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Thermodynamic Limits and Real Machine Efficiency · Mechanical Engineering Made Simple

0:00
Welcome back to Mechanical Engineering Made Simple Legends.
0:03
Lesson 1. Thermodynamics.
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I'm your host. Let's uncover what the textbooks
0:07
only hint at. Marcus really is taught that the
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obstacle is the way. In thermodynamics, energy itself
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is the obstacle we must respect. The first law tells us energy is
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never created or destroyed, only transformed.
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The second law reminds us every transformation creates waste and
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increases disorder. Heat engines, refrigeration,
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even the warmth in your own body all obey these quiet,
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unbreakable rules. School gives you equations.
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Life shows why perfect deficiency is impossible and why
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that truth frees you. Stay with me.
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We turn these natural limits into wisdom and power.
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Class in Casa. Man, it really is the great
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truth of our field, isn't it? And if we're really going to
0:47
master this, we have to kind of drag all that theory out of the
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pristine textbook and, you know, into the harsh, unforgiving
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light of reality because we're dealing with factual
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mathematical truths here, the stuff that governs every single
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physical system on this planet. There are no idealized fairy
1:01
tales about machines that run perfectly.
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Right, No unicorns. Exactly.
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No unicorns. If you are designing the
1:08
pipeline running under a city, or you know the the high
1:11
pressure compressor stage of a jet engine that's keeping a
1:13
plane suspended at 30,000 feet, you're essentially fighting a
1:16
war against physics. You really are.
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And to win that war, or honestly just to break even, you have to
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understand the weapons the universe uses against you.
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Which is exactly the mission of today's Deep dive.
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We are getting into the absolute bedrock, the first law.
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Now, pretty much everyone who has ever sat through a high
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school science class can regurgitate the phrase Energy is
1:40
conserved. Oh sure, everyone knows that
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one. Right.
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It cannot be created, it cannot be destroyed.
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But let's be real for a second. If you walk into a design review
1:48
for a A500 MW steam turbine and your only contribution is well
1:54
guys, energy is conserved, you are going to be laughed right
1:56
out of the room. Yeah, you're packing up your
1:57
desk that day. Exactly.
1:59
Yeah, we need to look at how that philosophical concept
2:01
actually applies to complex machines moving massive amounts
2:04
of high pressure fluid. Yeah, that phrase is a nice
2:07
philosophical starting point. Sure, but it completely lacks
2:11
the teeth required for actual engineering.
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So how do we give it teeth? Well, to give it teeth, we have
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to define our boundaries. So let's start with the simplest
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case, a closed system. Imagine a heavy steel box, just
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a solid box. No mask can enter and no mask
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can leave. The only things that can cross
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the boundary of that box are heat and work.
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Right. So like if you put a blowtorch
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to the box, you're adding heat. Precisely.
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You add heat and if the gas inside gets hot, expands and say
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pushes A piston outward, it does work.
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OK, so keeping a strict accounting of that box gives us
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the most basic mathematical form of the first law.
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Yep, which is the change in the total internal energy of the
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system equals the heat supplied to the system minus the work
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done by the system. That's the one.
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So if we write that out, we say DE equals DQ minus DW.
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Exactly, it's a strict Ledger. The DE is your balance, the heat
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DQ and the work DW. Well, those are your
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transactions. Here is the critical
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distinction. And honestly, this is the first
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major pain point for Mechanical Engineers.
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We rarely, if ever, deal exclusively with closed systems.
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Because machines flow right? Right.
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If you are working on turbines, compressors, pumps, or you know,
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aircraft engines, you are dealing with open systems.
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Mass is constantly rushing in and mass is constantly rushing
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out. So you can't just look at the
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heat and the shaft work. Yeah, you can't.
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You have to track the energy physically carried into and out
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of the machine by the fluid itself.
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And that physical reality forces us to introduce a property
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that's, well, it causes endless confusion enthalpy.
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Oh yeah, enthalpy. I remember just sitting in
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lecture halls staring at that word on the board, wondering why
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internal energy just wasn't enough.
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Like why invent a whole new thermodynamic property just for
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open systems? A lot of students feel that way.
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But enthalpy isn't just an abstract math trick, right?
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It represents a physical struggle.
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It absolutely does. It is the ultimate workhorse
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property of fluid mechanics. Enthalpy, which we denote with
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the lowercase letter H, is defined as the internal energy
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of the fluid U plus the pressure of the fluid P multiplied by its
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specific volume V. OK, so H = U + P * V.
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Exactly. Let's breakdown the physical
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reality of that equation, because just reading the
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variables doesn't really do it justice.
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The Internal Energy EU That's easy to visualize.
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Right, that's just the microscopic kinetic energy.
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Yeah, it's how fast the molecules are vibrating, how hot
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the steam is. But that second part, the P * V,
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that is what we call the flow work.
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Yes, the flow work. So imagine you are a single
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packet of fluid. Let's say you're a cubic inch of
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high pressure steam. OK, I'm with you.
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You are trying to enter the main inlet pipe of a massive power
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plant turbine, but that pipe is already jam packed with other
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steam at incredibly high pressure.
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You can't just casually stroll in.
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You'd get bounced right out. Right, you have to physically
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shove the fluid that is already in the pipe out of the way to
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make room for your own volume. That is a brilliant way to
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visualize it. You have to perform mechanical
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boundary work just to enter the control volume you are pushing
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against the pressure of the environment, the P to insert
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your specific volume, the V that shoving that requires energy.
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I always think of it like trying to get onto a crowded subway
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train in Tokyo at rush hour. Oh, man, yeah, you know.
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You aren't just bringing your body mass onto the train, you
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are expending actual physical calories, shoving people aside
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so your body can occupy space inside the car.
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That's perfect. That shoving effort is the flow
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work. And because mass is continuously
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entering and leaving an open system, that flow work is
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continuously being performed. The fluid entering does work to
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get in, and the fluid leaving does work as it pushes its way
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out into the exhaust piping. So it's a constant process.
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Exactly. Therefore, when we write the
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energy balance for a continuous steady state machine, which is
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what we call the steady flow energy equation, we don't use
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internal energy, we use enthalpy.
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So let's lay out that steady flow equation for the listener.
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We take the heat transfer rate, subtract the work transfer rate
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and that must equal the mass flow rate which we call
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m.multipliedbythetotal change in energy of the fluid from the
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inlet to the outlet. Yep, that's the core of it.
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And that total energy is made-up of three things, right?
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The change in enthalpy, the change in kinetic energy and the
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change in potential gravitational energy.
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That is the complete picture, but before we move further, we
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really must address the sign convention in that equation.
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Well, the signs. The heat transfer minus work
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transfer part. This is notorious for tripping
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up engineers, especially when they are writing code to model
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these systems. Let's use a bank account analogy
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to clear this up. But we have to clarify who
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actually owns the bank, right? So think of the fluids enthalpy
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as the checking account balance. Heat and work are the deposits
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and withdrawals. But you have to remember the
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bank is operated by a 19th century industrialist.
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You see, the classic thermodynamics sign convention
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was established during the industrial revolution.
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The entire reason these pioneers were studying thermodynamics in
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the 1st place was to build better steam engines.
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They just wanted power. Exactly.
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Their singular goal was to get useful mechanical shaft work out
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of a machine. Therefore they defined output
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work the stuff they wanted as a positive number.
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Right, so heat added to the system is a deposit.
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It's positive, the energy goes up, but work done by the system
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work leaving the control volume to say, spin.
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A generator is also defined as a positive number in the math.
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Which seems counterintuitive at first.
