A venule of radius and length carries blood of viscosity under a pressure difference…

PHYSICS · Subjective · Fermi University Physics · Fluids & Continuum Physics · Biophysics & Medical Physics · Viscous flow and dynamical similarity

Life at Thermal Energy, Ch Bones, muscles, blood and body size

Problem

A venule of radius

a = 20\,\mathrm{\mu m}

and length

L = 2.0\,\mathrm{mm}

carries blood of viscosity

\eta = 3.5\,\mathrm{mPa\,s}

under a pressure difference of

10\,\mathrm{mmHg}

between its ends. Treat the flow as steady and laminar in a long rigid tube (

1\,\mathrm{mmHg} = 133\,\mathrm{Pa}

). Use Poiseuille's law,

Q_{\rm v} = \pi a^4\Delta p/(8\eta L)

, to find the volume flow rate through the venule.