A bottle of a certain type of salad dressing can be considered to be a mixture o

Question

A bottle of a certain type of salad dressing can be considered to be a mixture of olive oil and vinegar. The oil has a density of 0.92 g/cm3 and the vinegar has a density of 1.01 g/cm3 . If an unopened and unshaken bottle of salad dressing contains 3 in. of oil on top of 5 in. of vinegar a. Estimate the gage pressure acting on the bottom surface of the bottle. b. What is the gage pressure acting on the side of the bottle at the line between the oil and vinegar? c. What is the gage pressure acting on the bottom surface of the bottle after the bottle is shaken so that the oil and vinegar are thoroughly mixed (temporarily)?

Explanation / Answer

density of oil , po = 0.92 gm/ml = 920 Kg/m^3

density of vinegar , pv = 1.01 g/cm^3 = 1010 Kg/m^3

a) for the gauge pressure at the bottom of bottle

gauge pressure at the bottom of bottle = po * g * ho + pv * g * hv

gauge pressure at the bottom of bottle = 920 * 9.8 * 3 * 0.0254 + 1010 * 9.8 * 5 * 0.0254

gauge pressure at the bottom of bottle = 1944.1 Pa

b) at the pressure at the line between oil and vinegar

pressure will be due to oil only

gauge pressure at the line between oil and vinegar = po * g * ho

gauge pressure at the line between oil and vinegar = 920 * 9.8 * 3 * 0.0254

gauge pressure at the line between oil and vinegar = 687.1 Pa

c)

even if they are thorughly mixed , the pressure at the bottom will not change

gauge pressure at the bottom of bottle = 1944.1 Pa

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