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*From*: Paul Lulai <plulai@stanthony.k12.mn.us>*Date*: Fri, 25 Jan 2013 17:33:52 +0000

We just take conservation of energy (figured out prior to Bernoulli in my class) and divide everything my Volume.

I do this:

Ek + Eg + W = Ek + Eg + W (I know it is strange to put W on both sides, but we talk about how this is like the W done on either end, not total W).

0.5mv^2 + mgh + Fd = 0.5mv^2 + mgh + Fd

Divide everything by V

0.5(m/V)v^2 + (m/V)gh + F(d/V) =...

0.5(rho)v^2 + (rho)gh + F/A = ....

If we talk about W on each side as being any work done by external agents on that side. Sloppy text, but hopefully this makes some sense. Gottta run...

Paul Lulai

Physics Teacher

St Anthony Village S.H.

3303 33rd Ave NE

St Anthony Village, MN 55418

612-706-1146

plulai@stanthony.k12.mn.us

http://www.stanthony.k12.mn.us/hsscience/ ;

-----Original Message-----

From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf Of R. W. Tarara

Sent: Friday, January 25, 2013 10:53 AM

To: Phys-L@Phys-L.org

Subject: Re: [Phys-L] Bernoulli's equation

Not so tedious--

Consider the total external energy by taking the work done on the fluid (Fs), the KE (1/2mv^2), and the gravitational PE (mgH) and divide the sum of these by volume. The assumption is some small volume near the boundaries of the fluid. Fs/V = Fs/As = P while the masses become mass volume densities.

Rick

Richard W. Tarara

Professor of Physics

Saint Mary's College

Notre Dame, Indiana

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Free Physics Instructional Software

www.saintmarys.edu/~rtarara/software.html

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From: "Anthony Lapinski" <Anthony_Lapinski@pds.org>

Sent: Friday, January 25, 2013 11:36 AM

To: <phys-l@phys-l.org>

Subject: [Phys-L] Bernoulli's equation

Teaching fluids now. Is there an "easy/conceptual" way to teach/derive

Bernoulli's equation?

P + 0.5pv2 = pgh = constant

Using conservation of energy and other formulas, this is the most

tedious/complicated derivation. I'm just looking for a different approach.

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**References**:**[Phys-L] Bernoulli's equation***From:*"Anthony Lapinski" <Anthony_Lapinski@pds.org>

**Re: [Phys-L] Bernoulli's equation***From:*"R. W. Tarara" <rtarara@saintmarys.edu>

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