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Re: [Phys-l] Bernoulli, enthalpy, work/KE theorem, etc.



Quick comment on my last post. ds is obviously taken as the length of the fluid parcel so Ads = V. Also, the pipe is just a visualization device. It can be replaced by streamlines surrounding the parcel.

The reason for considering enthalpy in the first place is for situations dealing with the change in energy of a fluid flowing through a fixed volume. There is the possibility of changing the energy within the volume by doing paddle work and heating, but one also must consider the enthalpy flowing across the boundaries of the volume. Here the enthalpy is considered to be (PV +mgh +1/2 mv^2) per unit volume times the volume flow rate in and out of the volume being considered. This works well for flow through ductwork, including fans and heat losses.

Bob at PC

-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-
bounces@carnot.physics.buffalo.edu] On Behalf Of LaMontagne, Bob
Sent: Monday, December 06, 2010 12:17 PM
To: Forum for Physics Educators
Subject: Re: [Phys-l] Bernoulli, enthalpy, work/KE theorem, etc.

I have sometimes used a "back of the envelope" approach to introducing
enthalpy in fluid flow.

Consider a pipe tilted upward at an angle theta. Then choose a small
element of mass, m, with a volume, V, in the pipe of cross sectional
area A. The net force on m is

PA - (P+dP)A - mgsin(theta) = -Adp - mgsin(theta)

Now apply the work-KE formula

[-AdP - mgsin(theta)]ds = d(1/2 mv^2)

this is

-VdP - mg[ds sin(theta)] = d(1/2 mv^2)

use dh = ds sin(theta) and rearrange

VdP + mg dh +d(1/2 mv^2) = 0

The left side of the equation can be called dH, H being a quantity
(call it enthalpy) that is a constant during the motion of the little
parcel. If this is compared to the energy equation dE = -PdV +mgdh +
d(1/2 mv^2) for the parcel, it is clear that H = E + PV.

Bob at PC

-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-
bounces@carnot.physics.buffalo.edu] On Behalf Of John Denker
Sent: Monday, December 06, 2010 6:15 AM
To: Forum for Physics Educators
Subject: [Phys-l] Bernoulli, enthalpy, work/KE theorem, etc.

I would like to inject an idea into this discussion: enthalpy.

It turns out that the so-called Bernoulli head (the quantity that
remains constant along a stream line) is essentially equivalent
to the specific enthalpy. If you think about it the right way,
this just what you would expect, since we are trying to keep
track of the energy of the parcel under conditions where the
parcel is free to do PdV work against the surrounding fluid.

This allows us to clearly understand that the energy of the parcel
is *not* constant (except in trivial cases).

Also the density, volume, and temperature are not constant. Not
even approximately constant.

That gives us an easy way of deriving and/or remembering the form
of Bernoulli's equation ... and understanding what it means.

I wrote this up in the form of a new section here:
http://www.av8n.com/physics/bernoulli.htm#sec-enthalpy

This includes (yet again) a discussion of why Bernoulli's principle
applies just fine to compressible fluids. Even the simplified
first-order approximation applies just fine to compressible fluids.
It already and inherently accounts for compressibility to first
order ... which is a good thing, since there are no incompressible
fluids.

This approach has the advantage of elegance. The disadvantage is
that it will scare away any students who don't have a comfortable
grasp of what enthalpy is.

==========

And now let me inject another idea: the work/KE theorem.

This gives us a second way of deriving and understanding Bernoulli's
equation.

I have not yet fully written up my notes on this, but the idea
is implicit in the equations here:
http://www.av8n.com/physics/bernoulli.htm#sec-force-work-ke

I suspect that just mentioning the idea is enough of a hint to rev
up the clever people on this list.

Note that "work" as in P dV is not necessarily the type of "work"
that connects to the work/KE theorem. Refer to the diagrams at
http://www.av8n.com/physics/bernoulli.htm#sec-force-work-ke

=================================

I have been contemplating the question, what makes fluid dynamics
so hard?

If you look at the derivation of Bernoulli's equation, it's really
pretty simple, simpler than the homework problems that are assigned
in any thermodynamics course. But then ... when I look around, I
see grossly wrong derivations that outnumber correct derivations
by some huge factor, on the order of 100 to 1.

I reckon that part of the answer is that people underestimate the
task. The result is so simple that people think they can treat
it as just a mechanics problem, when in fact it is inescapably a
thermodynamics problem.

The underestimation problem may be exacerbated by the fact that a
lot of people don't know enough thermodynamics to handle this
problem,
not anywhere near enough. So they either give up, or they "look
under
the lamp-post" (i.e. nonthermal mechanics) even though the thing they
are looking for isn't under that lamp-post.

What's even sadder is that a lot of people have learned /wrong/
thermodynamics, such that even if they approach the problem in the
nominally-correct way they are guaranteed to get the wrong answer.
I have in mind specifically the case where students have been taught
that the "FIRST LAW OF THERMODYNAMICS" is dE = -P dV + T dS. Alas
that is not the first law of anything. It is not even correct in
general, and certainly does not correctly describe a parcel of fluid
in the context of Bernoulli's principle.

I was just sitting here wondering what happens to somebody who starts
from the premise that dE = -P dV + T dS. They get stuck, and then
what? How long to they remain stuck before they realize what the
problem is? This equation was sold to them as the #1 most-
fundamental
starting point for the whole subject, so why should they question it?
Yet it's nowhere near good enough to handle this problem. Gack.
It's
too painful to contemplate.

_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
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_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l