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Yeah, because even though that work acts as a withdrawal that
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lowers the fluid's remaining energy, the equation uses a
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minus sign for work, meaning a positive work output correctly
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results in the subtraction from the fluids total energy.
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Exactly. So if you are designing a gas
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turbine, which is a work producing machine, the work term
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is positive, The machine is delivering power to a shaft.
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But if you were designing a gas compressor, a work absorbing
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machine, the work term must be negative.
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The external environment, like an electric motor, is forcing
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energy into the fluid to compress it.
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OK, that clears up the heat and work, but I really want to talk
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about that last term in the steady flow equation.
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Yeah, the change in potential gravitational energy.
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Oh boy. Right.
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Yeah, I've seen junior engineers run incredibly complex
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calculations to figure out the exact change in elevation
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between the inlet manifold of a gas turbine and the exhaust
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duct, trying to nail down the gravity times height term the g
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* Z. And this is where theory meets
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practical engineering wisdom. Please save them some time.
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In the real world, you learn to reflessly ignore that term
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unless you're designing one very specific type type of machine,
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which is well, the energy associated with a gas dropping 5
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or 10 feet in elevation is infinitesimally small compared
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to the massive violent changes in enthalpy and kinetic energy
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happening inside the turbine stages.
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Right, it's just nothing. For gases and vapors, we
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universally drop the potential energy turn completely.
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It is a rounding error that only clutters the calculation.
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So the only time you really care about gravity is if you are
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building a hydroelectric dam. Precisely, If your working fluid
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is heavy liquid water, and the entire principle of your machine
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relies on a 300 foot drop in physical elevation, then yes,
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potential energy is your primary driver.
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Makes sense. But if you are dealing with air,
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steam or refrigerants flowing through turbo machinery, just
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forget gravity. Focus entirely on the enthalpy
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and the velocity. OK, so the first law tracks the
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energy. It's the meticulous accountant
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making sure every Joule is accounted for between the heat,
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the work and the enthalpy, right?
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But as we all know, just because you have money in the bank
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doesn't mean you can spend it however you want.
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Definitely not. There are heavy taxes and the
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universe never, ever forgets to collect.
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That brings us to Section 2, the unbreakable limit, the second
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law of thermodynamics, and the concept of entropy.
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Yeah, if the first law is the accountant, the second law is
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the taxman. And let me tell you, the tax
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rate is brutal. It really.
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Is the first law alone implies a perfect symmetry, right?
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It implies that we should be able to convert heat perfectly
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into mechanical work, and then work perfectly back into heat
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running machines endlessly with 100% efficiency.
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Perpetual motion, basically. Exactly.
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But the second law steps in and shatters that illusion.
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It dictates that perfect efficiency is physically
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impossible. Every single real world process,
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without exception, creates waste, degrades the quality of
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the energy, and increases the overall disorder of the
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universe. See, I always hear entropy
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explained as disorder, like a teenager's bedroom getting
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messy. Oh, I hate that.
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One me too. Honestly I've always hated that
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analogy. It feels completely disconnected
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from engineering. When I'm designing a multi stage
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compressor, I'm not worried about my molecules for getting
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to fold their laundry. I want to know the actual
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physical mechanism of this loss. And you are right to hate that
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analogy. It is a severe
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oversimplification. For an engineer, it is much more
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accurate to think of entropy as a measure of irreversible
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dispersion. Irreversible dispersion, OK.
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Imagine you carefully pour a drop of black ink into a glass
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of Stillwater. OK, visualizing that.
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Initially you have a highly organized system, pure water
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here, pure concentrated ink there.
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But within seconds the ink disperses.
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The thermal motion of the molecules spreads the ink
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uniformly throughout the glass, right?
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Now ask yourself, what are the odds that those ink molecules
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will spontaneously, on their own, gather back together into a
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single perfect drop in the center of the glass?
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Statistically, 0 it's impossible.
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Exactly. The energy in the glass didn't
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change. The first law is satisfied, but
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the arrangement of that energy is permanently altered.
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The process is completely irreversible.
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Because to unmix that ink, you would have to intervene, right?
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You'd have to build a complex chemical separation plant,
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consume external electricity, and do massive amounts of.
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Work precisely in thermodynamics.
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The mathematical expression of this irreversible reality is the
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inequality of Clausius. OK, let's get into the math of
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it. It states that for any system
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undergoing A thermodynamic cycle, the integral of the heat
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transfer DQ divided by the absolute temperature T must be
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less than or equal to 0. And that less than or equal to
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is the dividing line between fantasy and reality.
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Correct. If a process is a theoretical
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perfect ideal, which is what we call a reversible process, that
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integral equals exactly 0. Right, the fantasy world.
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In reversible fantasy world, there is no fluid friction, no
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turbulent eddies, no heat leaking through the casing.
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You could theoretically run a turbine forward to get 100
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megawatts of power, and then use exactly 100 megawatts to run it
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backward as a compressor, returning the fluid and the
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universe to their exact original states.
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But unicorns don't exist. Reality is irreversible, and for
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any real process, that integral is strictly less than 0.
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This mathematical deficit introduces the property of
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entropy, denoted by S Because processes are irreversible, the
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total entropy of the universe always increases.
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Entropy is always generated, it is never destroyed.
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That's the cold, hard truth. I do want to pause on a crucial
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detail you mentioned though. Dividing heat transfer by
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absolute temperature. If you try to calculate entropy
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using Celsius or Fahrenheit, your numbers will be complete
13:43
garbage. Why is that distinction so
13:45
important? Because thermodynamics is
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fundamentally the mathematics of molecular motion. 0°C is just
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the temperature where liquid water freezes into ice, right?
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It is an arbitrary benchmark based on one specific substance.
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At Earth's atmospheric pressure, the molecules in ice are still
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vibrating. They still possess thermal
14:05
energy. So they aren't at 0 energy.
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Exactly. If you divide by an arbitrary
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scale like Celsius, you can end up dividing by zero or dividing
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by negative numbers, which mathematically breaks the
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entropy equations entirely. That makes sense.
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You must use an absolute thermodynamic temperature scale.
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Kelvin in the metric system or ranking in the imperial system.
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0 on these scales represents true absolute zero.
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It is the theoretical rock bottom limit where all
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microscopic molecular motion completely ceases.
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It is the true zero of energy. So we know entropy always
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increases because of friction and heat loss.
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But again, how does a mechanical engineer actually use this?
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How do we quantify the pain this causes us?
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This is where we introduce one of the most sobering powerful
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equations in all of engineering the Ghost Otola theorem.
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Oh yes. This theorem translates the
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abstract concept of entropy generation into hard financial
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reality. It states that the rate of lost
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available work, which engineers call exergy destruction, is
15:05
directly proportional to the rate of entropy generation
15:08
multiplied by the ambient temperature of the environment.
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The equation is W lost equals T 0 * s Gen.
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Yes, that is the literal invoice for your wasted potential.
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Let's say you have a high pressure steam pipe and you
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didn't insulate it properly. Heat leaks out into the cold
15:25
ambient air. That heat transfer across a
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finite temperature difference is highly irreversible.
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It generates entropy SGM. And the Guy Stotola theorem
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tells you exactly how many kilowatts of useful money making
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mechanical power you just permanently destroyed.
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Exactly. That energy could have spun A
15:43
turbine blade and generated electricity you could sell to
15:45
the grid. Instead you degraded it into
15:48
useless low grade warmth in the atmosphere.
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You can never, ever get that capacity back.
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Entropy generation isn't a measure of a messy room, it is a
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measure of destroyed financial and mechanical potential.
