Essential problems all students must work through once:
- Bernoulli effect (euler)
- Channel and pipe flow, laminar solution (they should see
parabolic velocity profile, gives a good idea of what
viscosity does, also shows importance of boundary conditions
on flows)
- Linear drag coefficient of sphere, at least discuss cylinder
result to show strong dependence on longest dimension
only (viscous flow, linearized `stokes' hydrodynamics)
- Reynolds number and Kolmogorov picture of turbulence
(see L&L for disturbingly rigorous-looking discussion of
the latter topic)
I'm sure there are other important things but if I had to
give an overview of hydrodynamics these would be the things
I would harp on.