Okay. Welcome back.

Hopefully, that was a pretty simple exercise.

So, we saw that under study state conditions we know that all time

variables are steady for the viewer. So, all time variant terms, like this

control volume term here, would be set equal to zero for the steady state

condition. If you have a system that's adiabatic you

would set all heat transfer terms equal to zero.

And again they don't alwyays happen at the same time.

You don't always involve both of those assumptions together.

But they're both pretty common. And in fact what we're going to look at

now are a number of very common flow devices.

Steady state steady flow devices well we're going to see those two assumptions

alot. So in fact we're going to say these

aren't just simple flow devices. We're going to call all of these devices

simple steady-flow devices. So this is a conservation of energy in

its most general form. As we've learned how to use these tools,

like the conservation of mass and the conservation of energy, I want you to

write out the four most generic, most general form of the expressions every

single time. It's going to be your instinct to try and

simplify these on the fly, so you simplify them as you're writing them

down. Oh yeah, and I'll invoke this, and I'll

assume there's one exit and two entrances, or things like that.

And that type of work, once you're. Once you've had a lot of experience

that's fine to use those type of methods, but for now when you're just getting

started with the introduction to these tools it's better to be very very careful

and very very rigorous. So we're going to use these big forms of

these expressions every time, as we get a feel for how these devices perform and

what are some of the governing principles for the devices, okay.

So we're going to start. We're going to look at like five or six

different categories of flow devices. We're going to assume every one of these

devices is steady flow. So for every one of these, that steady

flow and steady state. And you say, what's the difference?

Steady state addresses the time variable. Steady flow is really saying that we have

steady uniform conditions at the entrances and exits.

So that we can in fact define thermodynamic properties.

If they're undefined, like if something's changing and it's unsteady flow And I

can't define all velocity or a pressure or a temperature.

So that's, these are very specific assumptions that we're going to invoke

for all of these flow devices. And these are velocities, again just to

remind ourselves, those are velocity terms there.

So for nozzles and diffusers, these are simple systems that we'll find a lot of

flow systems you'll find them in agriculture.

You'll find them in turbo machinery like you find in power plants.

You'll find them in common, household devices.

You'll have nozzles and diffusers on your faucets on your hoses all sorts of

places. So a nozzle is a contracting surface, and

a diffuser is an expanding service. I'll draw them like this, and we always

want to get into the practice of again identifying what the system is, so we'll

draw our control volume around our nozzles.

So this my nozzle here and this is my diffuser over here.

And I always think the best example that most people understand right away.

For a nozzle, is imagine putting your thumb over the end of a garden hose.

That's a nozzle and you think to yourself, okay, is there any work

transfer in this process? So, look for mentally go through your

checklist. Are there any shafts portruding into or

out of the system? Do I have any electrical cords?

Hopefully not near water. In the into or out of the system.

You're like, nope, nope. You go through the checklist.

Expansion or compression? No, these are rigid control volumes.

So the volumes are fixed, so there's no expansion or compression work.

So both my nozzles and diffusers have, by definition, no work associated with that.

The other thing I wanted you to think about is when we consider heat transfer,

you have to consider heat transfer through the system boundary, and a couple

of, again we've seen the approximation of when things are adiabatic.

What does it do to the control conservation of energy.

Well, we've applied this simplification, the steady state simplification.

when we consider the heat transfer, you have to consider things like well, what

are the, when you become more advanced in your heat transfer analysis, you'd think,

Okay. What are the temperature differences that

we're considering? What are the mechanisms, convective,

conduction, radiation. And one of the things you have to

consider, the radiation is scales based on temperature to the fourth.

So low temperature systems have very low radiation in general.

So I'm left with conduction and convection, and some of the issues

associated with those, the fundamental physics associated with convection and

conduction are the speed of the fluid [COUGH].

If the fluid is moving, you tend to be dominated by convection and conduction

can be neglected. And then when you look at convection, you

also have to consider how long does the fluid have within the control surface to

transfer heat. So imagine your body is at 98.6 degrees.

Do you physically change the temperature of the water as it extis the hose.

