Is Enthalpy a Valid Concept Despite Dimensional Mismatch?

[Sailor Al]

By definition (Anderson J) enthalpy, h = e + pV
It looks to me like adding apples and oranges.
Look at the dimensional analysis:
e, energy is ML²T^-2
P, pressure is ML^-2
V, volume is L³
Thus PV is ML
which is quite different from e:ML²T^-2

Am I missing something?

 

[jedishrfu]

Your definition of pressure is wrong, it should be

$P = M L^{−1} T^{−2}$

https://en.wikipedia.org/wiki/Pressure

which yields $E = M L^{−1} T^{−2} L^3 = M L^2 T^{−2}$

 

[Sailor Al]

D'OH. Once again, I was confusing mass with weight. Thanks

 

[Sailor Al]

It seems that the theory of enthalpy was introduced in the 19th century to assist in understanding the way heat and energy behaved when water transitioned between the states of liquid and vapour. It turned out to be a really useful thermodynamic property.

I don't understand why enthalpy is of any interest in aerodynamics.
For an ideal gas: no intermolecular forces, no molecular radius (point molecules) no viscosity, but still modelled with molecular theory, so polyatomic and with atomic weights, so C_P/C_V = γ, then U = PV, right?

So, the enthalpy of an ideal gas: h = U + PV = PV + PV = 2PV, right?
So why do aerodynamic textbooks (Anderson et. al.), when developing aerodynamic theories based on air as an ideal gas, operating within the limited ranges of pressure, temperature and density that apply to subsonic flight in our atmosphere, involve enthalpy, when for all such situations H = 2PV = 2nRT?

I guess my original question should have been:
"In aerodynamics, is enthalpy a real thing?"

 

[russ_watters]

U = PV, right?

No, where are you getting that from?
https://en.wikipedia.org/wiki/Internal_energy#Internal_energy_of_the_ideal_gas

So why do aerodynamic textbooks (Anderson et. al.), when developing aerodynamic theories based on air as an ideal gas, operating within the limited ranges of pressure, temperature and density that apply to subsonic flight in our atmosphere, involve enthalpy, when for all such situations H = 2PV = 2nRT?
I guess my original question should have been:
"In aerodynamics, is enthalpy a real thing?"

I guess the basic answer is you don't know if something's relevant or not until you calculate it. My copy of Anderson (3rd ed) mentions enthalpy exactly once in the whole book.

...but also it's not just about low speed subsonic flight. My copy, anyway, has sections on both propulsion and hypersonic flight, both of which are very much thermodynamic issues.

 

[Sailor Al]

I guess the basic answer is you don't know if something's relevant or not until you calculate it. My copy of Anderson (3rd ed) mentions enthalpy exactly once in the whole book.

Anderson appears to have found it relevant since between your copy (3rd ed) and mine (6th ed), the pages on which it is mentioned has gone up to 41 pages.

 

[Chestermiller]

Enthalpy is not a fundamental physical parameter in thermodynamics, unlike internal energy U and entropy S. Thermodynamics can be completely developed without ever mentioning enthalpy. However, enthalpy is a very convenient grouping of parameters U + PV that occurs extensively in thermodynamics scenarios and systems, and it is a shorthand parameter for representing U + PV. Representing many thermodynamics relationships would be very inconvenient without making use of H in place U+PV.

 

[Sailor Al]

Enthalpy is not a fundamental physical parameter in thermodynamics, unlike internal energy U and entropy S. Thermodynamics can be completely developed without ever mentioning enthalpy. However, enthalpy is a very convenient grouping of parameters U + PV that occurs extensively in thermodynamics scenarios and systems, and it is a shorthand parameter for representing U + PV. Representing many thermodynamics relationships would be very inconvenient without making use of H in place U+PV.

Yes, I understand that enthalpy is not fundamental to thermodynamics, but is still a useful grouping of parameters, but my question is whether enthalpy is relevant to the specific field of aerodynamics, where air interacts with a body and if so, how?

 

[jack action]

The concept of stagnation point is where enthalpy is mostly useful.

$$h + \frac{V^2}{2} = h_0 \tag{7.54}$$
Equation (7.54) is important; it states that at any point in a flow, the total enthalpy is given by the sum of the static enthalpy plus the kinetic energy, all per unit mass. [...]

that is, the total enthalpy is constant along a streamline.

When converted to stagnation temperature, it gives us a very useful equation when compressible effects are relevant in aerodynamics (M > 0.3):
$$h_0 = h + \frac{V^2}{2}$$
$$T_0 = T + \frac{V^2}{2C_p}$$
Or:
$$\frac{T_0}{T} = 1 + \frac{M^2 \frac{C_p}{C_v}(C_p - C_v)T}{2C_pT}$$
$$\frac{T_0}{T} = 1 + \frac{\frac{C_p}{C_v} - 1}{2}M^2$$

 

[Sailor Al]

I came unstuck at: "that is, the total enthalpy is constant along a streamline."
Reading Anderson's definition of a streamline (p. 18, 6th ed):
"a moving fluid element traces out a fixed path in space. As long as the flow is steady (i.e., as long as it does not fluctuate with time), this path is called a streamline of the flow. "
"a fixed path" sounds to me like a geometrical line - i.e. one with no thickness. How can a line of no thickness have enthalpy?

