A schematic diagram of a turbo jet engine is shown below. The incoming air is decelerated...

 

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A schematic diagram of a turbo jet engine is shown below. The incoming air is decelerated in the diffuser from the flight velocity to a negligible velocity relative to the engine. The air is then sent through the compressor, the constant-pressure combustor, and the turbine, before going out through the thrust nozzle. The entirety of the work generated by the turbine is used to drive the compressor. The nozzle accelerates the flow to the exit velocity to produce thrust. Changes in potential energy can be neglected in the engine. (a) Write an equation for the velocity of the gas at the nozzle exit (V6) in terms of the inlet enthalpy, h1, the inlet velocity, V1, the exit enthalpy, h6, and the heat added in the combustor, Q/m. Assume that the flow rate of fuel into the combustor adds a negligible amount of mass flow to the air, that the compressor, turbine, nozzle, and diffuser are well insulated, and that kinetic energy changes are negligible for the compressor, combustor, and turbine. (b) Assuming that the air is an ideal gas, compute the thrust produced by the engine. At the inlet of the diffuser, the velocity of the air is V1 = 250 m/s, the temperature is T1 = 0 C, the density is 1.276 kg/m3, and the diameter is 48.9 in. At the exit of the nozzle, the temperature of the gas is T6 = 600 C. The energy input into the flow in the combustor per unit mass of air flowing is Q/m = 730 kJ/kg. The equation for the thrust is F = m (V6-V1). (c) If the power input required by the compressor per unit mass air flowing is W/m = 500 kJ/kg, determine the turbine inlet temperature, T4. Compressor Diffuser 2 OLE m Combustor W m Turbine Nozzle A schematic diagram of a turbo jet engine is shown below. The incoming air is decelerated in the diffuser from the flight velocity to a negligible velocity relative to the engine. The air is then sent through the compressor, the constant-pressure combustor, and the turbine, before going out through the thrust nozzle. The entirety of the work generated by the turbine is used to drive the compressor. The nozzle accelerates the flow to the exit velocity to produce thrust. Changes in potential energy can be neglected in the engine. (a) Write an equation for the velocity of the gas at the nozzle exit (V6) in terms of the inlet enthalpy, h1, the inlet velocity, V1, the exit enthalpy, h6, and the heat added in the combustor, Q/m. Assume that the flow rate of fuel into the combustor adds a negligible amount of mass flow to the air, that the compressor, turbine, nozzle, and diffuser are well insulated, and that kinetic energy changes are negligible for the compressor, combustor, and turbine. (b) Assuming that the air is an ideal gas, compute the thrust produced by the engine. At the inlet of the diffuser, the velocity of the air is V1 = 250 m/s, the temperature is T1 = 0 C, the density is 1.276 kg/m3, and the diameter is 48.9 in. At the exit of the nozzle, the temperature of the gas is T6 = 600 C. The energy input into the flow in the combustor per unit mass of air flowing is Q/m = 730 kJ/kg. The equation for the thrust is F = m (V6-V1). (c) If the power input required by the compressor per unit mass air flowing is W/m = 500 kJ/kg, determine the turbine inlet temperature, T4. Compressor Diffuser 2 OLE m Combustor W m Turbine Nozzle