1. Carbon dioxide gas flows through a well-insulated nozzle operating at steady state. At the inlet, the pressure is 5…

1. Carbon dioxide gas flows through a well-insulated nozzle operating at steady state. At the inlet, the pressure is 5 bar, the temperature is 450 K and the velocity is 100 m/s. At the exit, the pressure is 300 kPa and the temperature is 420 K. Ignore the effects of the potential energy, and assume the ideal gas model is applicable.

a. find the gas velocity at the nozzle exit

b. find the ratio of the nozzle exit area to inlet area.

2. (10 points) The inlet to a hydroelectric plant is located at an elevation of 100 m above the exit. The inlet duct has a diameter of 0.8 m and the exit duct has a diameter of 1.1 m. Water enters with a velocity of 11.3 m/s, a pressure of 15 bar and a temperature of 25°C. The water then passes through a turbine operating at steady state with negligible changes in temperature. Neglecting any heat transfer between the turbine and its surroundings, find the power developed by the turbine at steady state operation if the exit pressure is 2 bar. (Hint: use the incompressible substance model)

3. (10 points) Air enters a device operating at steady state at 10 bar, 600 K, and leaves at 1 bar, 460 K with a volumetric flow rate of 2.8 m3 /s. The specific heat transfer to the air is 560 kJ/(kg of air flowing). Neglecting kinetic and potential energy effects, determine:

a. The power developed/required, in kW

b. The volumetric flow rate at the inlet in m3 /s

4. (10 points) Steam enters a turbine operating at steady state at 600°C and 10 bar with a velocity of 60 m/s and leaves as a saturated vapor at 0.2 bar with a velocity of 120 m/s. The power developed by the turbine is 130 kW. Heat transfer from the turbine to the surroundings occurs at a rate of 25 kW. Neglecting the potential energy effects, determine the mass flow rate of the steam.

5. (10 points): A horizontal diffuser operating at steady state is used to slow the flow of CO2. The inlet volumetric flow rate is 10 m3 /s, and the inlet temperature and pressure are 600 K and 200 kPa, respectively. The exit area to inlet area ratio is 5. Specific heat transfer from the diffuser was determined to be 100 kJ/kg. The exit temperature and pressure are 580 K and 300 kPa, respectively. Determine the volumetric flow rate and the velocity at the exit.

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