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 dressing contains 3 in. of oil on top of 5 in. of vinegar, find the pressure distribution in the salad dressing bottle before it is shaken. What is the pressure distribution after the bottle is shaken?

1.) 183.21 Pascal, 125.7 Pascal

2.) 192.17 Pascal

Explanation:

Given that 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 dressing contains 3 in. of oil on top of 5 in. of vinegar, convert the inches to cm

1 inch = 2.54 cm

3 inches = 2.54 × 3 = 7.62 cm

5 inches = 2.54 × 5 = 12.7 cm

For oil:

P = dgh

Where

P = pressure

d = density

g = acceleration due to gravity

h = height

P = 0.92 × 9.8 × (7.62 + 12.7)

P = 0.92 × 9.8 × 20.32

P = 183.21 Pascal

For vinegar:

P = 1.01 × 9.8 × 12.7

P = 125.7 Pascal

The pressure distribution after the bottle is shaken will be

P = (1.01 + 0.92)/2 × 9.8 × 20.32

P = 0.965 × 9.8 × 20.32

P = 192.17 Pascal

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