Lec 13: Machines (except heat exchangers)

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Lec 13 Machines (except heat exchangers)
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• For next time
• Read 5-4
• HW7 due Oct. 15, 2003
• Outline
• Diffusers and nozzles
• Turbines
• Pumps and compressors
• Important points
• Know the standard assumptions that go with each
  device
• Know how to simplify the governing equations
  using these assumptions
• Consider what each device would be used for in
  real-world applications

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Applications to some steady state systems

• Start simple
• nozzles
• diffusers
• valves
• Include systems with power in/out
• turbines
• compressors/pumps
• Finish with multiple inlet/outlet devices
• heat exchangers
• mixers

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We will need everything we have covered

• Conservation of mass
• Conservation of energy
• Property relationships
• Ideal gas equation of state
• Property tables
• Systematic analysis approach

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Nozzles and Diffusers

• Nozzle--a device which accelerates a fluid as the
  pressure is decreased.

V2, p2
V1, p1
This configuration is for subsonic flow.
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Nozzles and Diffusers

• Diffuser--a device which decelerates a fluid and
  increases the pressure.

V2, p2
V1, p1
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For supersonic flow, the shape of the nozzle is
reversed.
Nozzles
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General shapes of nozzles and diffusers
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Common assumptions for nozzles and diffusers

• Steady state, steady flow.
• Nozzles and diffusers do no work and use no work.
• Potential energy changes are usually small.
• Sometimes adiabatic.

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TEAMPLAY

• For nozzles, diffusers and other machines--just
  how important is ?PE?
• The energy in the head of a kitchen match is
  reportedly about 1 Btu.
• How far does 1 lbm have to fall in a standard
  earth gravity field to match this much energy?
• Example 5-12 on p. 175 has an enthalpy change h1
  - h2 less than 20 Btu. What does your result
  mean physically for a nozzle or diffuser?

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We start our analysis of diffusers and nozzles
with the conservation of mass
If we have steady state, steady flow, then
And
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We continue with conservation of energy
We can simplify by dividing by mass flow
0
0
0
Applying the definition that w0 and using some
other assumptions...
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We can rearrange to get a much simpler expression
With a nozzle or diffuser, we are converting flow
energy and internal energy, represented by Dh
into kinetic energy, or vice-versa.
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Sample Problem
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Sample ProblemAssumptions

• SSSF (Steady state, steady flow) - no time
  dependent terms
• adiabatic
• no work
• potential energy change is zero
• air is ideal gas

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Sample problemdiagram and basic information
OUTLET P2167 kPa V235 m/s
INLET T1300?C P1100 kPa V1250 m/s m 7 kg/s
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Sample Problem apply basic equations
Conservation of Mass
Solve for A2
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How do we get specific volumes?
Remember ideal gas equation of state?
or
and
We know T1 and P1, so v1 is simple. We know P2,
but what about T2?
NEED ENERGY EQUATION!!!!
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Sample problem - cont
Energy
V1 and V2 are given. We need h2 to get T2 and
v2.
If we assumed constant specific heats, we could
get T2 directly
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Sample problem - cont
However, use variable specific heats...get h1
from air tables at T1 300273 573 K.
From energy equation
This corresponds to an exit temperature of 602.2
K.
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Now we can get solution.
and
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TEAMPLAY
Work problem 5-65
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Throttling Devices (Valves)
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Short tube orifice for 2.5 ton air conditioner
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Throttles (throttling devices)

• A major purpose of a throttling device is to
  restrict flow or cause a pressure drop.
• A major category of throttling devices is valves.

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Typical assumptions for throttling devices

• Do no work, have no work done on them
• Potential energy changes are zero
• Kinetic energy changes are usually small
• Heat transfer is usually small

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Look at energy equation
Apply assumptions from previous page
0
0
0
0
We obtain
or
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Look at implications
If fluid is an ideal gas
cp is always a positive number, thus
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Discussion Question
Does the fluid temperature
increase,
decrease, or
remain constant
as an ideal gas goes through an adiabatic valve?
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TEAMPLAY
Refrigerant 134a enters a valve as a saturated
liquid at 200 psia and leaves at 50 psia. What
is the quality of the refrigerant at the exit of
the valve?
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Turbine

• A turbine is device in which work is produced by
  a gas passing over and through a set of blades
  fixed to a shaft which is free to rotate.

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Turbines
Well assume steady state,
Sometimes neglected
Almost always neglected
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Turbines

• We will draw turbines like this

inlet
w
maybe q
outlet
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Compressors, pumps, and fans

• Machines developed to make life easier, decrease
  world anxiety, and provide challenging problems
  for engineering students.
• Machines which do work on a fluid to raise its
  pressure, potential, or speed.
• Mathematical analysis proceeds the same as for
  turbines, although the signs may differ.

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Primary differences

• Compressor - used to raise the pressure of a
  compressible fluid
• Pump - used to raise pressure or potential of an
  incompressible fluid
• Fan - primary purpose is to move large amounts of
  gas, but usually has a small pressure increase

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Compressors, pumps, and fans

Side view End view Centrifugal pump
Axial flow Compressor
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Sample Problem
Air initially at 15 psia and 60F is compressed
to 75 psia and 400F. The power input to the air
is 5 hp and a heat loss of 4 Btu/lb occurs during
the process. Determine the mass flow in lbm/min.
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Draw Diagram
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Assumptions

• Steady state steady flow (SSSF)
• Neglect potential energy changes
• Neglect kinetic energy changes
• Air is ideal gas

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What do we know?
INLET T1 60?F P1 15 psia
OUTLET T2 400?F P2 75 psia
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Apply First Law
0
0
0
0
Simplify and rearrange
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Continuing with the solution..
Get h1 and h2 from air tables
Follow through with solution
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TEAMPLAY
Work problem 5-73E
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TEAMPLAY

• Use EES and vary the exit pressure from 5 psia to
  0.5 psia in increments of 1.0 psia. Show the
  results as a table and a plot.
• Open EES and put in the basic equation

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TEAMPLAY

• You will have to use some new features of EES
• 1. Under options always check and set unit
  system, if necessary.
• 2. Under options, find function info, and select
  fluid properties.
• 3. For steam, use Steam_NBS.

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TEAMPLAY

• Parametric studies
• Under Tables, select New Parametric Table
• Click and drag the variables you want to see to
  the right--P2, Qdot, and h2.
• See that P2 is not specified in the problem
  statement in the Equations Window.

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TEAMPLAY

• Enter P2 via Alter Values under Tables
• Click on the column headings to be able to enter
  units.
• You must solve the table before you can plot it.
• Under Calculate select Solve Table.

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TEAMPLAY

• Under Plot select New Plot Window and X-Y
  Plot.