Drilling mud is pumped along a horizontal pipe of radius and length under a pressure…

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Solid continuum mechanics and complex fluids · Solid continuum mechanics and complex fluids

Bending, Ringing, Breaking and Flowing, Ch Non-Newtonian and viscoelastic fluids

Problem

Drilling mud is pumped along a horizontal pipe of radius

R = 25\,\mathrm{mm}

and length

L = 12\,\mathrm{m}

under a pressure drop

\Delta p = 60\,\mathrm{kPa}

between the ends. The mud behaves as a Bingham plastic with yield stress

\tau_y = 40\,\mathrm{Pa}

. ((a)) Find the radius

r_{\rm plug}

of the unyielded core at the centre of the pipe. ((b)) Find the minimum pressure gradient

(\Delta p/L)_{\rm min}

needed for the mud to move at all, and confirm that the applied gradient exceeds it.

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