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In the case of a fluid, does the $PV$ contribution to the enthalpy correspond to the pressure energy in fluid mechanics? (Related: What is Pressure Energy?)

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ergon
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  • Please define the term "pressure energy in fluid mechanics." – Chet Miller Mar 21 '16 at 19:11
  • the energy stored in a fluid that is under pressure and has thus the potential to produce work – ergon Mar 21 '16 at 20:13
  • OK. It is easy to string words together like this, but hard to provide a precise description of the concept. Let me ask it in another way. What is the mathematical definition of pressure energy? Please provide a specific example for how PV represents energy stored in a fluid, and how it does work. – Chet Miller Mar 21 '16 at 23:40
  • dPdV is the work done when there is no change in temperature – ergon Mar 22 '16 at 20:17
  • How can that be possible? This is the product of two differentials, so it must be taken as zero. In a closed system, irrespecitve of whether the temperature is constant, the work done by the system on the surroundings is always equal to the integral of $P_{ext}dV$, where $P_{ext}$ is the pressure at the interface between the system and the surroundings. Hasn't this been covered in your thermodynamics course? – Chet Miller Mar 22 '16 at 20:26
  • well, by dPdV I basically wanted to say d(PV). But what is your point? That there is no such thing as pressure energy? How do you call then the energy of a fluid in a container due to its pressure? – ergon Mar 23 '16 at 13:16
  • d(PV) is not the work either, except maybe with reference to the work required to push material into or out of an open system (in which case, the work per unit mass leaving is $P_{out}V_{out}$, where $V_{out}$ is the specific volume of the exit stream). I have never heard the term "pressure energy." Regarding "the energy of a fluid in a container due to pressure," I have never heard such terminology and it means nothing to me. Somehow, this has never limited my ability to obtain correct solutions to systems involving thermodynamics. – Chet Miller Mar 23 '16 at 14:04
  • Can you give a single reference to the concept of "pressure energy" in the literature (other than online references)? You seem obsessed with identifying a physical interpretation for PV as a "pressure energy" concept. Might I humbly suggest that you could employ your valuable time much more productively by solving a large number of textbook problems to solidify your understanding and ability. – Chet Miller Mar 23 '16 at 21:52
  • thanks but what is PV and how can it add up to internal energy to make enthalpy? – ergon Mar 24 '16 at 14:19
  • It is just the pressure times the volume in an equilibrium state. The real question is, what is the physical interpretation of enthalpy, which we obtain by adding PV to U? The answer is that there is not a really good physical interpretation for enthalpy; it is just a convenient function to work with in solving many kinds of thermodynamics problems. As I said, please don't spend too much of your valuable time trying to ascribe a physical interpretation to the quantity we call enthalpy. – Chet Miller Mar 24 '16 at 22:55
  • Chester Miller I finally found a reference for the term 'pressure energy'. It is in my lecturer's notes and it is synonym to the pressure head as in Bernoulli's equation. So there IS pressure energy and it is the energy due to the pressure of a fluid. The term also appears in http://hyperphysics.phy-astr.gsu.edu/hbase/pber.html – ergon Apr 10 '16 at 17:31
  • Yes, I can see that your lecturer would be inclined to call it "pressure energy" when discussing the Bernoulli equation, because it appears in conjunction with kinetic and potential energy. I can also see where it comes into play in the open system version of the 1st law of thermodynamics, where it is in the input and output streams of the control volume, and is as part of enthalpy in conjunction with the kinetic and potential energies (per unit mass) of these streams. So, the next time someone refers to it as "pressure energy," I will know what they are referring to. – Chet Miller Apr 11 '16 at 01:09
  • Still, in terms of fundamental physical significance in contexts other than in fluid mechanics (particularly thermodynamics), its significance eludes me. – Chet Miller Apr 11 '16 at 01:13
  • So I was right, pressure energy exists, right? It's afterall potential to do work, if you have a gas under pressure. And it's not due to its potential energy due to gravity. It can be part of the internal energy. – ergon Apr 11 '16 at 18:24
  • I agree that your lecturer uses the term "pressure energy" although I haven't heard it before (so it's not widely used). I don't agree with the interpretation that it's the overall potential to do work (whatever that means), particularly for a gas, and I definitely don't agree that it can be part of internal energy. It is part of enthalpy (internal energy + PV). Sorry if this doesn't make you happy. – Chet Miller Apr 11 '16 at 20:47
  • Regarding the open system version of the 1st law of thermodynamics, this is the only example of a situation I can think of in which PV can be directly associated with work. It comes into play for the inlet and outlet streams of the control volume. PV represents the work per unit mass done by the material in the control volume to force mass out against the back pressure of the fluid ahead. Similarly, for the material entering, it represents the work per unit mass done by the material behind to force mass into the control volume. – Chet Miller Apr 12 '16 at 10:56

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