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Let me give the listener an analogy to lock this in.
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Think of a heavy mass suspended on a thick steel spring.
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You pull the mass down and let it go.
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OK, simple harmonic motion. Right.
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In a perfect, reversible world, that mass oscillates up and down
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forever, returning exactly to its starting peak every single
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time, right? But in the real, physical world,
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it doesn't. Every time the spring stretches,
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the internal metallic bonds rub against each other, creating
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microscopic internal friction. This generates a tiny bit of
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heat within the steel. Furthermore, as the mass moves
16:32
up and down, it is physically slamming into air molecules,
16:35
pushing them out of the way, creating aerodynamic drag.
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Both of which are completely irreversible.
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Exactly. Both the internal friction and
16:43
the air drag are irreversible. They generate entropy, and
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because of that entropy generation, the mechanical
16:50
energy of the bouncing bass is slowly converted into useless
16:53
ambient heat. The bounces get shorter and
16:56
shorter until the mass comes to a dead stop.
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Left alone, entropy always wins. Always to make that mass bounce
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endlessly, the environment, meaning a human or a motor must
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actively intervene and do physical work on the system to
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replace the destroyed exergy. And bringing this back to heavy
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machinery, this irreversible reality causes massive design
17:16
headaches. Because the math of real,
17:18
irreversible processes is so incredibly complex, engineers
17:22
frequently designed systems by assuming the processes are
17:25
reversible and adiabatic. Adiabatic meaning perfectly
17:29
insulated 0 heat transfer. Exactly and reversible, meaning
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0 friction. We combine these two assumptions
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into an ideal state called an isentropic process, meaning
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entropy remains perfectly constant from the inlet to the
17:41
outlet. It makes the math beautifully
17:42
simple. You just set S1 equal to S2 and
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solve for your exhaust property. It's very tempting.
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But when you actually build the turbine and bolt it to the test
17:50
end, the real kinetic energy and the real exhaust temperatures
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are wildly different from your isentropic calculations.
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Why? How does friction literally
17:59
change the physical speed of the gas?
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This is the physical chain reaction of entropy.
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Let's walk through a real turbine.
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As the high pressure gas expands through the spinning blades,
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fluid friction occurs. The gas molecules rub against
18:12
the microscopic roughness of the titanium blades, and turbulent
18:15
shear layers rub against each other.
18:18
Tons of it. This friction acts like a
18:20
microscopic heater inside the fluid, generating waste heat.
18:24
Because of this internally generated heat, the gas at the
18:27
exhaust is physically hotter than it would have been in your
18:30
perfect isentropic fantasy. And what happens when a gas is
18:33
hotter? It expands.
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Yes, it expands its specific volume V increases.
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Oh, I see where this is going. Now remember that this is a
18:40
steady flow machine mass. Flow rate is constant.
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You have a larger, hotter, fatter volume of gas that must
18:47
be forced through the exact same physical cross-sectional area of
18:50
the turbine exhaust casing. Because the metal doesn't grow.
18:52
Exactly. To shove a larger volume of
18:55
fluid through a fixed area in the same amount of time, the
18:58
fluid must physically accelerate to a higher velocity.
19:02
So the actual kinetic energy of the gas leaving the turbine is
19:05
altered strictly because the specific volume increased due to
19:10
entropy generation. Your beautiful isentropic
19:14
assumption blinded you to how the physical fluid react to its
19:17
own internal friction. Exactly, assuming constant
19:20
entropy blinds you to the physical swelling of the gas.
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Which is the perfect bridge into our next major pillar, Section
19:26
3, governing the flow. We understand the energy
19:29
tracking, and we understand the brutal tax of entropy, but how
19:33
do we actually track the physical mass of the fluid as it
19:36
swells, accelerates, and navigates through a labyrinth of
19:39
pipes and compressor blades? We need governing rules.
19:42
Right, we need governing rules for the flow itself.
19:44
And the absolute foundation of fluid tracking is the equation
19:47
of continuity. It is the mathematical statement
19:50
of the conservation of math. Keep track of the stuff.
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Keep track of the stuff. Simply put, mass cannot
19:55
magically vanish into the ether, and it cannot spontaneously
19:58
appear out of nowhere if you have a steady one-dimensional
20:01
flow moving through a pipe. The mass flow rate must be
20:04
identical at every single cross section of that system.
20:07
The equation is m.equalsdensity rho multiplied by the normal
20:12
velocity C sub N multiplied by the cross-sectional area a.
20:16
So m.equals rho times C * a. Think about a river that is
20:22
flowing wide and slow. Suddenly it enters A narrow
20:25
rocky gorge. OK, the total amount of water
20:28
moving down the mountain hasn't changed.
20:30
M.isconstant liquid water is basically incompressible, so
20:34
it's density rho stays constant. Right, water doesn't compress
20:38
much. Therefore, mathematically and
20:40
physically, if the area a shrinks, the velocity C must
20:43
massively increase to push the same amount of mass through the
20:46
bottleneck. The water speeds up and becomes
20:48
a violent rapid. It's the exact same principle as
20:50
putting your thumb over the end of a garden hose.
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Oh yeah, perfect. Example, you decrease the area,
20:55
the velocity spikes and the water shoots across the yard.
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Now that planes that it accelerates, but what are the
21:02
physical forces causing that acceleration?
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That requires applying Newton's second law to a moving fluid.
21:09
When you look at a solid block sliding down a ramp, you use
21:12
force equals mass times acceleration.
21:15
The fluids deform continuously. We can't track a single solid
21:18
block. It's all squishy.
21:20
Exactly. Instead we use the momentum
21:22
equation. It states that the sum of all
21:25
external pressure and body forces acting on a specific
21:27
control volume of fluid equals the time rate of change of
21:31
momentum of the fluid passing through it.
21:33
OK, if you take this momentum principle, combine it with the
21:36
conservation of mass, and look at an idealized scenario where
21:39
there is no viscous friction and no spinning shafts doing work,
21:42
you arrive at Euler's equation of motion.
21:44
And Euler's equation is famous because of what happens when you
21:48
integrate it. If you integrate Euler's
21:50
equation along a single streamline of flow, you give
21:53
birth to the most famous, most tattooed equation in all of
21:56
engineering, the one that every student spends weeks deriving
21:59
Bernoulli's equation. Yes, Bernoulli, the integrated
22:03
form of Euler's equation. It states that the static
22:06
pressure of the fluid divided by its density plus 1/2 the fluid's
22:10
velocity squared plus gravity times height equals a constant
22:14
value anywhere along that streamline.
22:16
P over rho plus one half C ^2 plus GZ equals a constant.
22:22
It is a brilliant, elegant statement of the conservation of
22:25
mechanical energy. Truly.
22:27
Elegant and tied directly to Bernoulli is a concept that is
22:30
critical for aerodynamicists and turbine designers.
22:33
Stagnation pressure or total pressure?
22:36
The equation for this is P0 equals P + 1/2 rho times C ^2.
22:41
What does stagnation actually represent physically?
22:44
To feel stagnation pressure, just think about driving down
22:47
the highway at 70 mph and sticking your hand out the
22:49
window, palm facing forward. We've all done that.
22:51
Right. The ambient air you were driving
22:54
through has a specific static pressure.
22:55
It's the normal weight of the atmosphere.
22:57
It also has a relative velocity of purging your hand.
23:00
But when that air physically impacts the center of your palm,
23:04
it cannot pass through your skin.
23:06
It is forced to come to a complete dead stop.
23:09
Its velocity drops to 0. So where does the energy go?
