Past exam of the mathematics course of the University of Cambridge / 2020 / ii / Paper 3 / 38B / b / i

Table of contents
- Solution i

Solution

Conservation of volume flux through a circular arc of radius

r

gives

α r (- u_{r}) = α Q,

so the outer flow is the sink flow in a sector

u_{r} = - \frac{Q}{r}, u_{θ} = 0, ψ = - Qθ .

This is a potential flow and already satisfies the no-penetration boundary condition on the radial walls. It has nonzero tangential speed

Q / r

there, however, and therefore violates the no-slip boundary condition. Thin vorticity-bearing boundary layers are needed to reduce that speed to zero at each wall.

 Ancestors (11)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version