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*From*: "Anthony Lapinski" <Anthony_Lapinski@pds.org>*Date*: Fri, 25 Jan 2013 15:54:47 -0500

Thanks to all who responded. This is for my (high school) honors physics

class (non calculus).

Of all the equations we derive (range equation, work-energy theorem,

nonconservative work, impulse-momentum theorem, etc.), this one is the

toughest. So that's why I wanted something "simple."

Phys-L@Phys-L.org writes:

On 01/25/2013 09:36 AM, Anthony Lapinski wrote:

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

Bernoulli's equation?

P + 0.5pv2 = pgh = constant [1]

That's a good question. AFAICT the easy ways are not

good, and the good ways are not easy.

Using conservation of energy and other formulas, this is the mostapproach.

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

1) Several people have suggested the "energy" approach,

but alas it is not correct. The constant in equation [1]

has the same dimensions as energy per unit volume, but

it is *not* equal to E/V. In fact it is the /enthalpy/

per unit volume.

2) It must also be emphasized that equation [1] is

only a simplified first-order approximation to a

more-general result. Don't bother looking for an

exact derivation of equation [1], because there

cannot possibly be one.

I know of two ways of deriving Bernoulli's equation, one

using enthalpy balance, and the other using force balance.

Both are presented and discussed at

http://www.av8n.com/physics/bernoulli.htm

I'm not claiming that either derivation is "easy". As a

general rule, there is nothing easy about fluid dynamics.

As for "conceptual", I would say that both derivations

are reasonably "conceptual", strictly speaking:

-- The concept of force balance is simple enough; on the

other hand applying the concept to this situation is

tedious, insofar as it requires keeping careful track

of many different forces.

-- Meanwhile, applying the "concept" of enthalpy is

straightforward, and somewhat less tedious ... provided

the students have a good understanding of what enthalpy

is, which they probably don't.

-- The perfectly reasonable "concept" of first-order

approximations is required in order to reach equation [1].

===========

There is a proverb that says that if a difficult calculation

produces a simple result, it's a sign that you don't really

understand what's going on. I keep hoping to find a simple

(yet correct) derivation of equation [1]. If you come

across one, please let me know.

OTOH I don't lose toooo much sleep over equation [1], because

it is only a first-order approximation, and there are lots

of situation where the higher-order terms need to be taken

into account.

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**Follow-Ups**:**Re: [Phys-L] Bernoulli's equation***From:*John Denker <jsd@av8n.com>

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

**Re: [Phys-L] Bernoulli's equation***From:*John Denker <jsd@av8n.com>

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