The Navier-Stokes equations for incompressible Newtonian fluids (NSe) is the foundation for much of fluid mechanics. Three quarters of our course was simply about illustrating their power, and how to apply them in an organized manner.

(1) State in your own words what are the 3 key steps that got us and our ancestors from Newton’s Second Law for parcels-of-fluid to the NSe. Be specific about what was needed, for example, to quantify a particular part of the momentum equation, or what makes it awkward to deal with parcels of water. [9]

(2) Even for homogeneous fluids no general solution for the NSe has been found. Describe three methods that we used to overcome this problem and simplify the NSe. [9]

(3) On top of the issue above, there is the turbulence closure problem. Describe it and use the zonal NS equation (i.e., in $x$) to illustrate its connection to Reynolds averaging. [7]