23:12
According to Bernoulli, the kinetic energy of that moving
23:15
air doesn't just vanish as the air decelerates against your
23:18
hand. That kinetic energy is entirely
23:21
transformed into pressure. The heavy forceful pressure you
23:25
feel pushing your arm backward is the stagnation pressure.
23:29
It is the sum of the ambient static pressure plus the dynamic
23:32
pressure. That 1/2 root C ^2 term
23:35
stagnation pressure represents the absolute maximum pressure
23:38
you could achieve if you took a moving fluid and brought it to a
23:41
complete reversible halt. It is the total energy cache of
23:44
the fluid. Now here's where we have to talk
23:46
about a massive career ending trap.
23:49
I hear this from junior engineers who fall in love with
23:51
the elegance of Bernoulli. The math is so simple, just
23:54
basic algebra and they ask can I use Bernoulli to calculate the
23:57
pressure drop across the compressor stages of a jet
24:00
engine? And the answer must be a
24:03
resounding aggressive no. This is one of the most
24:06
catastrophic mistakes you can make in fluid mechanics.
24:09
You absolutely cannot use the standard Bernoulli equation for
24:12
a high speed gas turbine or a high pressure compressor.
24:15
But why not? The equation works perfectly for
24:17
water pipes. Why does it fail for a jet
24:19
engine? Because of 1 lethal hidden
24:23
assumption baked into the integration of Bernoulli's
24:26
equation constant density. The equation assumes that the
24:30
density of the fluid retro never changes.
24:33
This works beautifully for liquid water because water is
24:36
virtually incompressible. You can squeeze it with
24:39
thousands of pounds in pressure and its density barely shifts.
24:42
Bernoulli also works acceptably well for air moving at very low
24:46
speeds, like the airflow from a desk fan or the aerodynamics of
24:49
a slow moving sesson aircraft. The pressure changes are so
24:52
small that the air density essentially remains constant.
24:55
But inside a jet engine. Inside a jet engine compressor,
24:58
the air is being violently smashed into smaller and smaller
25:01
volumes, It is being compressed to 30 or 40 times atmospheric
25:05
pressure, and the temperature is skyrocketing.
25:08
The density rho is changing drastically and continuously
25:12
across every single millimeter of the machine.
25:15
So if you use Bernoulli. If you attempt to use the
25:17
incompressible Bernoulli equation on a high speed, highly
25:20
compressible gas, your mathematical predictions will
25:23
deviate from reality by massive margins, your pressure
25:27
calculations will be wrong, your structural load calculations
25:30
will be wrong, and your engine will stall or RIP itself apart
25:33
when density changes. You must abandoned Bernoulli and
25:37
use the full compressible flow equations, which require
25:40
incorporating thermodynamic properties like specific heat
25:43
capacities and absolute temperatures to track exactly
25:45
how the gas is squeezing and swelling.
25:48
Do not use water math on high speed air.
25:50
That is the take away. All right, so we have laid out
25:53
the overarching laws. We know how energy is tracked,
25:56
we know the brutal taxes of entropy, and we know the rules
26:00
for tracking the fluids, mass and momentum.
26:03
But equations on a chalkboard don't spin generators.
26:06
Hardware does. We need to take these physics
26:09
and slam them into real steel. Let's walk into Section 4, the
26:14
engine room. Let's breakdown the actual
26:16
components. Mechanical Engineers design and
26:18
troubleshoot every day. Let's start with the most basic
26:21
component in any piping system, valves and throttles.
26:24
A valve is fundamentally just a physical restriction, a
26:27
bottleneck in a pipe. OK, So what happens to the
26:29
fluids energy when it forces its way through a partially closed
26:32
valve? First, let's look at the first
26:34
law. There is no spinning shaft
26:35
attached to a valve, so there is zero mechanical work being done.
26:39
And because the fluid blast through the restriction so
26:41
incredibly fast and the surface area is relatively small, there
26:43
is no time for heat to transfer to the environment.
26:46
So DQ is 0 and DW is 0. If we look at our steady flow
26:51
energy equation and we assume the inlet and outlet pipes are
26:54
the same size so kinetic energy doesn't change drastically.
26:57
The first law dictates a very specific outcome.
27:01
The total enthalpy of the fluid at the inlet must perfectly
27:04
equal the total enthalpy at the outlet.
27:06
H1 equals H2. This is called an isenthalpic
27:09
process. Correct, The pure energy content
27:12
remains identical, but do not confuse constant energy with a
27:15
harmless process. What is the second law, say
27:17
entropy tax, exactly? Forcing a high pressure fluid
27:21
through a tiny restrictive gap creates massive, violent
27:25
turbulence. The fluid shears against itself,
27:27
creating immense internal friction.
27:29
Therefore, entropy generation is strictly heavily positive.
27:33
As the fluid expands through the valve, its pressure plummets.
27:36
So while the total enthalpy is conserved, the availability of
27:40
that energy, its exergy, its potential to do useful
27:43
mechanical work is permanently degraded.
27:45
You took high pressure, highly organized fluid that could have
27:48
spun A turbine, and you turned it into low pressure, highly
27:51
disordered fluid. And you can never get that
27:53
pressure back without plugging a compressor into the wall and
27:57
consuming external electricity. Yes, valves destroy potential.
28:01
Yes, they destroy potential. Next, on the floor, turbines and
28:04
expanders. These are the absolute
28:07
powerhouses of human civilization.
28:09
Whether it's steam in a nuclear plant or hot gas in a jet
28:11
engine, the goal is the same. The goal of a turbine is to
28:15
extract enthalpy. A high pressure, high enthalpy
28:19
fluid expands through rows of specifically shaped spinning
28:23
aerodynamic blades. Again, because the velocities
28:25
are so high, we generally model them as adiabatic, meaning
28:28
negligible heat loss to the casing.
28:31
The entire purpose of the machine is to produce work, so
28:34
applying the first law, the mechanical shaft work produced
28:37
is equal to the mass flow rate multiplied by the physical drop
28:40
in the fluid's enthalpy. W = m dot times the difference
28:44
between H1 and H2. Wow, just basic subtraction when
28:47
you get down to it. Right.
28:48
The fluid enters violently hot and highly pressurized.
28:51
It does massive flow work pushing against the spinning
28:54
blades, and it leaves the exhaust relatively cold and at
28:57
low pressure. That difference in enthalpy is
29:00
what spins your generator and powers the electrical grid.
29:03
And the exact mirror image of a turbine is our third component
29:06
category, compressors and pumps. Exactly.
29:09
If a turbine extracts enthalpy to produce work, a compressor
29:13
consumes work to force enthalpy into the fluid.
29:16
You supply electricity to a massive external motor to spin
29:20
the compressor blades. So it's backwards.
29:22
Completely backwards, these blades violently strike the
29:25
fluid, forcing it into a smaller volume and raising its pressure
29:28
and temperature. The mathematical work consumed
29:31
equals the mass flow rate times the rise in emphalpy.
29:34
The environment is actively doing work on the system.
29:37
Now let's look at nozzles and diffusers.
29:39
These always blew my mind as a student.
29:41
They're essentially just shaped metal tubes, like a valve.
29:45
There are absolutely no moving parts, no spinning shafts,
29:47
therefore no work is done. No.
29:49
No work. And heat transfer is negligible,
29:52
but unlike a valve, their entire design purpose is to manipulate
29:56
the velocity of the fluid. A nozzle takes a slow moving
29:59
high pressure fluid and accelerates it to immense
30:03
speeds. It is a thermodynamic exchange
30:06
machine. It trades enthalpy for kinetic
30:09
energy. OK, walk us through that.
