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

[Jeffrey Schnick <JSchnick@Anselm.Edu>]

I think the momentum flow animated gif for this problem, neglecting the mass of the bottle, would be an image of the bottle of milk with downward momentum (represented by little arrows) flowing into the fluid via gravity and out the bottom first through the fluid/bottom contact region and then out through the bottom/pan contact region (treating the bottle as resting on the flat horizontal surface of a pan).  In addition there would be a closed loop flow of downward momentum from the fluid, into the glass at the bottom of the bottle, up through the walls of the bottle into the portion of the bottle where the walls are sloped and through the interior surface of the sloped portion of the walls back into the fluid.  The closed loop flow explains why we have more downward momentum flowing from the fluid into the glass bottom at the fluid/bottom interface than we have flowing downward out through the bottom/pan interface--in other words how it could be that the pressure times the area of the bottom of the bottle could conceivably be greater that the weight of the bottle+fluid.  By shaking up the milk+cream we increase the momentum flow rate in the closed loop.

> -----Original Message-----
> From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf Of Chuck Britton
> Sent: Wednesday, January 29, 2014 5:52 PM
> To: Phys-L@Phys-L.org
> Subject: [Phys-L] Another Fluid/Density 'Problem'
>
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>  /      \
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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.
> ;-)
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