A water jet strikes a cylindrical rod of radius head-on with outer stream speed far…

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

Fluid Dynamics, Ch The Navier-Stokes equations and unsteady exact solutions

Problem

A water jet strikes a cylindrical rod of radius

a = 3.0\,\mathrm{cm}

head-on with outer stream speed

U = 2.0\,\mathrm{m\,s^{-1}}

far from the rod. Near the nose the outer flow behaves as Hiemenz stagnation-point flow with strain rate

S = 2U/a

. Water has

\rho = 998\,\mathrm{kg\,m^{-3}}

and

\mu = 1.00\times10^{-3}\,\mathrm{Pa\,s}

. Find the thickness of the layer near the nose within which the flow is within one per cent of the outer flow.

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