Fundamentals of Fluid Mechanics A Syllabus  
Course Objectives, Policies, and Grading
Course Calendar — Weekly Schedule
1.  Course introduction. Ideal gas law, definition of pressure, temperature, density. Collision and attractive forces in fluids. Surface tension, pressure in droplets.
2.  More surface tension examples: capillary rise. Moments and forces in fluids at rest. Conservation of mass in integral form.
3.  Conservation of mass in differential form. Momentum equation in differential form.
4.  Momentum equation in integral form. Accelerating control volume.
5.  Rocket equation derived using the acceleration control volume. Derivation of stagnation pressure and importance in fluid dynamics. Conservation of stagnation pressure on a streamline. Effect of gravity on stagnation pressure.
6.  Choice of reference frame to apply Bernoulli's equation (submarine paradox). Pelton turbine. Energy in a fluid: why another equation is needed. Derivation of 1st law of thermo. Conservation of energy in a fluid: differential form.
7.  Conservation of energy in integral form. Solution of fluid problems with energy equation.
8.  Dimensional analysis principles. Use of dimensional analysis to analyze capillary rise, prototypes in wind tunnels, drag force on sphere.
9.  Further Dimensional analysis examples. Rotational flow and vorticity. Irrotational vs rotational vortices. Velocity potential and stream function for irrotational incompressible flow.
10.  Fundamental solutions to the potential equation: uniform flow, source and sink. Example of potential flow downstream of body.
11.  Fundamental solutions to the potential equation: doublet. Example of potential flow around a cylinder. Circulation. Fundamental solutions to the potential equation: potential vortex.
12.  Example of potential flow around a spinning cylinder: lift and drag calculations. Kutta-Joukowski lift theorem.
13.  Bernoulli equation for potential flow. Virtual hydrodynamic mass concept. Potential flow over a wedge.
14.  Potential flow over a stagnation point. Review problems (if time permits).
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