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MAE 320 Thermodynamics HW 5 Assignment

The homework is due Friday, March 13th, 2015. Each problem is worth the points indicated. Copying of the solution from another is not acceptable.

1. Multiple choices questions (18 points)

(1a). Please circle the invalid statements regarding the control volume:

(A) Under the steady-flow condition, the volume, mass and energy contents of a control volume always remain constant with time.

(B) Under the steady-flow condition, the fluid properties at an inlet or exit always remain constant with time but their values at the inlet and exit can be different.

(C) Under the steady-flow condition, the intensive properties of the substance at any location must be homogeneous (uniform) everywhere inside a control volume.

(D) Gas turbines, throttling valves, nozzles and diffusers operated under steady condition can be treated as the steady-flow control volume systems.

(1b). Please circle the invalid statement(s) regarding heat exchangers

(A) Heat exchangers are devices where two moving fluid streams are mixed together to obtain the same temperature.

(B) Heat exchangers are devices where two moving fluid streams exchange the mass. (C) Heat exchangers are devices where two moving fluid streams exchange the thermal energy

(heat) without mixing together. (D) There is no heat transfer between the two fluids in an insulated heat exchanger.

(1c). Please circle the invalid statement(s) regarding a steady-flow control volume device?

(A) The mass within the control volume always remains constant with time (B) The energy within the control volume always remains constant with time (C) The fluid properties may change with location over the cross section of the inlets or exits. (D) The fluid flow at any point of any inlet and exit is uniform and steady, and the fluid properties

do not change with time or location over the cross section of an inlet or exit. (1d). For diffusers, we generally consider

(A)

W =0 (B) ke 0

(C)

Q >0 (D) pe 0

(1e). The change in the kinetic energy can usually be ignored for

(A) Diffusers (B) Nozzles (C) Throttling valves (D) Heat exchangers

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(1f). Steam (H2O) flows through a pipe at mass flow rate of 10kg/hour, pressure of 200 kPa and temperature of 300 oC. The specific flow energy of steam in the pipe is closest to (A) 263.2 kJ/kg (B) 2808.8 kJ/kg (C) 3072.1 kJ/kg (D) 3072.1 kJ

2. Concept and short answer questions (20 points)

(2a) Please draw a schematic diagram of an electricity powered hot water tank designed to continuously provide hot water for a shower system, describe the thermodynamic process involved, and list the assumptions, equations, and parameters needed for you to find the energy needed. (4 points)

(2b)The general equation of 1st law of thermodynamics for control volume system can be expressed as equation (a):

( ) ( )dt

dEpekehmpekehmWQ CVoutoutinin =+++++ (a)

Please list the assumptions needed for this general equation to be simplified to equation (b), which can be applied to calculate the power output of turbine.

( )outinturbine hhmW = (b). (4 points)

(2c). Water enters an adiabatic throttling valve at 1 MPa and 400 C, and exits at 200 kPa. Neglecting the change in the kinetic energy and the potential energy, please find the temperature of water exiting this throttling valve. (6 points)

(2d). Please find the heat transfer needed when a 10 kg of watermelon is heated from 5 C to 15C. (6 Points)

3. Water enters a steadily operating steam turbine with a flow rate of 10 kg/s at 60 bar and 800 C, and exits at 1 bar and 120 C at a velocity of 100 m/s. The heat loss from turbine to ambient air is 100 kW. You can ignore the change in the potential energy, and the kinetic energy at inlet. (12 points)

(a) List the terms that can be ignored in this question. (b) Find the cross-section area of the exit port, in m2. (c) Find the power output from this turbine, in kW. 4. Nitrogen at 80 kPa and 400 K enters an adiabatic diffuser steadily at a flow rate of 6000 kg/h at 200 m/s and leaves at 100 kPa at 40 m/s. (12 points) (a) Draw a schematic diagram of a diffuser, and describe its main functions (2 points) (b) Find the exit temperature of nitrogen (6 points) (c) The cross-section area at the exit of the diffuser (4 points)

5. An adiabatic compressor compresses the R-134a from 2 bar, 0oC to 4 bar and 50oC at a flow rate of 0.02 kg/s. Ignoring the changes in the potential energy and the kinetic energy, determine (10 points) (a) The volume flow rate of R-134a at the exit.

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(b) The power needed for this compressor; 6. An heat exchanger is designed to cool 60 kg/min of water vapor at 2 bar and 400 oC to a saturated liquid at 100 kPa. The cooling water is taken from a local river at an inlet at 15 oC. After passing through the condenser, the temperature of the cooling water is not allowed to exceed 20 oC as regulated by the environmental code. Please determine the minimum mass flow rate of cooling water. (12 points)

7. A 4 L (volume) of pressure cooker operates at 200 kPa with an exit area of 10 mm2. With well controlled heat transfer from electrical range, liquid water is vaporized to saturated vapor, which exits the pressure cooker at a constant mass flow rate. Initially, the pressure cooker contains 3 kg of saturated water. After two hours of cooking operation, 2 kg of saturated water vapor left the pressure cooker. During this process, the heat loss from the pressure cooker to the ambient air is 100 kJ. The changes in the potential energy can be ignored. (16 points)

a) The water exits this pressure cooker at constant velocity. Please explain whether this pressure cooker is operating under steady-flow process or not.

b) Find the exit velocity of saturated vapor, in m/s c) Find the specific volume, quality, total internal energy of water in pressure cooker at State 1 and

State 2; d) The heat transferred from the range to the pressure cooker during this process, in kJ; e) With the assumed 100% efficiency of the range in converting electricity to heat, and the price of

electricity is 10 cents per kWh, please find the cost of electricity during this cooking process.

P1=2bar T1=400 oC

m s=60 kg/min

P2=200 kPa

m s=60kg/min

T3=15 oC

m w=?

T4, max=20 oC

m w=?