For simplicity, you may assume that the weight and density of the cream is negli

Question

For simplicity, you may assume that the weight and density of the cream is negligible compared to that of the milk.

psep>pmix
psep=pmix
psep<pmix Floating Cream In the 1950s, fresh unhomogenized milk in glass bottles was delivered to suburbanites' back doorsteps well before dawn. When delivered, the milk was thoroughly mixed, so that it appeared homogenized, but anyone rising much after sunrise would find that the milk had separated, the cream having risen to the top. (Figure 1) Cream and milk are immiscible (like oil and water), and the total volume of liquid does not change when they separate. The top part of the bottle was intentionally given a much smaller diameter than the bottom, so that the cream, typically 3 percent of the total volume, occupied much more than 3% of the total vertical height of the milk-bottle. For this problem, assume that the total height of the milk bottle is h and the depth of the cream layer is d Assume that before separation, the pressure at the bottom of the milk bottle is pmix. How does the pressure at the bottom of the milk bottle after separation, psep, compare to pmix? For simplicity, you may assume that the weight and density of the cream is negligible compared to that of the milk.

Explanation / Answer

Pmix > Psep

This is because the pressure at the bottom of the milk is due to a grater height and density of water than at the top layer of the milk which has smaller height and less density.

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