To obtain an in-dept understanding of fluid mechanics theory, model problems, fundamental elementary solutions, and various flow regimes as represented by dimensionless parameters. Understanding model reduction via scaling and develop the capability to independently model, analyse and solve flow prolems.
- Knowing the conservation laws of fluid mechanics and the stress tensor, and regimes of flow
- Ability to analytically solve fundamental problems in fluid mechanics
- Understanding the concept of vorticity
- Understanding potential flow and knowing fundamental solutions of the Laplace equation.
- Being able to use fundamental solutions of the Laplace equation to solve potential flow problems
- Knowing and being able to scale the flow equations and derive relevant dimensionless numbers
- Able to derive the thin layer equations for boundary layers, free surface layers, and confined layers in lubrication assumption.
- Able to indepently study relevant problem and describe results in technical report.
To obtain an in-dept understanding of fluid mechanics theory, model problems, fundamental elementary solutions, and various flow regimes as represented by dimensionless parameters. Understanding model reduction via scaling and develop the capability to independently model, analyse and solve flow prolems.
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Fluid Mechanics II is the sequel to the introductory course Fluid Mechanics I and provides essential fundamental insights into the nature of the flow equations, flow regimes and solutions of problems in specific regimes. The course aids the ability to develop solve flow problems, to find approximate solutions, and provides essential knowledge to interpret numerically obtained solutions in the future engineering or scientific career.
The first part proceeds by careful re-introduction of the conservation laws and the stress tensor. An extensive set of fundamental flow problems is discussed and solved analytically. The concept of vorticity is introduced and several transport theorems are derived and discussed. The reduced-order model of potential flow is presented and the fundamental solution of the Laplace equation is derived and used to formulate a boundary integral formulation of the potential flow. The resulting models can be used to obtain good engineering approximations to many flow problems.
The second part of the course addresses the equations and the behaviour of flow in the specific regime of thin layers is considered. First the scaling of the Navier Stokes equations is considered. Next, the case of the thin layer scaling (Lubrication assumption) is considered. The Navier Stokes equations and energy equation in the thin layer limit are presented. Subsequently equations for boundary layers, thin free surface layers, and confined layers are derived and discussed including the concept of self-similarity with many practical model problems as illustration.
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