 

[Chestermiller]

I came unstuck at: "that is, the total enthalpy is constant along a streamline."
Reading Anderson's definition of a streamline (p. 18, 6th ed):
"a moving fluid element traces out a fixed path in space. As long as the flow is steady (i.e., as long as it does not fluctuate with time), this path is called a streamline of the flow. "
"a fixed path" sounds to me like a geometrical line - i.e. one with no thickness. How can a line of no thickness have enthalpy?

It can have enthalpy per unit mass.

 

[Juanda]

I came unstuck at: "that is, the total enthalpy is constant along a streamline."
Reading Anderson's definition of a streamline (p. 18, 6th ed):
"a moving fluid element traces out a fixed path in space. As long as the flow is steady (i.e., as long as it does not fluctuate with time), this path is called a streamline of the flow. "
"a fixed path" sounds to me like a geometrical line - i.e. one with no thickness. How can a line of no thickness have enthalpy?

Let's describe a scalar field to describe the temperature of a sheet of metal. Each of the points at the surface will have a temperature so that $T(x,y)$ if it is only dependent on the position or $T(x,y,t)$ if it also changes in time.
For the moment, let's consider the stationary case that doesn't change with time so $T(x,y)$. Such a field may be represented as a 3D surface where the height represents the temperature or a 2D surface with colors representing the temperature.

These graphs have no relation with one another. They are the first I could find to help transmit what I'm trying to say. By the way, I am aware the 3D surface has color too which is technically not necessary unless you're representing an additional variable but it's what I found on the internet.

The main idea is that each point has a temperature value. However, according to your reasoning, how could that be possible? Temperature is a property of mass and a point has no volume hence no mass by definition. Therefore, points should not have any temperature associated (I'm not sure about black holes but let's leave that for another day).
That clearly makes not much sense so the initial reasoning is faulty.

If we study the case from a numerical/practical perspective by dividing the metal sheet and associated temperature field into chunks and then start increasing the resolution of the mesh by making the chunks smaller and smaller, at the very end we reach continuity which is a useful mathematical concept to describe many situations.
This can cause quite some headaches. For example, with integration, you're fundamentally adding up an infinite number of vertical rectangles with infinitely small withs and this turns up to a number. It is weird but it works and mathematicians put some effort into making it consistent and solid so roll with it.

 

[Juanda]

Enthalpy is not a fundamental physical parameter in thermodynamics, unlike internal energy U and entropy S. Thermodynamics can be completely developed without ever mentioning enthalpy. However, enthalpy is a very convenient grouping of parameters U + PV that occurs extensively in thermodynamics scenarios and systems, and it is a shorthand parameter for representing U + PV. Representing many thermodynamics relationships would be very inconvenient without making use of H in place U+PV.

If other properties such as $U$ or $S$ can be derived from $P$, $v$ and $T$. Could we consider $U$ or $S$ not fundamental either?

For example, in an ideal gas, $u=c_vT$ because of the equation of state $Pv=RT$ according to Maxell relations and experiments like the one done by Joule from 1843. Then, I can either know $T$ or $u$ and immediately derive the other in the same way that $h$ can be derived from other properties.

I'm aware the ideal gas is mostly an approximation and it only works within a certain range. This is just a thought about an ideal gas.

 

[Chestermiller]

If other properties such as $U$ or $S$ can be derived from $P$, $v$ and $T$. Could we consider $U$ or $S$ not fundamental either?

For example, in an ideal gas, $u=c_vT$ because of the equation of state $Pv=RT$ according to Maxell relations and experiments like the one done by Joule from 1843. Then, I can either know $T$ or $u$ and immediately derive the other in the same way that $h$ can be derived from other properties.

I'm aware the ideal gas is mostly an approximation and it only works within a certain range. This is just a thought about an ideal gas.

An ideal gas is a special case.

 

[Sailor Al]

My question is whether enthalpy is relevant to the specific field of aerodynamics, where air interacts with a body and if so, how.

 

[Juanda]

My question is whether enthalpy is relevant to the specific field of aerodynamics, where air interacts with a body and if so, how.

Didn't @jack action already mention a case at post #9?

 

[Sailor Al]

Didn't @jack action already mention a case at post #9?

No, his link was to a Wikipedia article on stagnation temperature, not an answer to the question posed.

 

[Juanda]

No, his link was to a Wikipedia article on stagnation temperature, not an answer to the question posed.

The original question was: Is enthalpy a real thing?
Yes, it's real.

Then, the question shifted to: In aerodynamics, is enthalpy a real thing?
It still is.

Later it changed to: but my question is whether enthalpy is relevant to the specific field of aerodynamics, where air interacts with a body and if so, how?
Then, post #9 gave you an example of how it can be relevant in aerodynamics. The post does have more than just a link to Wikipedia as you suggest in #17. If the Wiki article and the provided formulas by him are not enough, he also gave you a source you can check.

