Course overview
This course introduces the mathematical modelling of fluid flow. Learners will formulate the partial differential equations governing fluid flow based on the principles of conservation of mass and momentum. They will solve these models in a number of special cases relevant to common physical situations, including inviscid flow, irrotational flow, flows with conservative forces and very viscous flow. Skills in interpretating mathematical results in the context of real-world problems will also be developed.
Course learning outcomes
- Find the equations of pathlines, streamlines and streaklines for a given flow field, and be able to change from Eulerian to Lagrangian flow descriptions
- Recall the continuity, Euler and Navier-Stokes equations, and able to derive them from the principles of mass and momentum conservation
- Recall the definition of the streamfunction for two dimensional or axisymmetric flows, and be able to calculate the streamfunction for such flows
- Formulate and solve problems in inviscid flow by applying appropriate theories and techniques from the course e.g., potential flow theory, Bernoulli’s streamline theorem, complex potential and conformal mapping
- Formulate and solve problems in viscous flow e.g. plane and pipe Poiseuille flow, plane Couette flow, paint scraper problem by applying appropriate theories and techniques from the course
- Interpret and explain the results from mathematical models of flows in the context of the physical problem being studied and be able to critique when the assumptions underpinning the model may lead to unrealistic predictions
Degree list
The following degrees include this course