Wind blows along the face of a skyscraper facade panel at ; take the along-wind…

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Viscous flow and dynamical similarity · Viscous flow and dynamical similarity

Fluid Dynamics, Ch Scaling, similarity and similarity solutions

Problem

Wind blows along the face of a skyscraper facade panel at

U = 25\,\mathrm{m\,s^{-1}}

; take the along-wind length of the panel array as

L = 4.0\,\mathrm{m}

and use

\rho = 1.20\,\mathrm{kg\,m^{-3}}

and

\nu = 1.51\times10^{-5}\,\mathrm{m^2\,s^{-1}}

for air. ((a)) Form

Re = UL/\nu

, say which balance sets the pressure scale, and give that pressure scale in pascals. ((b)) Estimate

\delta \sim L\,Re^{-1/2}

, the thickness of the region next to the facade where the viscous term returns to order one, and explain why the inviscid slip velocity there does not decrease as

Re

is made larger still. ((c)) If the facade were instead suddenly set moving from rest at speed

U

through still air, as a flat plate moving in its own plane (a limiting model), give the similarity variable and the form of

u/U

from the Pi theorem and linearity, and say for roughly how long this form can hold, given the array's length

L

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