Wednesday, October 22, 2008

TE 303 - HW #5, P1 - Adiabatic Steam Nozzle - 10 pts

Steam at 3 MPa and 400oC enters an adiabatic nozzle at a velocity of 40 m/s and leaves at 2.5 MPa and 300 m/s. Determine…

a.) The temperature of the steam when it leaves the nozzle.

b.) The ratio of the inlet cross-sectional area to the outlet cross-sectional area, A1 / A2.

Assume the process operates at steady-state.

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TE 303 - HW #5, P2 - Adiabatic Gas Turbine - 10 pts

Argon gas enters an adiabatic turbine at 900 kPa and 450oC with a velocity of 80 m/s and leaves at 150 kPa and a velocity of 150 m/s. The inlet cross-sectional area is 60 cm2. If the power output of the turbine is 250 kW, determine the exit temperature of the argon. The process operates at steady-state and argon behaves as an ideal gas.

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TE 303 - HW #5, P3 - Effluent Pressure in a Non-Adiabatic Steam Diffuser - 10 pts

Steam enters a diffuser at a pressure of 14.7 psia, a temperature of 300oF and a velocity of 500 ft/s. Steam exits the diffuser as a saturated vapor with negligible kinetic energy. Heat transfer occurs from the steam to the surroundings at a rate of 19.59 Btu/lbm of flowing steam. Neglecting potential energy effects, determine the exit pressure in psia. Assume the diffuser operates at steady-state.

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TE 303 - HW #5, P4 - Analysis of a Two-Stage, Adiabatic Turbine - 12 pts

A well-insulated two-stage turbine operating at steady-state is shown in the diagram. Steam enters at 3 MPa and 400oC with a volumetric flow rate of 85 m3/min. Some steam is extracted from the turbine at a pressure of 0.5 MPa and a temperature of 180oC. The rest expands to a pressure of 6 kPa and a quality of 90%. The total power developed by the turbine is 11,400 kW. Changes in kinetic and potential energies are negligible. Determine:

a.) The mass flow rate of the steam at each of the two exits.

b.) The diameter in meters of the duct through which the 0.5 MPa steam is extracted if the velocity there is 20 m/s.

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TE 303 - HW #5, P5 - COMPUTER ANALYSIS: Adiabatic Steam De-Superheater - 15 pts

As shown in the diagram, 15 kg/s of steam enters a de-superheater operating at steady-state at 30 bar and 320oC where it is mixed with liquid water at 25 bar and temperature T3 to produce saturated vapor at 20 bar. Heat transfer between the device and its surroundings and changes in kinetic and potential energies are negligible.

a.) If T3 = 200oC, determine the mass flow rate of stream 3.

b.) Plot the mass flow rate of stream 3 in kg/s as a function of T3 as T3 ranges from 20 to 220oC.

Note that the use of ThermalFluids will avoid the need to interpolate in this problem!

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TE 303 - HW #5, P6 - Pump Horsepower Requirment - 10 pts

The pump shown here increases the pressure in liquid water from 200 to 4000 kPa.

What is the minimum horsepower motor required to drive the pump for a flow rate of 0.1 m3/s ?

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TE 303 - HW #5, P7 - Waste Heat Steam Generator - 15 pts

At steady-state, water enters the waste heat recovery steam generator shown in the diagram at 42 psia and 220oF and exits at 40 psia and 320oF. The steam is then fed into a turbine from which it exits at 1 psia and a quality of 90%.

Air from an oven exhaust enters the steam generator at 360oF and 1 atm with a volumetric flow rate of 3000 ft3/min and exits at 280oF and 1 atm. Ignore all heat exchange with the surroundings and any changes in potential and kinetic energies. Determine the power developed by the turbine in horsepower.

CP,air = 7.05 Btu/lbmole-oF.

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TE 303 - HW #5, P8 - Transient Heating of an Office Space - 18 pts

The air supply to a 20000 ft3 office has been shut off overnight to conserve utilities, and the room temperature has dropped to 40oF. In the morning, a worker resets the thermostat to 70oF, and 200 ft3/min of air at 120oF begins to flow into the office through a heating duct. The air is well-mixed within the room and an equal mass flow of air at room temperature is withdrawn through a return duct. The air pressure is essentially 1 atm everywhere. Ignoring heat exchange with the surroundings, as well as any changes in kinetic or potential energies, estimate how long it takes for the room temperature to reach 70oF. Assume g = 1.4 for the air.

This is a transient or unsteady process because helium enters the system (the balloon). Assume the He behaves as an ideal gas, but check to see if this is a good assumption. Use the IG EOS to determine the initial mass of He in the balloon. After you determine V2, calculating Wb is easy ! Then, simultaneously solve two equations in two unknowns. The equations are: the IG EOS applied to the final state of the balloon and the transient form of the 1st Law applied to this process. The two unknowns are: T2, mHe,2 .
The catch is that we must determine values for U1, U2 and Hin. These are NOT ΔU's and ΔH's but real U's and H's. In order to do this (just like the steam tables) we MUST choose a reference state. A reference state is a T, P and phase at which YOU choose to make EITHER U or H zero kJ/kg. I want you to use a reference state of U = 0 for He gas at 22 oC and 100 kPa. The P doesn't actually matter because He is treated as an IG in this problem so U and H are not functions of P anyway.

Once you have a ref state, use a Hypothetical Process Path from the ref state to states 1, 2 and inlet to evaluate U1, U2 and Hin using the IG EOS and CV and CP given in the problem.

For He, use: CP = 5.1926 kJ/kg-K and CV = 3.1156 kJ/kg-K.

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