1. Lec 13: Machines (except heat exchangers)

2. 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

3. 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

4. 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

5. 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.

6. Nozzles and Diffusers
Diffuser--a device which decelerates a fluid and increases the pressure.
V2, p2
V1, p1

7. For supersonic flow, the shape of the nozzle is reversed.
Nozzles

8. General shapes of nozzles and diffusers

9. 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.

10. 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?

11. We start our analysis of diffusers and nozzles with the conservation of mass
If we have steady state, steady flow, then:
And

12. We continue with conservation of energy
We can simplify by dividing by mass flow:
Applying the definition that w=0 and using some other assumptions...

13. 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.

14. Sample Problem

15. Sample Problem:Assumptions
SSSF (Steady state, steady flow) - no time dependent terms
adiabatic
no work
potential energy change is zero
air is ideal gas

16. Sample problem:diagram and basic information
OUTLET
P2=167 kPa
V2=35 m/s
INLET
T1=300C
P1=100 kPa
V1=250 m/s
m = 7 kg/s

17. Sample Problem: apply basic equations
Conservation of Mass
Solve for A2

18. 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!!!!

19. Sample problem - con’t 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

20. Sample problem - con’t
However, use variable specific heats...get h1 from air tables at T1 = = 573 K.
From energy equation:
This corresponds to an exit temperature of K.

21. Now we can get solution.
and

22. TEAMPLAY
Work problem 5-65

23. Throttling Devices (Valves)

24. Short tube orifice for 2.5 ton air conditioner

25. 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.

26. 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

27. Look at energy equation:
Apply assumptions from previous page:
We obtain: or

28. Look at implications: If fluid is an ideal gas:
cp is always a positive number, thus:

29. Discussion Question Does the fluid temperature increase, decrease, or
remain constant
as an ideal gas goes through an adiabatic valve?

30. 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?

31. 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.

33. Turbines We’ll assume steady state, Sometimes neglected
Almost always neglected

34. Turbines
We will draw turbines like this:
inlet w
maybe q
outlet

35. 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.

36. 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

37. Compressors, pumps, and fans
Side view End view
Centrifugal pump
Axial flow Compressor

40. Sample Problem
Air initially at 15 psia and 60°F is compressed to 75 psia and 400°F. 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.

41. Draw Diagram

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

43. What do we know? INLET T1 = 60F P1 = 15 psia OUTLET T2 = 400F

44. Apply First Law:
Simplify and rearrange:

45. Continuing with the solution..
Get h1 and h2 from air tables
Follow through with solution

46. TEAMPLAY
Work problem 5-73E

47. 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

48. 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.

49. 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”.

50. 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.”

51. TEAMPLAY
Under “Plot” select “New Plot Window” and “X-Y Plot”.