A large flat plate immersed in water is impulsively started from rest and moves in…

PHYSICS · Multi-part · 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 large flat plate immersed in water is impulsively started from rest and moves in its own plane at

U = 0.5\,\mathrm{m\,s^{-1}}

. Water has

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

and

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

. No slip holds at the plate and the fluid is at rest far away. ((a)) Find the wall shear stress

\tau_w

t = 5\,\mathrm{s}

after the start. ((b)) Find the thickness of the layer within which the fluid moves at more than one per cent of

U

, at the same instant.

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