2 For next time:Read: § 5-4HW7 due Oct. 15, 2003Outline:Diffusers and nozzlesTurbinesPumps and compressorsImportant points:Know the standard assumptions that go with each deviceKnow how to simplify the governing equations using these assumptionsConsider what each device would be used for in real-world applications
3 Applications to some steady state systems Start simplenozzlesdiffusersvalvesInclude systems with power in/outturbinescompressors/pumpsFinish with multiple inlet/outlet devicesheat exchangersmixers
4 We will need everything we have covered Conservation of massConservation of energyProperty relationshipsIdeal gas equation of stateProperty tablesSystematic analysis approach
5 Nozzles and DiffusersNozzle--a device which accelerates a fluid as the pressure is decreased.V2, p2V1, p1This configuration is for subsonic flow.
6 Nozzles and DiffusersDiffuser--a device which decelerates a fluid and increases the pressure.V2, p2V1, p1
7 For supersonic flow, the shape of the nozzle is reversed. Nozzles
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 TEAMPLAYFor 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.
33 Turbines We’ll assume steady state, Sometimes neglected Almost always neglected
34 TurbinesWe will draw turbines like this:inletwmaybe qoutlet
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 differencesCompressor - used to raise the pressure of a compressible fluidPump - used to raise pressure or potential of an incompressible fluidFan - primary purpose is to move large amounts of gas, but usually has a small pressure increase
37 Compressors, pumps, and fans Side view End viewCentrifugal pumpAxial flow Compressor
40 Sample ProblemAir 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.
47 TEAMPLAYUse 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 TEAMPLAYUnder “Plot” select “New Plot Window” and “X-Y Plot”.