Chapter(s) : Ch 3 Due Date : April 21, 2011 Total Problems / Points : 10 / 65

Cengel & Boles: Ch 5:

5.35 - Adiabatic Steam Nozzle - 5 pts
5.54 - Adiabatic Gas Turbine - 5 pts
5.112 - Steam Flow in a HEX Tube - 5 pts
5.138 - Filling a Balloon with Helium - 10 pts
5.142 - Charging a Cylinder with a Spring-Loaded Piston - 8 pts

Special Problems
WB-1 - Effluent Pressure in a Non-Adiabatic Steam Diffuser - 5 pts
WB-2 - Steady-State, Polytropic Air Compressor - 5 pts
WB-3 - Analysis of a Two-Stage, Adiabatic Turbine - 6 pts
WB-4 - Analysis of an Adiabatic Steam De-Superheater - 8 pts
WB-5 - Waste Heat Steam Generator - 8 pts

 WB-1 Effluent Pressure in a Non-Adiabatic Steam Diffuser - 5 pts Problem Statement : Steam enters a diffuser at a pressure of 14.7 psia, a temperature of 300°F 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. Hints : The keys to this problem are the 1st Law for open systems and the relationship between mass flow rate, volumetric flow rate, velocity, specific volume and cross sectional area for flow. Ans.: P2 ≈ 61 psia
 WB-2 Steady-State, Polytropic Air Compressor - 5 pts Problem Statement : Air enters a compressor at steady-state with a pressure of 14.7 psia, a temperature of 70°F, and a volumetric flow rate of 500 ft3/min. The air velocity in the exit pipe is 700 ft/s and the exit pressure is 120 psia. If each unit mass of air passing through the compressor undergoes a process described by PV1.34 = constant, determine the exit temperature, in oF, and the diameter of the exit pipe in inches. Hints : The keys to this problem are the ideal gas equation of state and the relationship between mass flow rate, volumetric flow rate, velocity, specific volume and cross sectional area for flow. Remember to verify whether the IG EOS is applicable at both the inlet and outlet conditions. Ans.: T2 ≈ 440°F , D2 ≈ 0.68 in
 WB-3 Analysis of a Two-Stage, Adiabatic Turbine - 6 pts Problem Statement : A well-insulated two-stage turbine operating at steady-state is shown in the diagram. Steam enters at 3 MPa and 400°C 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 180°C. 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. Hints : The key to this problem is the splitter. It is just like a tee in a pipe. So, the properties of streams 2, 3 & 4 are the same. A fast solution for part (a) can be done by applying the 1st Law to the entire system and solving the equation simultaneously with a mass balance on the entire system...2 equations in two unknowns. Ans.: m4 ≈ 3 kg/s, D4 ≈ 29 cm
 WB-4 Analysis of an Adiabatic Steam De-Superheater - 8 pts Problem Statement : As shown in the diagram, 15 kg/s of steam enters a de-superheater operating at steady-state at 30 bar and 320°C 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 = 200°C, 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 220°C. Hints : This problem is an application of the multiple-inlet, multiple-outlet (MIMO) form of the 1st Law. The de-superheater behaves much like a mixer except the outlet pressure is not necessarily the same as the inlet stream pressures. Interpolation between saturated liquid and the lowest pressure subcooled liquid table is required in order to determine the enthalpy of the subcooled liquid entering the de-superheater. Use Excel to construct your plot. Make columns for T3, Psat(T3), Hsatliq(T3), H3 and m3. The values of Psat(T3) and Hsatliq(T3) come from the steam tables, NIST or the TFT add-in. Enter the interpolation formula for H3 in the first cell in the H3 column and FIX the row and column of all the cells other than the cell for H3 by using "\$" for the cell references. For example: \$C\$14. Then, just copy the formula for this cell down to fill the column and complete the interpolation calculations for all of the H3 values. Put a formula in the last column for m3 (using the \$ method again) and then copy the formula downward to complete the table. Use the Excel chart wizard to help you construct a nice looking, fully-labeled plot. Ans.: a.) H3 ≈ 850 kJ/kg , m3 ≈ 1.8 kg/s
 WB-5 Waste Heat Steam Generator - 8 pts Problem Statement : At steady-state, water enters the waste heat recovery steam generator shown in the diagram at 42 psia and 220°F and exits at 40 psia and 320°F. 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 360°F and 1 atm with a volumetric flow rate of 3000 ft3/min and exits at 280°F 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-°F. Hints : The key here is to aply the 1st Law to the HEX to determine the mass flow rate of the water in streams 1, 2 & 3. Then, apply the 1st Law to the turbine to determine its power output in hP. The analysis of the turbine is straightforward. The analysis of the HEX can be approached in at least two different ways that yield the same result. The key is that the HEX does not exchange heat with the surroundings. Therefore, all of the heat that leaves the air enters the water. Assume each device is adiabatic, changes in kinetic and potential energies are negligible and the air behaves as an ideal gas with a constant CP. Ans.: m1 ≈ 2.8 lbm/min , WS ≈ 13 hP