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

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

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

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

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

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

If the mass can’t change with time

If the energy can’t change with time

Some common steady flow devices Only one in and one out

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

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

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

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

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

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

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

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.

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

Throttling Valves  h in = h out  P in > P out  For gases that are not ideal, the temperature goes down in a throttling valve  Try Example 5-8

Throttling Valves  What happens if the gas is ideal?  For ideal gases h = C p T But h = 0 So… T = 0 The inlet and outlet temperatures are the same!!!

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

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

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

Mixing Chamber  Material Balance Try example 5-9, page 241

Mixing Chamber Energy Balance Material Balance

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

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

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

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

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

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

Pipe Flow  Try Example 5-11 Electric Heating of Air in a House

It’s time to do some more homework problems  You are now prepared to do any of the problems in the book, up to  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

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