Project ForgeFluid Mechanics
Flow Through Pipes
GATE 2020
Hard
A Bingham plastic flows in fully-developed laminar flow through a tube of radius 0.01m, with ΔP=10kPa over L=1.0m. The velocity profile is flat for r<rc and parabolic for r≥rc. A force balance gives d(rτrx)/dr=r(−ΔP)/L. If rc=0.001m, the magnitude of the yield stress (Pa) is
- A1
- 5
- C8
- D12
Explanation
Integrating with τrx finite at r=0 gives τrx(r)=r·ΔP/(2L). The yield stress equals the shear stress exactly at the plug boundary r=rc: τ0=rc·ΔP/(2L)=0.001×10,000/2=5 Pa.
Source: GATE CH 2020 (2020)
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