30:10
As the fluid forces its way through the converging,
30:13
narrowing shape of the nozzle, continuity dictates it must
30:17
speed up as its velocity increases dramatically.
30:20
The first law dictates that this kinetic energy must come from
30:23
somewhere It comes from the fluid's internal energy and flow
30:26
work. The static pressure and the
30:28
enthalpy drop correspondingly. That makes total sense.
30:31
A diffuser does the exact mathematical opposite.
30:33
It takes a high velocity fluid and gradually slows it down by
30:36
expanding the cross-sectional flow area.
30:38
As the fluid slows, its kinetic energy drops.
30:41
That kinetic energy doesn't disappear is converted back into
30:44
a rise in enthalpy and a rise in static pressure.
30:47
This simple exchange of enthalpy for kinetic energy is the entire
30:51
basis of how a jet engine generates thrust.
30:54
The core of the jet engine, the compressor, combustor and
30:56
turbine exists purely to generate extremely high
30:59
pressure, high enthalpy gas. Then a massive converging nozzle
31:03
at the very back of the engine trades.
31:05
All of that stored end will be for pure high speed kinetic
31:08
energy shooting out the rear. Cure Genius.
31:10
By Newton's third law, that massive rearward kinetic
31:13
momentum propels the multi ton aircraft forward.
31:16
No moving parts of the nozzle, just pure thermodynamic
31:19
conversion. And finally, we must discuss the
31:21
unsung heroes of the thermal world.
31:23
Heat exchangers, radiators, condensers, evaporators,
31:26
boilers. These are devices designed
31:29
specifically to transfer heat energy from a hot fluid stream
31:32
to a separate cold fluid stream, usually through conductive metal
31:35
walls, without the two fluids ever physically mixing.
31:37
And bringing up heat exchangers forces us to confront a massive,
31:42
widespread misconception. When students or junior
31:45
engineers model a heat exchanger in a thermodynamic cycle like a
31:49
rank Einstein cycle, they almost always draw a perfectly
31:52
horizontal line on the pressure volume diagram.
31:56
They assume the pressure of the fluid remains perfectly constant
31:59
from the inlet of the heat exchanger to the outlet PN
32:02
equals PO. Oh, I see this all the time.
32:04
I cannot emphasize enough how dangerous and costly that
32:08
assumption is when you transition from the classroom to
32:10
the real world. I must call this out explicitly.
32:13
A pressure drop always occurs in the direction of flow inside any
32:16
real heat exchanger. Why is it unavoidable?
32:18
Think about how a heat exchanger is built.
32:21
To maximize heat transfer, you have to maximize surface area.
32:24
So you force the fluid through hundreds of miles of incredibly
32:26
narrow tubes, or zigzagging over corrugated metal plates, or past
32:30
thousands of tiny, densely packed fins.
32:33
You're basically creating a physical obstacle course for the
32:35
fluid. Exactly an obstacle course.
32:38
And that obstacle course creates immense fluid friction and
32:41
aerodynamic drag. To force a fluid to overcome
32:45
that friction and keep moving forward, you must have a high
32:48
pressure at the inlet pushing toward a lower pressure at the
32:51
outlet. Friction demands a pressure
32:53
differential. So if you ignore it.
32:55
If you design a massive chemical plant and ignore the pressure
32:58
drop across your heat exchangers, your entire system
33:01
will fail on day one. The physical pump or compressor
33:05
pushing the fluid through that exchanger will have to work
33:07
significantly harder, drawing massively more electrical
33:10
current than your idealized constant pressure math
33:13
predicted. Your efficiency calculations
33:15
will be ruined and your motors will likely burn out.
33:18
The real world has friction. You must account for the
33:21
pressure drop. That is the difference between
33:22
passing a Thermo exam and actually keeping a refinery
33:25
online. All right, so throughout this
33:27
entire discussion, we've been relying on a hidden crutch.
33:30
We've been assuming our fluids behave nicely.
33:32
We've been assuming they follow simple mathematical rules.
33:35
But nature absolutely hates being put in the box.
33:38
Fluids are messy. Molecules interact.
33:42
This brings us to Section 5. Ideal gases versus real fluids.
33:47
When do fluids stop acting ideal?
33:49
Well, to understand when they break the rules, we first have
33:53
to define what the rules of an ideal gas actually are.
33:57
The most famous equation of state in physics is the ideal
33:59
gas law P * V / T = R, where R is the specific gas constant for
34:05
whatever fluid you are using. We all know that one.
34:07
But for that beautiful simple equation to work, it makes 2
34:10
massive fictional assumptions about reality.
34:13
First, it assumes that the gas molecules are infinitesimally
34:16
small point masses, that they take up exactly 0 physical
34:19
volume themselves. Which is impossible.
34:20
Right. Second, and more importantly, it
34:22
assumes that these molecules exert absolutely 0
34:25
electromagnetic attractive forces on one another.
34:28
They are essentially modeled as microscopic, perfectly hard
34:31
billiard balls that bounce perfectly off the container
34:34
walls and each other with no stickiness whatsoever.
34:37
Exactly, and tied intimately to the ideal gas law are the
34:41
specific heats. We have C sub P the specific
34:44
heat at constant pressure, and C sub V the specific heat at
34:48
constant volume. These values tell us how much
34:50
thermal energy it takes to raise the temperature of 1 kilogram of
34:54
the gas by 1°. Now a classic interview question
34:57
for Mechanical Engineers is why are there two different specific
35:00
heats for gases? And why is C so P mathematically
35:04
always greater than C sub? That's a good one.
35:06
It comes back to flow work and boundary work.
35:09
Imagine heating a gas that is trapped inside a rigid sealed
35:12
heavy steel tank. The volume cannot change, that
35:15
is constant volume. When you add a blowtorch to the
35:18
tank, 100% of the heat you add goes directly into increasing
35:22
the internal kinetic energy of the molecules.
35:24
It all goes into raising the temperature that is C sub B.
35:27
OK, all heat becomes temperature.
35:28
Right. Now imagine heating that same
35:31
gas, but this time it is inside a cylinder capped with a heavy
35:35
sliding piston. The piston maintains a constant
35:38
pressure on the gas. As the gas heats up, it expands,
35:42
and as it expands, it physically pushes that heavy piston upward
35:45
against the weight of the atmosphere.
35:47
It's doing mechanical work on the environment.
35:49
Exactly. In this constant pressure
35:51
scenario, the heat you add from the blowtorch is forced to do 2
35:55
distinct jobs. It must raise the internal
35:57
temperature of the gas, and it must provide the mechanical
36:00
energy required to push that heavy piston upward.
36:03
Because the heat is split doing 2 jobs, it takes more total heat
36:07
to raise the temperature of the gas by 1°.
36:10
Therefore, C sub B must always be numerically greater than C
36:13
sub V. The difference between them is
36:15
exactly the boundary work done by the expansion.
36:18
But again, the ideal gas law is a mathematical fiction.
36:22
Real molecules are not point masses.
36:24
They do take up physical space, and they are absolutely sticky.
36:28
Water molecules, for example, are highly polar.
36:31
The oxygen and hydrogen atoms create magnetic poles that
36:34
desperately want to attract and stick to other water molecules.
36:38
When fluids get cold or highly compressed, they are shoved so
36:41
close together that these idealized assumptions completely
36:45
collapse. Which is why brilliant physicist
36:47
spent decades developing more complex, realistic equations of
36:50
state equations like the van der Waals equation or the Dieteriche
36:53
equation. These mathematical models
36:55
attempt to fix the glaring flaws of the ideal gas law.