To me, it seems you want enthalpy to not be relevant. As Chestermiller said in #7 you can avoid using enthalpy if you prefer it. I am not a huge fan of enthalpy myself but there is no point in going against the world. For example, data is already tabulated and ready to use so not using it just to prove a point seems very inefficient.

 

[Sailor Al]

The original question was: Is enthalpy a real thing?
Yes, it's real.

Then, the question shifted to: In aerodynamics, is enthalpy a real thing?
It still is.

Later it changed to: but my question is whether enthalpy is relevant to the specific field of aerodynamics, where air interacts with a body and if so, how?

I apologise for my earlier questions. They were poorly phrased and did not accurately reflect my underlying issue. I think it is more accurately expressed my question in my post #8:

Yes, I understand that enthalpy is not fundamental to thermodynamics, but is still a useful grouping of parameters, but my question is whether enthalpy is relevant to the specific field of aerodynamics, where air interacts with a body and if so, how?

I would also qualify the question to address relative speeds considerably below Mach 1 and in our normal atmospheric conditions.
Sorry for the confusion.

 

[jack action]

So why do aerodynamic textbooks (Anderson et. al.), when developing aerodynamic theories based on air as an ideal gas, operating within the limited ranges of pressure, temperature and density that apply to subsonic flight in our atmosphere, involve enthalpy, when for all such situations H = 2PV = 2nRT?

I would also qualify the question to address relative speeds considerably below Mach 1 and in our normal atmospheric conditions.

In Anderson 5th ed., the enthalpy is introduced in the compressible flow section (Part 3: Inviscid, Compressible Flow; Chapter 7.7.2: Internal energy and enthalpy, p. 518). It is not mentioned in Part 1 (Fundamental Principles) nor Part 2 (Inviscid Incompressible Flow).

 

[russ_watters]

Looks like Chet gave you a good/concise answer about 8 months ago. How was it insufficient?

https://physics.stackexchange.com/questions/729947/is-enthalpy-relevant-to-aerodynamics

 

[JT Smith]

Why bowlines? They're not even real knots. Wouldn't a figure-8 make more sense?

 

[Sailor Al]

Looks like Chet gave you a good/concise answer about 8 months ago. How was it insufficient?

https://physics.stackexchange.com/questions/729947/is-enthalpy-relevant-to-aerodynamics

The problem was, as I indicated then in response to his explanation:

But the fact is that the temperature of the air does change due to compression, whether that change is large or small is irrelevant to the discussion. If the process (air over a wing or sail) is not exothermic or endothermic and there's no change of state between solid, liquid or gas, why is Anderson introducing enthalpy into the explanation?

and to niels nielsen on the same thread:

But the pressure changes are big enough to provide the lift, so while they may be small compared to the atmospheric pressure, they are still very significant and thus will generate temperature changes (PV = nRT). It's not the use of thermodynamics that I am questioning. It's the use of enthalpy that I'm questioning.

As there were no responses to my inquiries on Stack Exchange, I am hoping that Physics Forums may be able to provide an answer.

 

[Chestermiller]

The problem was, as I indicated then in response to his explanation:

and to niels nielsen on the same thread:

As there were no responses to my inquiries on Stack Exchange, I am hoping that Physics Forums may be able to provide an answer.

Why don’t you just set up the equations yourself and let’s see what you come up with?

 

[berkeman]

Why don’t you just set up the equations yourself and let’s see what you come up with?

+1

 

[jack action]

But the fact is that the temperature of the air does change due to compression, whether that change is large or small is irrelevant to the discussion. If the process (air over a wing or sail) is not exothermic or endothermic and there's no change of state between solid, liquid or gas, why is Anderson introducing enthalpy into the explanation?

How about a change across a shock wave?

The appearance of pressure-drag on supersonic aircraft is mostly due to the effect of shock compression on the flow.

More info: https://en.wikipedia.org/wiki/Wave_drag

 

[Sailor Al]

Why don’t you just set up the equations yourself and let’s see what you come up with?

I don't see how that would answer my question:

my question is whether enthalpy is relevant to the specific field of aerodynamics, where air interacts with a body and if so, how?

 

[PeterDonis]

I don't see how that would answer my question

What that suggestion from @Chestermiller means is: multiple people have already given you answers to your question. So if what they've already said is not enough for you, then it's time to work through the math in order to see what's going on in more detail. And that is something you need to do the heavy lifting on.

 

[PeterDonis]

The problem was, as I indicated then in response to his explanation:

If the process (air over a wing or sail) is not exothermic or endothermic...

Why would you assume that? You do know that, for example, airplane wings and fuselages heat up in response to air flowing by them, yes?

 

[Sailor Al]

Why would you assume that? You do know that, for example, airplane wings and fuselages heat up in response to air flowing by them, yes?

Yes, but it's not an exothermal process. According to Young and Freedman, University Physics with modern physics, Sears and Zemansky 15th Edition p. 1466:

When Q is negative, the mass increases and the kinetic energy decreases, and the reaction is called an endoergic reaction. The terms exothermal and endothermal, borrowed from chemistry, are also used.

I think you will find that the temperature rise from the compression of air on airplane wings and fuselages is not a chemical process and so is not exothermic.