The answer is, probably not. The contact exposure is so short, a short

period of time. That it's unlikely that you're changing

the temperature in the fluid. So, even though your temperature is

different than the temperature of the water flowing in the hose, is not a large

heat transfer. In that system, the nozzle system is

considered adiabatic, and same with the diffuser, for sort of the inverse

rationale. the other key properties that we need to

understand about nozzles and diffusers. So the purpose of the nozzle is generally

to accelerate the flow. So if we say this is the exit state here

and if this is the entrance state so the fluid is moving like this and the

diffuser of the fluid moves like this. The entrance state, the exit state, and

some of the things that we know about these systems is that, again, the purpose

of the a nozzle is to accelerate the flow.

Well, what's the price you pay for accelerating the flow?

You're going to decrease the velocity. And we know that we achieve this through

changing the area of the exit and the entrance.

So we know typically that we're going to see a shrinking area with a nozzle and

you're going to see an increasing area, all of these terms will flip in their

scale with the diffuser. So here we have the area is greater at

the exit, the pressure is greater at the exit but the velocity is lower at the

exit. Okay.

So those are the general assumptions associated with nozzles and diffusers.

And again, you'll find them in in numerous systems and applications.

Turbines we've talked about a lot already, because they are literally the

work horse of the power plants around the world.

So turbines we should you know, this should be pretty straightforward for us.

you'll see turbines are generally represented by this sort of trapezoidal

shape. You'll see people show the flow in and

out like this, some folks prefer to show turbine flow like this.

And I think this, this, representation makes a little bit more sense.

It just depends on, you know, what your physical interpretation is, of looking at

these devices, these turbo machinery devices.

well, again, they all have shafts. because that's how we generate work in

these systems, we have the turbine blades, which are pushed, the fluid comes

into the turbine, pushes into the blade, and rotates the shaft.

So we know with, all of the, I'll just one of these diagrams now.

That all turbines better generate work, and its shaft work to be specific.

And we would represent this as an arrow showing that the, work transfer is out of

the turbine. And we have the mass transfer into and

the mass transfer out of the system and if we assume again like we were going to

do that these were all steady state, steady flow devices this terms going to

be equal to zero. And because we actually have, let me go

ahead and write down the general form, sorry, general form of the conservation

of mass expression here. In this system, just like with the nozzle

and diffuser, we didn't write it down last time.

There's only one mass, there's only one inlet and one exit, and because this is a

steady state, steady flow device, we know that there's only one mass transfer, mass

transfer rate, mass flow rate in the system.

So we really don't need subscripts on the entrance and exit.

There is only one mass flow rate in the system.

we generally approximate the turbines as being adiabatic, and I've already

mentioned once before. There's actually a lot of heat transfer

that happens between turbines and compressors and pumps as well.

The issue is those heat transfer rates are actually very small, relative to the

other energy transfer rates in the system.

So, this is, really what we should be saying, we call them adiabatic.

In, in reality, it's negligible, relative to the other energy transfers.

And we're going to do an example on this shortly to show you exactly what we're

talking about here, in terms of the relative magnitude of the terms.

if you ever seen a turbine, they generally don't have a whole lot of

vertical movement in the fluid. Some can be pretty big.

They can be a story or too tall, but again, not a whole lot.

So these, they have negligible potential energy changes, and what we're left with

is essentially that the work transfer is balanced by the mass transfer, and again

because its a control volume, we have enthalpy instead of internal energy and

I'm going to leave those kinetic energy terms in there.

What we're going to find is that the kinetic energy, while it seems like that

would be a potentially really large contribution, it actually isn't.

So what we'll alternately find is that, so, and we'll prove this to you here

shortly, is that the work transfer for a turbine is simply governed by the mass,

mass flow rate times the enthalpy difference between the inlet and the

outlet. So hn minus h exit or h out, or how,

whatever exit term you want to subscript you want to use to make that notation.

But it's simply a difference between enthalpy in and the enthalpy out.

So, those are turbines. Compressors and pumps are the inverse to

turbines. So they're just like nozzles have their

mirror image in diffusers. Turbines have their mirror image in

compressors and pumps. So compressors because they are mirror

images we like to denote them using a trapezoid reflected around that axis

here. And we would have, again, flow-in,

flow-out of my turbine. We'll call this state one, we'll call

this state two. The purpose of a compressor and a pump is

exactly what the names imply. The compressor is to increase the

pressure. It's actually to increase the internal

energy of the fluid. And same with the pump.

It's to increase the pressure or the internal energy associated with the

fluid. Some folks get really rigorous about

saying compressors are only associated with gases, that pumps are only

associated with liquids. I tend to be a little bit more flexible.

I quite often call pumps, devices that actually compress gases.

So again I'd encourage you to be kind of flexible yourself, in your interpretation

of what does it mean, when I call something a compressor a pump.

The purpose of the device is to increase the energy, the internal energy, the end

enthalpy thereby enthalpy of the fluid. So that's its purpose, and whether or not

its liquid phase or gas phase really depends on what the fluid is.

Okay, so again we're going to draw our control surface just like we did before,

and if I start with a low energy fluid on one side and end up with a high energy

fluid on the other side. And if it's like its sister device, the

turbine, where it's adiabatic, so we're going again assume adiabatic, well then

you better go through the math and say, hey, in order for that to be consistent

with the conservation of energy, this has to be a system where it works into the

compressor or the pump. Okay.

So we know for compressors and pumps we're going to have work in.

Also, you'll see a pump represented with this sort of a schematic type form.

So you'll see again, state one, there's the inlet state.

And here's state two. And again, be flexible on your

interpretation here. So, this is work into the pump.

and again, these systems are considered adiabatic.

So, if this is the conservation of energy, invoking a few assumptions, for a

turbine. Then we know for a pump or a compressor,

that it's going to have the exact same expression, except we're going to have

reverse signs. Okay, because remember, we like work out

in the power generation sector, we like to see work out as a positive number.

This is a high energy state going into a turbine.

This is a low energy state coming out of it.

So this number's going to be positive. Work out is positive.

For this pump, we know we're going to have the exact same governing equation,

except we're going to have h in minus h out, but this term will now be negative.

Because the high-energy term is associated with the exit state, and the

low-energy term is associated with the entrance state.

And I've mentioned multiple times, we're very notation intense in this class.

We like subscripts, and superscripts, and accents on top of our variables, and they

all have specific meaning. Having said that, I also want you to be

flexible on, is it an inlet, is it an outlet, is it an exit, is it a one or

two, any of those is fine. What I want you to do is just be able to

recognize what's into the system and what's out of the system.

So there isn't a convention, or a standard convention, for in/out.

Like what's the right notation? There is no right subscript notation,

except for the one that you apply and just make sure you use it consistently,

right, throughout your analysis. Okay, that again will develop those tools

through example or kind of develop that, habits I should say, you will develop

good habits and how to make these notations.

Okay, so the last one that I wanted to consider today.

Actually second to last, I apologize. There's one more I want to squeak in, is

a heat exchanger. So a heat exchanger the whole purpose of

the device is to move heat transfer energy, move energy from one fluid to

another by heat transfer. So the simplest way we can represent a

heat transfer device, our heat exchange is, we'll just do this simple counter

flow, and you're going to have flow into the system on one side, and out of the

system on the other. And we'll do a nice little counter flow

heat exchanger here so we have two fluids, we're not going to allow them to

mix. We're going to say they can't mix in this

example, and Work in a move these fluids past each other, and we're going to have

conduction and convection heat transfer through the walls of the heat exchanger.

So we're going to move energy from one fluid to another.

Let's call this top fluid the hot fluid, and we're going to call this the cold

fluid here. And that allows us to go if the hot fluid

is on the top in the cold fluids on the bottom Then the heat transfer has to

occur in this direction, ok. heat exchangers by definition do not

require any work so there is no, we're not going to use any electrical heating

or anything like that. We're going to allow these heat

exchangers to exchange heat through convection and conduction, no shafts,

nothing like that. So if I chose to draw the boundaries like

this. The control volume around the entire heat

exchanger. Two key outcomes happen.

One is, the work transfer for that system is zero.

