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:
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:
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.
Picture and definition. http://en.wikipedia.org/wiki/Potential_flow
Example sheet 4, question 1: