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



OK - thanks for checking this. I obviously made a sign error in transcribing my notes to the list - the lead term is Vdp, leading to nRTln(P2/P1), or else the pressure would increase in the narrower opening.

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: Thursday, December 09, 2010 12:54 PM
To: Forum for Physics Educators
Subject: Re: [Phys-l] Bernoulli, enthalpy, work/KE theorem, etc.

On 12/09/2010 10:19 AM, LaMontagne, Bob wrote:
The gas law for an isothermal process is PV = constant so the
polytropic exponent is gamma=1. The obvious problem is that
gamma/(gamma-1) is infinite in this case.

What I would like comment on is the following: In the constant
enthalpy form of Bernoulli's Eqn we have

-VdP + mgdh + d(mv^2/2) = 0.

I would use PV=nRt to replace V with nRT/P and use that when
integrating -VdP. That would make the pressure term of the Bernoulli
Eqn

-nRTln(P2/P1)

and the complete equation

nRTln(P1/P2) + mg(h2-h1) + mv2^2/2 - mv1^2/2 = const

Am I making any unjustified assumptions when doing this?

Works for me.

The result is widely known within the community of people who
understand such things, which is to say, not very widely known.
See e.g. Richard von Mises _Theory of Flight_ page 29.
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