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 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?

Answer 1

Answer:

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