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Solving Problems in Thermodynamics - Examples and Solutions

## Problem 1: Air Heating and Flow Rate Determination

1. Air enters a 30-cm diameter pipe steadily at 250 kPa and 50°C with a velocity of 7 m/s. Air is heated as it flows and leaves the pipe at 180 kPa and 40°C. Determine the following: [MO1, MO2]

a. The volume flow rate of air at the inlet
b. The mass flow rate of air
c. The velocity and volume flow rate at the exit

2. A pump increases the water pressure from 100 kPa at the inlet to 1000 kPa at the outlet. Water enters this pump at 20°C through a 1-cm-diameter opening and exits through a 1.5-cm-diameter opening. Determine the velocity of the water at the inlet and outlet when the mass flow rate through the pump is 0.5 kg/s. Will these velocities change significantly if the inlet temperature is raised to 40°C? [MO1, MO2]

3. The refrigerant-134a enters a valve at 800 kPa and 32°C. The pressure downstream of the valve is measured to be 80 kPa. Calculate the internal energy downstream. Neglect kinetic energy changes. [MO1, MO2, MO5]

4. A pump is used to increase the pressure of water from 100 kPa to 20 MPa. The water enters at 25°C and exits at 40°C. The mass flow rate of water is 15kg/s. The heat loss from the pump is 15kW. Determine the power required by the pump. [MO1, MO2, MO3]

5. Water vapor is passed through a nozzle. The water enters at 0.3 MPa. 500K. At a velocity of 5 m/s, and exits the nozzle at 0.1MPa, 460K, and 75 m/s. The cross-sectional area of the inlet is 0.005 m2. Determine the following: [MO2, MO5]

a. The mass flow rate of the water vapor
b. The rate of heat transfer that occurs in the nozzle

6. An insulated air compressor receives 3 ft3/sec of air from the surrounding at 14.7 psi and 75°C. The air exits the compressor at 75 psi and 420°F. Assuming that there are no significant changes in potential or kinetic energy, determine the power consumed by the compressor using an assumption of constant specific heat. [MO2, MO3, MO4]

7. Air enters an insulated compressor at 400K and 15 m/s and exits at 1000 K and 60 m/s. The mass flow rate of the air is 15 kg/s, and the cross-sectional area of the outlet is 0.075 m2. Considering that the specific heats of the air are variable, determine the following: [MO2, MO3, MO5]

a. The pressure of the air at the compressor outlet
b. The power used by the compressor

8. Refrigerant-134a enters an insulated diffuser as a saturated vapor at 80°F with a velocity of 800 ft/s. The inlet area is 1.5 in2. At the exit, the pressure is 400 lbf/in2 and the velocity is negligible. The diffuser operates at steady state and potential energy effects can be neglected. Determine the mass flow rate, in lb/s, and the exit temperature, in °F. [MO4, MO5]

9. Steam enters a converging-diverging nozzle at steady state with P1 = 40bar T1 = 400°C and a velocity of 12m/s. The steam flows through the nozzle with negligible heat transfer and no significant change in potential energy. At the exit P2 = 15bar and the velocity is 700 m/s. The mass flow rate is 2.5 kg/s. Determine the exit area of the nozzle in m2. [MO1, MO2, MO5]

10. The pressure of 250kg/s of water is to be increased by 5MPa. The water enters through a 22-cm diameter pipe and exits through a 15-cm diameter pipe. Calculate the minimum horsepower required to operate the pump. [MO1, MO2, MO3]