36:58
How do? They fix it.
36:59
Well, van der Waals, for instance, introduced 2 specific
37:02
corrective constants to the equation, universally referred
37:05
to as A&B. The constant is a mathematical
37:09
correction for intermolecular attraction.
37:11
It accounts for the fact that as molecules approach the wall of a
37:14
container, the other molecules behind them are magnetically
37:17
pulling them backward, which effectively reduces the actual
37:20
pressure they exert on the wall. Interesting.
37:21
And the B constant. The B constant is a geometric
37:24
correction. It accounts for the actual
37:26
physical chunkiness of the molecules.
37:29
Because the molecules themselves take up physical space, the
37:32
actual empty void volume available for them to fly around
37:36
in is significantly less than the total volume of the steel
37:39
tank. And understanding how these real
37:41
fluids behave becomes absolutely critical when you push a fluid
37:44
toward its critical point. Let's explain this to the
37:47
listener, because it sounds like sci-fi.
37:49
Every pure substance in the universe has a specific critical
37:53
temperature TCA, critical pressure PC, and a critical
37:56
specific volume VC. What physical madness happens at
38:01
this exact thermodynamic coordinate?
38:03
Oh, it is madness. At the critical point, the
38:05
fundamental distinction between what we call a liquid and what
38:08
we call a gas completely and utterly breaks down.
38:10
Really. Yes.
38:11
If you are at normal atmospheric pressure below the critical
38:14
point and you heat liquid water, you witness a distinct phase
38:18
change. You see boiling.
38:19
You see a physical visible surface boundary separating the
38:23
heavy, dense liquid water at the bottom of the pot from the
38:26
light, invisible steam floating above it.
38:28
Like making pasta. Exactly like making pasta.
38:31
But if you put that water in an ultra high pressure vessel and
38:34
you compress it to a pressure higher than its critical
38:37
pressure, which is over 3200 PSI for water, and then you heat it,
38:42
it never boils it. Just doesn't boil.
38:43
It never boils. You never see bubbles, you never
38:45
see a surface boundary. The fluid just continuously,
38:49
seamlessly morphs from a highly dense fluid into a less dense
38:53
fluid. There is no phase change.
38:55
The fluid exists in a state that defies the simple binary
38:57
categories of liquid or gas. That is wild, and studying this
39:02
critical point gave us something incredibly useful, right?
39:05
The Law of Corresponding States Based on Vander Waal's work,
39:09
scientists realize that if you normalize any fluids, current
39:12
pressure, temperature, and volume by dividing them by their
39:14
absolute critical values, creating a ratio we call reduced
39:17
properties, a fascinating pattern emerges.
39:21
Whether it is nitrogen, methane, or water, all fluids will behave
39:24
roughly the same way at the same reduced properties.
39:27
It proved that the deviations from the ideal gas law are
39:30
universally tied to how close a substance is to its critical
39:33
point. It is a profound realization of
39:36
universal symmetry. However, for daily boots on the
39:40
ground engineering work, complex equations like van der Waals are
39:43
often too mathematically cumbersome or simply too
39:45
imprecise for highly complex mixtures or fluids nearing
39:49
condensation. So what do we do instead?
39:51
That is why in practice we rely heavily on empirical
39:55
thermophysical property tables. If you are designing an
39:58
industrial refrigeration system using R134A or a modern eco
40:02
friendly heat pump using supercritical carbon dioxide,
40:06
you do not calculate the enthalpy from an equation of
40:08
state. You look it up in meticulously
40:10
experimentally derived data tables.
40:13
Especially because these machines operate deliberately
40:15
inside the two phase region. That's the area underneath the
40:18
saturation Dome on a thermodynamic chart where the
40:21
fluid is actively boiling or condensing A chaotic mixture of
40:24
liquid and vapor. Inside that Dome, properties
40:28
like specific volume, enthalpy and entropy change drastically,
40:31
nonlinearly and completely independently of temperature.
40:34
Exactly. The math breaks down entirely
40:35
Under the Dome. But let me push back here on
40:38
behalf of the students who just spent a semester learning PV
40:40
equals RT. If the ideal gas law is a
40:44
fiction, if it ignores the physical chunkiness of
40:47
molecules, if it ignores intermolecular magnetic
40:50
attraction, and if we have access to massive databases of
40:53
highly accurate empirical tables, why do we still teach
40:58
the ideal gas law? Why are we using a flawed
41:00
equation? Because context is everything in
41:03
engineering. The ideal gas law is flawed,
41:05
yes, but in a very specific, very common thermodynamic
41:09
regime, it is incredibly accurate and infinitely faster
41:14
than interpolating massive data tables.
41:16
OK, what regime? The ideal gas law works
41:18
beautifully at high temperatures and low pressures.
41:20
Think about the air intake of a jet engine cruising at altitude.
41:24
The air is at a low atmospheric pressure and once inside the
41:27
engine it gets incredibly hot. Under these conditions, the gas
41:30
molecules are moving at blistering speeds and because of
41:33
the low pressure, they are physically very far apart from
41:35
one another. So they're moving too fast and
41:37
they are too far apart for their magnetic stickiness to grab hold
41:40
of each other. Precisely.
41:42
And because they are so far apart, the physical volume of
41:45
the molecules themselves becomes mathematically insignificant
41:49
compared to the vast empty space between them.
41:52
In that specific high temp low pressure regime, the A&B
41:56
corrections of van der Waals effectively dropped to 0.
41:59
Real gases behave almost exactly like ideal gases.
42:03
The simple math is highly accurate.
42:05
However, the ideal gas law will fail catastrophically if you
42:09
attempt to use it near the saturation line where the gas is
42:12
cold and dense and about to condense into a liquid.
42:15
A master engineer knows the limitations of their tools.
42:19
You use PV equals RT to calculate the airflow through a
42:22
wind tunnel. You absolutely never ever use it
42:25
to calculate the state of the boiling refrigerant moving
42:27
through the evaporator coils of your home air conditioner.
42:30
That right there is the master class difference, knowing
42:33
exactly when the rules apply and when the physical reality
42:36
breaks. Them you have to know.
42:37
So we know how to track the fluids, we know when they act
42:39
perfectly, and we know when they act like real sticky molecules.
42:44
This brings us to section 6, the efficiency illusion.
42:48
If we design a massive multi stage turbine, how do we grade
42:51
its performance? To know if a machine is good, we
42:54
have to compare it to a standard of perfection.
42:57
But as we discussed earlier with entropy, perfection is a moving
43:00
target depending entirely on how you define your boundaries.
43:03
And the most universal metric we use to grade turbo machinery is
43:06
isentropic efficiency. We look at the actual mechanical
43:09
work a machine produce, and we divide it by the theoretical
43:12
work it would have produced if the expansion had been perfectly
43:14
reversible and adiabatic, if the entropy had remained perfectly
43:18
constant. It is a ratio of reality versus
43:20
theoretical perfection. But even within that ratio,
43:24
there's a massive debate that causes endless confusion.
43:27
Let's talk about total to total is entropic efficiency versus
43:30
total to static. This hinges entirely on how we
43:34
treat the kinetic energy of the fluid exhaust.
43:37
When steam leaves a turbine blade, it is moving fast.
43:40
It has significant kinetic energy.
43:42
Is that exhaust velocity considered wasted energy, or is
43:45
it useful energy? It completely and utterly
43:48
depends on the physical application of the machine.
43:50
Let's look at a massive stand alone steam turbine in a coal or
43:54
nuclear power plant. The sole purpose of that turbine
43:57
is to spin a copper generator to make electricity.
