# Chapter 9 Behavior of Fluids I. Fluids and Pressure

```Chapter 9 Behavior of Fluids
I.
Fluids and Pressure
A.
Fluid = compound that readily flows and takes the shape of its container
1) Solids: maintain their own shape
2) Liquids: take container’s shape, but keep same volume
3) Gases: take the container’s shape and spread out to fill the whole volume
B.
Pressure
1) Standing on soft ground
a) Weight alone does not determine if you will sink
b) Area of contact over which the weight is distributed is also important
i. Area is a 2D measure of the amount of surface of an object
A=LxW
1cm x 1cm
1m=L
1m=W
(1m)(1m)  1m 2
(100cm)(100cm)  10,000cm 2
1m 2  10,000cm 2
A = pr2
3)
Pressure = ratio of force per unit area
a) P 
b)
C.
F (N )
 Pascals  Pa
2
A(m )
Woman’s heel sinks because F/A is larger than man’s F/A
Pascal’s Principle
1) Force exerted on a piston
a) Weight = downward force
b) Fluid exerts an equal and opposite force upward on the piston
c) Fluid is compressed like a spring, but it pushes back in all directions
2) Pascal’s Principle = any change in the pressure of a fluid occurs
uniformly in all directions
3) Hydraulic Jack
3)
Hydraulic Jack
a) Moderate force on the small piston creates a large pressure
b) This same pressure is exerted on the large area piston
c) Area of the large piston = 100 x the area of the small piston
d) F2  PA2  P(100 A1 )  100F1
e) Mechanical advantage: Fout/Fin = large for hydraulic jack
i. Work done at both pistons is same
ii. W = Fd so Distance moved of small piston is much larger
f)
1.
Example
F1 = 10 N
A1 = 2 cm2 A2 = 100 cm2
F2 = ???
Convert A to m2:
 1m 2

  0.0002m 2
A1  (2cm )
2 
 10,000cm 

1m 2
2 
  0.01m 2
A2  (100cm )
2 
 10,000cm 
2
2.
3.
P1 = F1/A1 = (10 N)/(0.0002 m2) = 50,000 Pa
F2 = P2A2 = (50,000 Pa)(0.01 m2) = 500 N
II.
Gases and Atmospheric Pressure
A.
Atmosphere of Earth is made of gases (78% nitrogen, 21% oxygen)
1) Can feel air when we move quickly through it, or see it when hazy
2) As a fluid, we must consider pressure
B.
Atmospheric Pressure
1) Density = mass of an object / its volume
a) Density is constant for a given compound
b) Density of water = 1 g / cm3
c) Density of mercury = 13 g / cm3
weight
F
2) Barometer uses mercury to measure the air pressure
 
area
A
a) Vacuum above the mercury, so no pressure
b) Atmospheric pressure pushes the mercury up the barometer ~76cm
c) Converts (using Volume, density, Area) to Pascals
d) Standard Atmospheric Pressure = 1.01 x 105 Pa = 1 atm
e) The same as 14.7 lbs. per square inch
i. Why don’t we feel it?
ii. Fluids inside us are pushing back at the same pressure
P
C.
Variations in Atmospheric Pressure
1) Gaining altitude reduces atmospheric pressure—less air on top of us
2) Like the difference in pressure at the top or bottom of a swimming pool
3) Balloon with low pressure inside will expand as it gains altitude
4) Atm. Pressure helps predict the weather
a) Falling pressure indicates bad weather coming
b) Rising pressure indicates good weather coming
D.
Weight of a column of Air
1) Mercury (liquid) gets compressed very, very little by pressure
2) Air (gas) is easily compressed by pressure
a) As Pressure increases, Volume decreases
b) As Pressure increases, Density (m/V) increases
E.
Relationship of Volume and Pressure
1) Temperature affects volume and pressure of gases—we will hold it constant
2) Boyle’s Experiment (1627-1691)
a) Double the pressure, volume is cut in half (inversely proportional)
b) PV = constant
P1V1 = P2V2
H
V = L x W x H (m3)
W
L
3)
Example: P1 = 1 atm V1 = 0.3 m3 P2 = 3 atm V2 = ???
P1V1 = P2V2
P1V1 (1atm)(0.3m3 )
V2 

 0.1m3
P2
(3atm)
```