Physics APPH4200 of Fluids: Homework 5
1. K&C, Chapter 8, problem 2. The correct answer for the velocity in the wind tunnel
may seem unrealistic, and strictly, would require us to consider an additional nondimensional parameter not discussed in class, but that is mentioned in the chapter.
Extra credit for saying what this parameter is.
2. Consider the thermal energy equation for an incompressible ow satisfying Fouriers
law, eq. 4.68 of K&C. Non-dimensionalize this equation, assuming a single length
scale and velocity scale. should You obtain one non-dimensional parameter. Interpret this parameter physically, i.e., what does it mean if it is small or large?
3. Review the deep water equations derived in class. Then, describe the gravity surface
waves with viscosity. Assume wavelike solutions, e.g.
= Re{0 ei(kxt) },
where, 0 is a complex amplitude, and the frequency must be assumed complex.
Do the disturbances grow or decay in time? Is this physically reasonable? Verify
that the phase speed reduces to the expected value in the limit 0.
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