44:00
Once the steam leaves the very last row of aerodynamic blades,
44:04
any forward velocity it still possesses is entirely useless.
44:08
It just shoots into the massive void of the condenser and slams
44:11
into the cooling tubes. It doesn't help spin the shaft
44:13
does. Waste.
44:14
In that specific context, the exhaust kinetic energy is pure
44:17
waste. Therefore we evaluate that
44:19
machine using a total to static efficiency metric.
44:22
This metric strictly penalizes the turbines grade for leaving
44:24
UN extracted kinetic energy in the exhaust stream.
44:27
But what if that exact same turbine geometry was bolted onto
44:31
the back of a military fighter jet?
44:34
Then the rules of the game change entirely.
44:36
If it is the final turbine stage of an aircraft jet engine, that
44:40
high speed exhaust kinetic energy isn't waste at all.
44:43
It is the entire point of the machine.
44:45
That high velocity exhaust is the propulsive thrust keeping
44:49
the jet in the sky. Or consider an intermediate
44:53
stage in a multi stage turbine. The high speed fluid exiting
44:56
stage 1 shoots directly into the inlet guide veins of stage 2.
45:01
That velocity isn't lost. It is highly useful input energy
45:05
for the next row of blades. So you don't penalize it.
45:07
Exactly. In both of those cases, we use
45:09
total to total isentropic efficiency.
45:11
This metric mathematically credits the machine for the
45:14
kinetic energy remaining in the exhaust, treating it as a highly
45:17
useful output rather than a thermodynamic loss.
45:20
You have to draw your control volume carefully and understand
45:23
the physical intent of the machine.
45:24
That makes perfect sense. Context dictates the metric.
45:28
But here is where the math of efficiency plays a cruel hidden
45:32
trick on engineers. Let's dive into the hidden
45:35
thermodynamic effect, which is also commonly known as the
45:38
Preheat effect in compressors or the reheat effect in turbines.
45:42
Oh this is a mind Bender. It absolutely is.
45:44
This concept is just mind blowing when you first encounter
45:46
it. The mathematical truth is this.
45:49
The overall isentropic efficiency of finite multi stage
45:53
compressor is always less than the isentropic efficiency of its
45:56
small individual stages. If every individual row of
45:59
blades is 90% efficient, the overall 10 stage compressor will
46:03
somehow be less than 90% efficient.
46:05
Why does the math penalize the whole machine?
46:07
It goes directly back to our discussion of entropy, friction
46:10
and waste heat. Let's carefully walk through a
46:12
large compressor made of 10 individual stages, 10 rows of
46:16
spinning blades. OK, visualizing that.
46:18
As the air gets violently compressed through stage 1,
46:21
fluid friction generates waste heat.
46:25
This is irreversible entropy generation.
46:28
Because of this internally generated waste heat, the air
46:31
entering stage 2 is physically hotter than it theoretically
46:34
should have been. Now recall the first law
46:37
boundary work principle we discussed with specific heats.
46:40
The mechanical work required to compress a gas is directly
46:43
proportional to its specific volume.
46:46
Pushing a large, hot, swollen volume of gas takes
46:49
significantly more mechanical work than pushing a small, cold,
46:52
dense volume of gas. So the aerodynamic inefficiency
46:56
of stage 1 generates heat which swells the gas, making the
47:00
actual physical job of compression harder for stage 2.
47:02
Exactly. Stage 1's thermodynamic failure
47:05
makes Stage 2's mechanical job fundamentally harder, and then
47:08
Stage 2 generates its own frictional heat, compounding the
47:11
problem and making Stage 3's job even harder.
47:14
The heat penalty compounds exponentially down the line.
47:16
So it's snowballs. It's snowballs.
47:19
Because of this compounding thermal penalty, the overall
47:23
isentropic efficiency of the entire 10 stage machine will
47:26
calculate out to be lower than the aerodynamic efficiency of
47:29
the individual blade rows. The overall metric is
47:32
mathematically polluted by the thermodynamics of heating.
47:36
And this hitter thermodynamic effect leads to a massive real
47:39
world pain point that catches junior engineers constantly.
47:43
Imagine you are LED engineer on a new chemical plant.
47:47
A vendor comes into your office pitching two different
47:49
industrial compressors. Compressor A is a standard
47:52
machine with a moderate pressure ratio of five to one.
47:55
Compressor B is an absolute beast.
47:57
It has a massive pressure ratio of 20 to 1.
47:59
I've seen this play out so many times.
48:01
The young engineer takes the vendors spec sheets, calculates
48:04
the overall isentropic efficiencies and sees that the
48:07
high pressure compressor B has a lower overall isentropic
48:10
efficiency score. They immediately conclude that
48:13
Compressor B is a poorly designed machine built with
48:15
inferior aerodynamic blade profiles.
48:18
And that conclusion is entirely mathematically invalid.
48:21
It is a completely unfair comparison.
48:23
Because of the snowball effect. Exactly.
48:25
Compressor B is being heavily penalized by the hidden
48:27
thermodynamic effect simply because it compresses the gas to
48:31
a much higher pressure, thereby generating vastly more
48:34
compounding waste heat across a larger number of stages.
48:38
Compressor B might actually have vastly superior highly advanced
48:41
blade aerodynamics compared to compressor A, but the overall
48:44
isentropic efficiency metric completely masks the aerodynamic
48:48
brilliance because it is overwhelmed by the thermodynamic
48:51
heat penalty of the 20 to 1 compression ratio.
48:53
So how do you actually compare them fairly?
48:55
If isentropic efficiency lies to us across different pressure
48:59
ratios, what metric do we use to see the true and dynamic quality
49:02
of the blades? You must abandoned isentropic
49:04
efficiency and use polytropic efficiency.
49:06
Polytropic efficiency. Atrophic efficiency is a
49:09
brilliant mathematical workaround.
49:11
It essentially takes the compressor and mathematically
49:14
slices it up into an infinite number of infinitesimally small
49:18
compression stages. By doing this, it completely
49:21
removes the compounding heat penalty from the equation.
49:25
Polytropic efficiency reveals the true unpolluted aerodynamic
49:29
quality of the machine, completely independent of its
49:32
overall pressure ratio. If you are comparing machines
49:34
with different pressure ratios, you must use polytropic
49:37
efficiency. That is a multi $1,000,000
49:39
nugget of practical engineering wisdom.
49:42
It really is. All right, we are entering the
49:44
final stretch, Section 7, answering the Internet's biggest
49:48
questions. We scoured the engineering
49:50
subreddits, the mechanical forms, the dark corners of the
49:53
Internet where engineers go at 2:00 AM when their CFD
49:56
simulations are crashing and their real world hardware is
49:59
failing on the test stand. We are going to take the factual
50:02
thermodynamic principles we've discussed today and use them to
50:05
definitively answer the most common points of confusion.
50:08
Let's address the pain points. I am ready.
50:10
Question number one, this is a classic desperate plea from the
50:14
forums. Why is my real world compressor
50:17
drawing significantly more electrical power than my simple
50:21
P * V = R times key calculation predicted?
50:24
My math says I only need 100 horsepower motor, but the actual
50:28
physical compressor on the floor is tripping the 150 horsepower
50:31
breaker. What went wrong?
50:33
Well, if you have been following this master class, we have
50:36
already provided all the puzzle pieces to solve this mystery.
50:39
If you sized your motor using PV equals RT, you made two massive,
50:44
highly idealized assumptions that reality is actively
50:47
punishing you for. Which are.
