Flow around a cylinder

This week we will be going through some examples where we can apply Bernouilli’s equation.

We were first looking at a flow around a cylinder. Before we could do anything, we have to make observations of this. We need to see if:

  • Flow tangential to cylinder.
  • Streamlines = Solid surfaces in inviscid flow.
  • Neglect boundary layer effects due to viscosity.

We are given the stream function:

CodeCogsEqn (16)

If we play around with this equation, getting terms for Ur and Utheta when r=a:

We can now substitute this into Bernouilli’s equation which is:

CodeCogsEqn (15)

We get:

CodeCogsEqn(8)

Ps is the stagnation pressure at the point where u=0.

We have also looked at Potential flow this week. This describes the velocity field as the gradient of a scalar function; the velocity potential.

Sources:

Picture and definition. http://en.wikipedia.org/wiki/Potential_flow

Example sheet 4, question 1:

IMG_0092[1] IMG_0094[1]

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