HW5_SOLN EGR/MET 340 - Thermo-Fluids I - HOMEWORK SET 5|ALL YOU NEED

EGR/MET 340 - Thermo-Fluids I - HOMEWORK SET 5 (It is due on Tuesday, Apr. 1 at the beginning of the class period.) TOTAL POINTS: 100 NAME: ______________________________________ Recommended Reading/Additional Problems for further practice: It will be best to study these problems before attempting the homework problems. Examples 5.15, 5.16, 5.17, Self Test 5.11 pp. 358-363. Problem 1: The main engine of the Space Shuttle utilizes a converging-diverging nozzle to expand high-pressure, high-temperature propellant to very high exhaust speeds. Let’s calculate the engine’s performance by assuming ideal gas and constant γ=1.2 throughout our calculations. Operation is steady state. a) The rocket engine combusts liquid hydrogen, H2 with liquid oxygen, O2 after they are mixed at an average boiling temperature of Tb = 70K. The heat released per unit mass during the approximately isobaric combustion is 13 MJ/kg. (Also referred to as the heat of combustion similar to the heat of vaporization we discussed in class.) It raises the stagnation temperature to To=3000K at stagnation pressure of po=200atm. Use the first law of thermodynamics to calculate the molecular weight of the combusted propellant mixture and then calculate its density. (We can assume that the combustion chamber is a closed system.) [10] b) The propellant is then expanded through the converging-diverging nozzle to an exhaust temperature of 800K and pressure of 0.05atm. Assuming steady-state, adiabatic expansion, develop an expression for the exhaust velocity, Uex by properly simplifying the mass and energy conservation equations. Then calculate Uex. [10] c) The thrust from the engine is about F = 400,000lbf , ( F=mUex ɺ ). Calculate the exit diameter of the nozzle assuming 1-D normal flow. [5] Problem 2: A well-insulated turbine operating at steady state develops 10MW of power for a steam flow rate of 20kg/s. The steam enters at 320o C with a velocity of 25m/s and exits as saturated vapor at 0.06bar with a velocity of 90m/s. Sketch the T-υ diagram and identify the inlet and exit states and determine the inlet pressure, in bar. Neglect potential energy effects. [15] Problem 3: Air enters a compressor operating at steady state at a pressure of 1bar, a temperature of 290K and a velocity of 6m/s through an inlet wit