50:48
First, you assume the gas behaves like a perfect ideal
50:51
gas. But if you were compressing an
50:53
industrial fluid to very high pressures, or if the fluid is
50:55
particularly cold, you might be nearing the saturation Dome.
50:59
You are entering a state where the actual physical
51:01
compressibility of the fluid changes drastically.
51:03
The physical volume of the gas is different than your simple
51:06
equation predicted, which alters the flow work required.
51:09
And the second assumption. 2nd, and far more importantly, your
51:12
simple calculation assumed a 100% reversible isentropic
51:16
compression process. You mathematically assumed there
51:19
was 0 friction. They ignored the tax.
51:21
Ma'am, exactly. In reality your compressor is
51:24
violently thrashing the fluid. It is generating massive amounts
51:28
of entropy through mechanical bearing friction, aerodynamic
51:31
turbulence over the blades, and heat loss through the heavy
51:34
steel casing. You failed to account for the
51:37
Goystodolith theorem. So that extra 50 horsepower?
51:40
That extra 50 horsepower your electric motor is desperately
51:43
drawing from the grid that is the physical electrical
51:46
manifestation of T 0 * S Gen. It is the real world financial
51:51
penalty for irreversibility. You cannot use a theoretical
51:55
ideal calculation to size real hardware.
51:57
You must use the empirical isentropic or polytropic
52:00
efficiency of that specific compressor model to scale up
52:03
your theoretical ideal work to find the actual brutal shaft
52:07
work reality demands. Beautifully explained.
52:09
It's always the entropy tax question #2 we touched on this
52:12
during the efficiency discussion, but let's make it
52:15
crystal clear for the aeronautical guys.
52:18
Does kinetic energy at the exhaust of a turbine always hurt
52:21
my system's overall efficiency? No, absolutely not.
52:26
Context is the supreme ruler of thermodynamics.
52:30
If you are designing a massive stand alone steam turbine in a
52:33
geothermal plant and exhaust directly into a gigantic
52:36
stationary cooling condenser, then yes, any residual velocity
52:40
in that steam is wasted kinetic energy.
52:42
It could have been extracted by adding one more row of blades to
52:45
spin the shaft. But if you are designing the
52:48
high pressure turbine of a military turbofan engine, that
52:51
exhaust kinetic energy is emphatically not waste.
52:54
It is the entire functional output of the engine.
52:56
It is your jet drust. Or if you are doing
52:59
thermodynamic analysis on a 15 stage industrial compressor, the
53:02
high speed exit velocity of stage 4 is the required inlet
53:05
kinetic energy for stage 5. It isn't wasted, it is simply
53:09
passed sequentially down the thermodynamic line.
53:11
You just have to know your boundaries.
53:12
You must draw your mathematical control volume boundary with
53:15
extreme care, and you must understand the specific
53:18
engineering purpose of the fluids kinetic energy at that
53:21
exact location in the machine. And finally, question #3 this
53:25
one comes constantly from HVAC engineers, refrigeration
53:29
technicians, and anyone designing thermal management
53:32
systems. How do I avoid getting
53:35
completely lost in the massive thermal physical property tables
53:39
for refrigerants like R134A? There are hundreds of pages of
53:43
numbers and none of them seem to follow a simple equation.
53:47
How do I know which number to pick?
53:49
Surviving the property tables requires absolute respect for
53:52
the thermodynamic phase boundaries.
53:54
You must always, always check your physical pressure and your
53:57
physical temperature against the saturation lines first.
54:00
Always check where you are. Yes, if your measured
54:02
temperature is higher than the boiling point for your given
54:04
pressure, you are in the Super heated vapor regime.
54:07
You go to the Super heated tables where the fluid acts
54:10
relatively close to a normal gas.
54:12
If your temperature is lower than the boiling point, you are
54:14
a subcooled liquid. But the trap is the saturation
54:18
line. Exactly.
54:19
If your pressure and temperature match exactly on the saturation
54:22
curve, you are trapped underneath the thermodynamic
54:25
Dome. You are dealing with a violent
54:27
two phase mixture of boiling liquid and expanding vapor.
54:31
And Under the Dome, pressure and temperature are completely
54:34
locked together. Knowing the temperature tells
54:36
you absolutely nothing about how much energy is in the fluid,
54:39
because it could be 1% vapor or 99% vapor at that exact same
54:43
temperature. Precisely when you are Under the
54:45
Dome, to find your actual emphopy and your actual entropy,
54:49
you must calculate a property called quality.
54:53
Quality, usually denoted by the letter X, is the strict
54:56
mathematical ratio of the mass of the vapor to the total mass
54:59
of the mixture. OK, so you find the X.
55:02
Once you calculate the exact quality, you use it as a
55:04
percentage to mathematically interpolate between the pure
55:08
liquid enthalpy value and the pure vapor enthalpy value listed
55:11
in the tables. If you don't calculate the
55:13
quality, you are flying completely blind in the two
55:16
phase region and your refrigeration cycle calculations
55:18
will be completely worthless. Find the quality, find your
55:22
enthalpy. That is how you survive the
55:24
Dome. We have covered incredible
55:26
ground in this master class today, from the absolute
55:29
foundations of the 1st and 2nd laws through the physical
55:33
reality of enthalpy and the brutal taxes of entropy
55:36
generation. We've exposed the limits of
55:39
Bernoulli's equation, explored the hidden thermodynamic
55:42
penalties of high pressure compressors, and navigated the
55:45
messy, sticky reality of real world fluids and two phase
55:50
refrigerants. It's a lot, but it's the
55:51
foundation of everything we build.
55:53
It is, but I want to leave you, the listener, with one final
55:56
provocative thought to Mull over as you step back out into the
55:59
real world. We talked about the critical
56:01
point, that bizarre thermodynamic coordinate where
56:04
the math of van der Waals starts breaking down and the distinct
56:07
line between a liquid and the gas completely blurs.
56:10
But what happens if you push a fluid way, way past that
56:13
critical point? You engineer something called a
56:15
supercritical fluid. It is one of the most bizarre
56:17
states of matter in the universe.
56:19
It physically expands to fill his container exactly like a
56:22
gas, but it retains the dense, heavy dissolving power of a
56:26
liquid. It's honestly incredible.
56:29
It sounds like a physics anomaly, but it is the absolute
56:32
frontier of modern engineering. Today we use supercritical water
56:36
operating at mind boggling pressures and temperatures to
56:39
drive the most advanced, ultra efficient power generation
56:42
turbines on Earth. And on the complete opposite end
56:45
of the spectrum, we use supercritical carbon dioxide as
56:48
a massive industrial solvent to naturally dissolve and extract
56:51
caffeine from coffee beans without leaving behind any toxic
56:54
chemical residues. From turbines to decaf coffee.
56:58
Exactly. All of this world changing
57:00
cutting edge technology was born simply from engineers
57:04
aggressively pushing the extreme limits of the pressure, volume,
57:07
and temperature surface we explore today.
57:10
These equations aren't just dry math on a page, they're the
57:13
literal glue prints for controlling the physical
57:15
universe. If this helped you even a little
57:19
say something. We're putting this out for free.
57:20
No paywall, no subscription, nothing locked.
57:22
Buying a card that only works if we know it's actually reaching
57:27
people and doing what it's supposed to do.
57:29
If you're a young engineer trying to figure this stuff out
57:31
and this gave you clarity you weren't getting anywhere else,
57:34
drop a like, leave a comment. It takes 2 seconds on your end,
57:37
but it tells us this is worth continuing instead of just
57:39
talking into the void. We're excited for your feedback.
57:42
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