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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: Applying the definition that w=0 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 Problem:Assumptions**

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 problem:diagram and basic information**

OUTLET P2=167 kPa V2=35 m/s INLET T1=300C P1=100 kPa V1=250 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 - 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

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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.

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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: 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 We’ll 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 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.

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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 = 60F P1 = 15 psia OUTLET T2 = 400F**

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Apply First Law: 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”.

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