Past exam of the mathematics course of the University of Cambridge / 2022 / ib / Paper 3 / 7C / a

Table of contents
- Solution a

Solution

Choose the polar axis along

d

and write

d = ∣ d ∣

. Since

d = d (cos θ e_{r} - sin θ e_{θ}),

the velocity components are

u_{r} = \frac{d c o s θ}{r ^{2}}, u_{θ} = \frac{d s i n θ}{r ^{2}} .

Their divergence is

\nabla \cdot u = \frac{1}{r} \frac{\partial}{\partial r} (r u_{r}) + \frac{1}{r} \frac{\partial u _{θ}}{\partial θ} = - \frac{d c o s θ}{r ^{3}} + \frac{d c o s θ}{r ^{3}} = 0.

Thus the flow is incompressible for $r \neq = 0$ .

 Ancestors (10)

 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