A thin film of water is sheared so that , ,

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Kinematics, conservation laws and ideal flow · Kinematics, conservation laws and ideal flow

Fluid Dynamics, Ch Kinematics in three dimensions and Cauchy's equation of motion

Problem

A thin film of water is sheared so that

u=Gy

v=0

w=0

, with

G=200\,\mathrm{s^{-1}}

(

y

in metres). A tiny spherical float is embedded in the film, small enough to be carried by the local rigid rotation of the fluid without disturbing the flow. ((a)) Compute the vorticity

\boldsymbol\omega=\nabla\times\mathbf u

of this flow. ((b)) Find the angular speed and axis about which the float spins. ((c)) State this spin rate in revolutions per second.

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