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Mass and Energy Analysis of Control Volumes

Mass and Energy Analysis of Control Volumes. Chapter 5a. In Chapter 4…. In the last chapter we looked at closed systems For example a piston-cylinder device is a closed system We developed an energy balance for closed systems We used a closed system analysis to define C p and C v.

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Mass and Energy Analysis of Control Volumes

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  1. Mass and Energy Analysis of Control Volumes Chapter 5a

  2. In Chapter 4… • In the last chapter we looked at closed systems • For example a piston-cylinder device is a closed system • We developed an energy balance for closed systems • We used a closed system analysis to define Cp and Cv

  3. Now we can move on to Control Volumes • How are control volumes different from closed systems? • What effect does this have on the energy balance? Energy can flow in with the matter We are interested in rates

  4. Material Balance • We also need to worry about a material balance, since matter can flow in and out

  5. Methalpy Total Energy of a flowing fluid Remember this from chapter 2? The fluid possesses an additional form of energy –the flow energy (flow work)

  6. The flow work is included in the enthapy term This work represents everything but the flow work We can rewrite the energy balance using the rate form of the equation

  7. This is getting pretty complicated! • Let’s look at a special case • The Steady flow process • A process during which a fluid flows through a control volume steadily • Steady means no change with time

  8. If the mass can’t change with time

  9. If the energy can’t change with time

  10. Some common steady flow devices Only one in and one out

  11. Single Stream Steady Flow System • Nozzles • Diffusers • Turbines • Compressors • Throttling Valve Often the change in kinetic energy of the fluid is small, and the change in potential energy of the fluid is small

  12. Nozzles and Diffusers A nozzle is a device that increases the velocity of a fluid at the expense of pressure A diffuser is a device that slows a fluid down

  13. Nozzles and Diffusers What happened to the m? It divided out NO Is there work in this system? Is there heat transfer? Usuallyit can be ignored Does the fluid change elevation? NO

  14. In a nozzle, enthalpy is converted into kinetic energy How can you find the mass flow rate in a nozzle? Try examples 5-4 and 5-5

  15. Turbines and Compressors A turbine is a device that produces work at the expense of temperature and pressure A compressor is a device that increases the pressure of a fluid by adding work to the system

  16. Turbines and Compressors Yes! Is there work in this system? Is there heat transfer? Usuallyit can be ignored Does the fluid change elevation? NO Usuallyit can be ignored Does the kinetic energy change?

  17. Turbines and Compressors Try Examples 5-6 (Compressor) and 5-7 (Turbine)

  18. Throttling Valve A throttling valve reduces the fluid pressure For example, the water that comes into your house goes through a throttling valve, so it doesn’t have excessive pressure in your home.

  19. Throttling Valve NO Is there work in this system? Is there heat transfer? Usuallyit can be ignored NO Does the fluid change elevation? Usuallyit can be ignored Does the fluid change velocity?

  20. Throttling Valves • hin = hout • Pin > Pout • For gases that are not ideal, the temperature goes down in a throttling valve • Try Example 5-8

  21. Throttling Valves • What happens if the gas is ideal? • For ideal gases • Dh = CpDT • But Dh = 0 • So… DT = 0 • The inlet and outlet temperatures are the same!!!

  22. Throttling Valve For an ideal gas, the temperature does not change in a throttling valve!!!

  23. Mixing Chamber Mixing two or more fluids is a common engineering process Mixing Chamber

  24. Is there any work done? No Is there any heat transferred? No Is there a velocity change? No No Is there an elevation change? Mixing Chamber We no longer have only one inlet and one exit stream

  25. Mixing Chamber • Material Balance Try example 5-9, page 241

  26. Mixing Chamber Energy Balance Material Balance

  27. Heat Exchanger A heat exchanger is a device where two moving fluids exchange heat without mixing.

  28. Heat Exchangers Your analysis approach will depend on how you define your system

  29. Heat Exchangers • Energy balance is the same as a mixing chamber, but… • Two inlets • Two outlets • Material Balance • Divide into two separate streams with equal inlet and outlet flow rates • Try example 5-10

  30. Pipe Flow A steady flow model is usually a good approximation W Q

  31. . Pipe Flow There’s work going into the pump There’s an elevation change

  32. Pipe Flow Sometimes Is there work in this system? Is there heat transfer? Usually Does the fluid change elevation? Sometimes Not usually Does the kinetic energy change?

  33. Pipe Flow • Try Example 5-11 • Electric Heating of Air in a House

  34. It’s time to do some more homework problems • You are now prepared to do any of the problems in the book, up to 5-120 • Do the assigned problems, and as many additional problems as you need to feel comfortable • Be sure to review the example problems in the text

  35. Next time … • We’ll finish chapter 5 • The remaining material covers control volumes that are not at steady state

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