# Fluids - boundary conditions for rotating sphere

## Homework Statement

A sphere under uniform rotation R, in a simple shear flow, given at infinity by
ui = G(x2 + c)deltai1
The centre of sphere is fixed at x2

Boundary conditions are ui = EijkRjxk on sphere,
and ui = G(x2 + c) at infinity

## Homework Equations

dij is the kronecker delta
Eijk is the permutation symbol

## The Attempt at a Solution

Just trying to understand the boundary condition on the sphere.

tiny-tim
Homework Helper
hi davcrai!

ui = εijkRjxk is the standard formula for rotational velocity …

usually written v = ω x r, which is the same as vi = εijkωjrk

(in other words, the fluid velocity at the surface of the sphere is the same as the velocity of the surface, as one might expect)

Thanks