Question: A nuclear rocket nozzle of circular cross section has the geometry shown in Fig. The working fluid is helium, and the stagnation pressure and temperature are 2100 kPa and 2475 K, respectively. Assuming one dimensional isentropic flow, constant specific heats, and a specific heat ratio of 1.67, calculate the mass flow rate and the gas pressure, temperature, and density as functions of distance along the axis. Then, assuming that a laminar boundary layer originates at the corner where the convergence starts, calculate the momentum thickness of the boundary layer and the momentum thickness Reynolds number as functions of

distance along the surface. Assume that a transition to a turbulent boundary layer takes place if and when the momentum thickness Reynolds number exceeds 162. An approximate analysis may be carried out on the assumption of constant fluid properties, in which case let the properties be those obtaining at the throat. Alternatively, a better approximation can be based on the results of Prob. 11·5. In either case it may be assumed that the viscosity varies approximately linearly from µ = 5.9 x 10-5 Ns/m2 at 1400 K to fl = 8.3 X 10-5 Ns/m" at 2500 K.