For now, we are moving back to inviscid flows. I will remind myself of what a fluid actually is.
What is a fluid?
A fluid is a substance that continues to deform in the presence of sheer stress.
We can model a fluid with a continumm model, where the fluid properties are defined by:
- velocity u(x,t) [vector]
- temperature T(x,t) [scalar]
- density p(x,t) [scalar]
- viscosity mu(x,t) [scalar]
- and many more..
We can also visualise fluids. One way we can do this is by using pathlines and streamlines.
Pathlines are defined as trajectories of marked fluid parcels. These can be written mathematically:
This can also be adapted for polar coordinates:
Streamlines are defined as a curve which is always tangential to the fluid velocity. These can be written mathematically:
We can now use these equations to calculate fluid flows and we can show the graphically.
We have also seen that pathlines and streamlines are identical if they do not depend on time.
Please find below examples on pathlines and streamlines.
This week I need to work on a few more of these examples and try to find some useful links which would help me understand more about how to display the pathlines and steamlines on a graph.
To start of with, I was really struggling to understand pathlines and streamlines, but since we have been working through the example sheets it feels like I’m starting to understand it more and have a go at some of the harder examples.