Incompressible Flow 4 - Ideal Flow over a Sphere

Question 1

What is ideal flow around a sphere?

Answer 1

Steady, incompressible, inviscid flow
No surface friction

Question 2

Approach to find properties of ideal flow around sphere

Answer 2

Find a stream function that satisfies the flow conditions
Work out velocity and pressure distributions

Question 3

Navier-Stokes equation for ideal flow around a sphere

Answer 3

Reduces to Bernoulli’s equation along a streamline

Question 4

Define superposition

Answer 4

New stream function may be constructed by the sum of the existing stream functions

Question 5

What combination of models is used to draw ideal flow over a sphere?

Answer 5

Uniform flow + doublet (source+sink)

Question 6

Observations of ideal flow over a sphere

Answer 6

Maximum speed at the top of the surface
Symmetrical pressure before and after sphere

Question 7

What combination of drawings can be used for ideal flow over a sphere?

Answer 7

Uniform flow + doublet (source+sink)

Question 8

Observations of ideal flow over a sphere

Answer 8

Maximum speed at top of the surface
Symmetrical pressure distribution before and after (no drag) - not correct in reality
Boundary layer development and separation missing from this model