The other thing is, and this is really important conceptually, there's no heat

transfer with the ambient. That's a fundamental assumption of a heat

exchange. All the heat transfer occurs between the

hot and the cold fluid. So in this control volume, the system is

adiabatic. And this Q is only relevant If I chose

this to be my control volume, now you would go, oh, look there's energy

transfer across that control boundary. So for this system, the blue system, the

work transfer is still zero, but now I have a non-zero heat transfer.

So heat exchanges require you to be thinking.

Notice also in the blue control surface, I have the mass flow rate of one equal to

the mass flow rate of two. And I have energy transfer associated

with those fluids. In the red control volume, I have mass

transfer From both the hot fluid and the cold fluid.

So my continuity expression, the conservation of mass, for the red control

volume, is actually the mass flow rate at state 1 plus the mass flow rate at state

3. Has to be identically balanced by the

mass flow rate at state two and the mass flow rate at state four.

OK. So be careful how you choose your control

surface and whenever you look at the control surface you have to identify all

of the energy transfer and all of the mass transfer that cross the system

boundary. If they don't the system boudry, they're

interior. They're either completelly inside the

control surface, or completelly outside the control surface.

And either way, they will not be considered.

You don't have to consider those terms in your conservation equations.

Okay, so, Remember I told you there's parallels between conservation of mass

and conservation of energy. Well let's take the conservation of

energy, for this system. For the for the red system which includes

both fluids. Well again we've, there's no heat

transfer, across we've assumed the heat exchanger does not have (no period) You

know significant heat with the ambient or the environment and we're going to have

assume there's no work transfer and for these systems they're going to have

negligible kinetic and potential energy changes.

So these guys are going to neglect the changes in ke, kinetic energy and

potential energy. For heat exchangers.

Right, that's not the purpose of the device.

So I look at all these simplifications, it's a steady state, steady flow, it's,

you know, no heat transfer, no work transfer, well heck, all I have is a

simple enthalpy balance. And it has the exact same structure, as

the mass, conservation of mass equation. Okay, so again, these are your checks and

balances. If you wrote one expression for the mass,

you should see an exact parallel for the energy.

I want to squeeze in one last flow device onto this slide before we move on, and

thats a throttle, and throttles are kind of interesting.

Throttles are valves, so we'll calle throttles valves and the purpose of a

throttle or a valve is to restrict flow. So that', I mean we've all turned valves

many times, I mean every time you open your faucet you're opening and closing a

throttle or a valve. So we're very familar with those devices,

schematically we like to represent them as these little Xs.

Cause again representing kind of that handle on my throttle.

these are really funny devices. Their purpose is not to do work, just

like my nozzle, my diffuser. There's no heat transfer.

The fluid really doesn't have time to change temperature as it goes through the

throttle. So if I draw my little control surface

here, we rapidly see, OK, there's no work.

There's no heat transfer. Okay.

We're going to again neglect kinetic and potential energy changes.

We have one mass flow rate into and out of this system, and we look at the

conservation of energy. And, again, it's the same simplifications

we had for the heat exchanger, except now look what happens to the conservation of

energy. So we have m dot in, the mass flow rate

at the entrance times the enthalpy at the entrance, equals the mass flow rate at

the exit times the enthalpy at the exit, except, from the conservation of mass, we

know that the mass flow rates, there's just one mass flow rate in the system, so

we can cancel these. And what we end up with is a constant

enthalpy device. kind of a strange little world.

But throttles are isenthalpic. So there's a good word for you.

So again, just kind of a unique little simplification that happens with

throttles and valves that we need to be aware of.

we'll add some complexity to throttles later, but not right now.

But for conservation of energy, conservation of mass, couldn't be simpler

for throttles [UNKNOWN]. Okay, so I want to leave you with a

couple of thought questions. And I want you to come up with a, you can

either use a system example, you know, you can think of, you know, some actual

device. Or you can just think again in terms of

the generic forms, or the conservation of mass, and the conservation of energy.

I want you to answer these two questions. Can a system have unsteady mass-flow and

steady energy transfer? Can a system have both of those

assumptions happening simultaneously, or conditions happening simultaneously?

And, when can you have a system which has only flow in and no flow out?

So imagine a system that has one entrance, but no exits.

What's the condition that allows that to happen?

Think about those, come up with the answers and we'll talk about em next time.

04.02 - Steady State, Steady Flow Devices

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