Nose

(Book 18.4)

We can add simple flows and thus make more complicated ones. The reason we can do this is that the Laplace equation for the velocity potential is linear. Or, in terms of the complex potential, the sum of two differentiable functions is differentiable.

Add a source and a uniform flow:

We can replace the fluid coming out of the sink with a solid semi-infinite body:

Conversely, we can get the flow field around a body of this shape in a uniform stream by imagining a source inside the body.

Exercise:

Study the shape more closely:

• Find the location of the stagnation point for given U and m.
• Find the asymptotic thickness of the body.
• What is the mathematical equation for the contour of the body?