A Newtonian fluid of viscosity μ flows laminarly through a radius-R tube under a constant axial pressure gradient, with no slip. At radial position r, which hold?
Correct answer: (A) Velocity ∝(1−r²/R²); (D) Shear stress is zero at r=0
Explanation
For fully developed Poiseuille flow, v(r)=ΔP(R²−r²)/(4μL), a parabolic profile, proving A. Shear stress μdv/dr is proportional to r, zero at the centreline and greatest in magnitude at the wall. Thus D also holds, while B,C fail. Select A,D.
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