A mustard sauce is a Bingham plastic with plastic viscosity and yield stress

PHYSICS · Subjective · 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

A mustard sauce is a Bingham plastic with plastic viscosity ηp=50 Pa s\eta_p = 50\,\mathrm{Pa\,s} and yield stress τy=90 Pa\tau_y = 90\,\mathrm{Pa}. It is to be pushed through a pipe of radius R=8 mmR = 8\,\mathrm{mm} and length L=4 mL = 4\,\mathrm{m} under a pressure drop Δp=3 kPa\Delta p = 3\,\mathrm{kPa}. Someone works: V˙=πR4Δp8ηpL=π(0.008 m)4(3000 Pa)8(50 Pa s)(4 m)≈2.4×10−8 m3 s−1\dot V = \frac{\pi R^4 \Delta p}{8\eta_p L} = \frac{\pi (0.008\,\mathrm{m})^4(3000\,\mathrm{Pa})}{8(50\,\mathrm{Pa\,s})(4\,\mathrm{m})} \approx 2.4\times10^{-8}\,\mathrm{m^3\,s^{-1}} and concludes the sauce flows at this rate. Find the error in this reasoning, and give the correct flow rate.

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