Consider a rocket nozzle as shown in the figure to the right. Because the gases coming from the combustion chamber are so hot and at high pressure, the rocket nozzle needs to be cooled, especially in the region of the throat. Cooling O Channels h, (a) Develop an algebraic expression that gives the velocity of the exhaust fluid (u.) as a function of h the inlet fluid's stagnation enthalpy (hai). the exhaust fluid's static enthalpy (h), and the heat lass per unit mass of flow entering the nozzle (Q/m). u, (b) If 75 kg's of burned propellants enter the nozzle at a stagnation enthalpy of 10 MJkg the static enthalpy of the propellants at the nozzle exit is 5 MJkg and the heat loss from the nazzle required to maintain a uniform nozzle wall temperature of 727C is 50 MW, find the velocity of the propellants at the nozzle exit. (c) Propellants typically enter the nozzle at a sufficiently low Mach number that the stagnation and static enthalpies can be considered the same. If the gas flowing through this nozzle had a specific heat ratio of y = 1.3 and a molecular weight of W, = 7.3 g/mol, what would be the temperature change across the nozle? (d) What is the entropy change of the gas across the nazzle, i.e., (Sai -Se), assuming the flow is reversible? (Hint: See the integral form of the entropy conservation equation. You mayassume the low Mach number condition holds.)