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

As you may have noticed from a response of mine, it *IS* possible to arrange two columns of immiscible liquids so that the pressure at the base of the columns is given by the average of the two fluid densities, but the conditions are quite constrained, and do not apply to the general case of a head of cream on milk in an old style bottle, which is more carefully represented as a density proportionate to the column height of each fraction, when separate, and proportionate to the volumes of each fraction, when homogenized. I was unable to check if either text mentioned the word "average" in this context.

Brian Whatcott Altus OK.

On 1/30/2014 7:41 AM, Anthony Lapinski wrote:
For those interested, I found my references for this problem:

Aarons - Teaching Introductory Physics - page 328

Jargodzki & Potter - Mad About Physics - page 29



Phys-L@Phys-L.org writes:
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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 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.
;-)