A dolphin's dorsal fin of chord moves through water at ; use and for water.

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

A dolphin's dorsal fin of chord

L = 0.25\,\mathrm{m}

moves through water at

U = 4.0\,\mathrm{m\,s^{-1}}

; use

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

and

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

for water. ((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 fin where the viscous term returns to order one, and explain why the inviscid slip velocity at the fin's surface does not shrink as

Re

is increased further. ((c)) If the fin were instead suddenly set into motion from rest at speed

U

through still water, treat its surface locally as a flat plate moving in its own plane. Give the similarity variable and the form of

u/U

implied by the Pi theorem and linearity, and say for roughly how long this form can hold, given that the fin has its own length

L

Browse the problem library