Some Examples from past Qualifying Examinations for Section A Briefly discuss each of the following in a couple of sentences. Use no more than a quarter of a page for each answer. A realistic picture of circulation inside a drop as described by potential flow The boundary layer over a wedge, the nature and assumptions The Oseen analysis for the drag of a sphere The primary need for analytical solutions to the Navier-Stokes equation The integral momentum balance equation and it relation to Newton's law of motion The need for integral and dimensional analysis Transition between rotating cylinders at high rotational rates of the inner cylinder with the outer cylinder at rest. Reynolds rules of averaging and why are they necessary to describe turbulent flow Prandtl's mixing length concept: it value and its limitations The 'closure problem' of turbulence: its source and ramifications Why do we use a velocity potential instead of a solution of Euler's equation? How to best describe circulation inside a drop as described by potential flow! The concept of balanced sources and sinks. The boundary layer in a diverging conical shape pipe. The integral momentum balance equation to determine forces on the fluid within a pipe. The mechanical energy balance equation to solve real fluid problems. The eddy viscosity concept and Prandtl's mixing length concepts. The problem associated with using eddy viscosity and mixing lengths at the centerline of a pipe flow. The concept of energy cascade as used in turbulence. The concept of balanced sources and sinks The boundary layer over a circular cylinder The integral energy balance equation and the mechanic al energy balance equation Von Karman's similarity hypothesis The velocity potential Sources and sinks The Stokes' formula for the drag of a sphere The boundary layer over a flat plate The 'closure problem' of turbulence Coherent structures in turbulent shear flows and random turbulent fields The assumptions behind the Navier-Stokes equations. We have considered isothermal flow mostly, how would you approach the problem of non- isothermal laminar flow? What additional equations would you use? How would you extend the analysis for a non-Newtonian material? The concept of energy cascade as used in turbulence The boundary layer assumption and the basis for making the assumption The boundary layer thickness from the Blasius analysis The displacement thickness and its physical meaning The momentum thickness and its physical meaning The von Karman approach for analysis of the boundary layer The boundary layer thickness from the von Karman analysis