

We know that maximum shear stress at wall,

τo=R2px

316K(px)R=R2px

or K=83=2.66

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