Read my notes on Boyle’s Law and Viscosity. Do the following questions based on those notes:
1. The density of
air at room temperature is about 1.29 kg/m3. Use this together with the definition of 1
atm above to find the constant C in the Law of Atmospheres written
above. Use you result to estimate the atmospheric pressure on top of the Blue
Ridge (say 4000 feet), Snowmass (11,000 feet) and Mount Everest (29,000 feet).
2. Suppose a mass m of fluid moving at v1 in the x-direction mixes with a mass m moving at v2 in the x-direction. Momentum conservation tells us that the mixed mass 2m moves at ½( v1 + v2). Prove that the total kinetic energy has decreased if v1, v2 are unequal.
3. Plot on a graph the velocity profiles for two rivers, one of depth h and one 2h, having the same values of r, g, q and h. What is the ratio of the surface velocities of the two rivers? Suppose that one meter below the surface of one of the rivers, the water is flowing 0.5 m×sec-1 slower than it is flowing at the surface. Would that also be true of the other river?
Also do from Halliday page 344: 54P, 55P, page 345: 59.