Chapter 9

Solids, Liquids, & Gases

 

Hydrostatic Pressure:

The pressure P exerted by a fluid is the magnitude F of the force acting perpendicular to a surface embedded in the fluid divided by the area A over which the force acts:

(2)

Units: which is a pascal (Pa).

 

Example 4

Find the pressure exerted on the skin of a balloon if you press with a force of 2.1 N using (a) your finger or (b) a needle. Assume the area of your fingertip is , and the area of the needle tip is . (c) Find the minimum force necessary to pop the balloon with the needle, given that the balloon pops with a pressure of .

 

 

Solution:

(a)

(b)

(c)

 

 

Example 5

The mattress of a water bed is 2.00 m long by 2.00 m wide and 30.0 cm deep. (a) Find the weight of the water in the mattress. (b) Find the pressure exerted by the water on the floor when the bed rests in its normal position. Assume that the entire lower surface of the bed makes contact with the floor.

 

Solution:

(a)

(b)

 

Gravity is the principal cause of hydrostatic pressure.

Pressure at some height in a liquid:

(3)

Total pressure at any point within a liquid:

(4)

atm =

 

Example 6

The Titanic was found in 1985 lying on the bottom of the North Atlantic at a depth of 2.5 miles. What is the pressure at this depth?

 

Solution:


 

Example 7

A cubical box 20.00 cm on a side is completely immersed in a fluid. At the top of the box the pressure is 105.0 kPa; at the bottom the pressure is 106.8 kPa. What is the density of the fluid?

Solution:

 

Example 8

One day, while swimming below the surface of the ocean, you let out a small bubble of air from your mouth. As the bubble rises toward the surface, does its diameter (a) increase, (b) decrease, or (c) stay the same?

 

Solution:

(a) The diameter of the bubble increases.

 

Pressure in a Container

Points A, B and C are at the same pressure.

The pressure at a given depth is independent of the shape of the vessal.

Points A and C are at the same pressure and Points B and D are at the same pressure.

 

Example 9

A U-shaped tube is filled mostly with water, but a small amount of vegetable oil has been added to one side, as shown in sketch. The density of the water is , and the density of the vegetable oil is 920 . If the depth of the oil is 5.00 cm, what is the difference in level h between the top of the oil on one side of the U and the top of the water on the other side?

Solution:

Find the pressure at point A:

Find the pressure at point B:

Set the pressures equal and solve the :


Find the difference between the heights:

 

On to Static Part 2