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Re: [Phys-L] Another Fluid/Density 'Problem'



How do you define average density?
If it is the total mass/total volume then it stays the same.
The definition of rho g h is not an applicable formula because there is a
discontinuity in rho.
While the explanation has some appeal, remember that the density in the
former cream area his increased, while the density in the former milk area
has decreased. So a real proof requires a bit more calculation to get rid
of the hand waving. A good explanation involves the fact that the pressure
is proportional to the height, but the actual density has to do with volume.
So the explantion is a bit more subtle. So it is true that the horizontal
extent is important, but to truly understand this you have to use a bit of
proportional reasoning on dimensions. The density at the top increases a
lot, while the density of the milk is only changed by a very small amount.

John M. Clement
Houston, TX

-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf Of
Brian Whatcott
Sent: Wednesday, January 29, 2014 7:41 PM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] Another Fluid/Density 'Problem'

Pressure is proportional to head in a homogeneous liquid,
where horizontal extent is immaterial.
Pressure changes where the less dense component occupies a
greater proportion of the head because it is confined to a
reduced horizontal extent. Which is to say - horizontal
extents of components of differing density are material!

Brian Whatcott Altus OK

On 1/29/2014 4:51 PM, Chuck Britton wrote:
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An Old Fashioned Glass Milk Bottle with a narrow neck is
delivered to your doorstep in the morning and because it is
no(t) homogenized, the Cream has risen up into the narrow(er) region.

The fluid pressure exerted on the bottom of the bottle is (rho) g h.
Where (rho) is the average density of the column of
milk/cream that extends from the top surface to the bottom.

Now we will thoroughly MIX the bottle of milk and we note
that the average density of this same column of milk is
GREATER than (rho). Let's call this new density (RHO).

How can the pressure have increased while the area of the
bottom has stayed constant?
How can we accept a greater amount of downward fluid force
caused by 'just' mixing the milk?

(This is reprised from back in the last century.) Probably
presented
better back then.
;-)
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_______________________________________________
Forum for Physics Educators
Phys-l@phys-l.org
http://www.phys-l.org/mailman/listinfo/phys-l