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Re: Bernouli formula



When there is an elevation change, the earth's gravitational field is an
external force which contributes to the CM work to change the KE. This
has been included as a change in PE.

Bob Sciamanda (W3NLV)
Physics, Edinboro Univ of PA (em)
trebor@velocity.net
http://www.velocity.net/~trebor
----- Original Message -----
From: "kowalskil" <kowalskil@MAIL.MONTCLAIR.EDU>
To: <PHYS-L@lists.nau.edu>
Sent: Thursday, November 15, 2001 5:40 PM
Subject: Bernouli formula


Bernoulli formula (incompressible and nonviscous fluid) is:

P+0.5*rho*v^2+rho*g*y=const.

Most textbooks derive it in the same way. There is a
picture of a pipe which is narrower on the left and
progressively wider on the right. The right side is
at a higher elevation than the left side. A massless
piston on the left is pushed to the right with F1=P1*A1.
The massless piston on the right is pushed to the left
with F2=P2*A2. Presumably both pistons move horizontally
without acceleration.

In other words, the force on the left does the work
W1=P1*vol, while the force on the right does the
negative work W2=-P2*vol. The net work, P1*vol-P2*vol,
is then compared with dKE+dPE. That leads to the
above formula. What kind of work are we talking about?
Should it be the work done on the CM of the small
volume ("particle of water") as it is moving from
one end of the pipe to another?

The first impression is that KE decreases at the
expense of PE. But this is not so. Think about a
pipe which is wider at the lower end than at the
upper end; in this case both PE and KE will be
increasing. In fact, water gains kinetic energy
even when PE=constant (when the tube becomes
narrower but the average elevation does not change).

The CM work contributes only to changes of KE. Which
work contributes to changes of PE? How to interpret
this process in terms of the First Law? Are all
forces conservative? Where is "the system boundary?"
Ludwik Kowalski