LECTURE 2
PASCAL’S PRINCIPLE
Lecture Instructor: Kazumi Tolich
Lecture 2
2
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Reading chapter 11-4 to 11-6
¤  Pressure
and depth
¤  Pascal’s principle
Force and depth in static fluid
3
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¨ 
¨ 
Consider a cylinder with a cross-sectional area of A, filled with a fluid with
a density ρ.
The force pressing at the top is less than the force pressing at the bottom
because of the weight of the water.
At the surface, the pressure must
be at atmospheric pressure.
Ftop = Pat A
Fbottom = Ftop + ρ ( Ah ) g
Pressure and depth
4
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Since the pressure is the force divided by area, if the force
increases as you go deeper, the pressure also increases as you
go deeper in the fluid.
P2 = P1 + ρ gh
Demo: 1
5
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Pressure vs. Depth in water and alcohol
¤  Demonstration
pressure
P2 = P1 + ρ gh
of the depth and density dependence of
Clicker question: 1
6
Example: 1
7
¨ 
A diver swims to a depth of
d = 3.2 m in a freshwater
lake. What is the increase in
the force pushing in on her
eardrum, compared to what
it was at the lake surface?
The area of the eardrum is
A = 0.60 cm2.
Example: 2
8
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Many people have imagined that if they were to
float the top of a flexible snorkel tube out of the
water, they would be able to breathe through it
while walking underwater. However, they generally
do not take into account just how much water
pressure opposes the expansion of the chest and the
inflation of the lungs. Suppose you can just breathe
while lying on the floor with a 400-N (90-lb) weight
on your chest. How far below the surface of the
water could your chest be for you still to be able to
breathe, assuming your chest has a frontal area of
0.090 m2?
Mercury barometer
9
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¨ 
A barometer can measure atmospheric pressure using
the variation of pressure with depth of a fluid.
A glass tube is filled with a fluid with a density ρ and
placed upside-down in the same fluid in a bowl.
Pat = ρ gh
¨ 
Mercury is often used because of its high density.
1 atmosphere ≡ Pat ≡ 760 mmHg
vacuum
Demo: 2
10
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Mercury barometer in vacuum
¤  Demonstration
pressure
of mercury barometer to measure
Clicker question: 2
11
Water level
12
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Fluids flow until equilibrium is reached.
¨ 
The pressure at the surface exposed to air is at Pat.
¨ 
In equilibrium, the net force on each section of the fluid is zero.
¨ 
The pressure in the fluid
Demo: 3
13
¨ 
Pascal’s vases
¤  Demonstration
of water levels
Demo: 4
14
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Water and mercury in U-tube
¤  Measurement
of relative densities of water and
mercury from the heights of liquid boundaries
Clicker question: 3
15
Example: 3
16
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A U-shaped tube is filled mostly with
water, but a small amount of oil has
been added to both sides. The density
of water is ρw = 1.00 × 103 kg/m3,
and the density of the oil is
ρo = 9.20 × 102 kg/m3. On the left
side of the tube, the depth of the oil is
dL = 3.00 cm, and on the right side of
the tube, the depth of the oil is
dR = 5.00 cm. Find the difference in
fluid level between the two sides of the
tube.
Pascal’s principle
17
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According to Pascal's principle,
an externally applied pressure changes the pressure at every point in a
confined liquid or gas by the same amount.
An example of Pascal’s principle in action is hydraulic lift.
F1 F2
ΔP =
=
A1 A2
A1d1 = A2 d2
Example: 4
18
A hydraulic lift has two pistons with
different diameters initially at the same
height. The smaller piston has a diameter
of D1 = 1.5 m, and the larger piston has
a diameter of D2 = 21 m.
¨ 
a) 
b) 
If a weight with a mass m = 2000 kg is
placed on the large piston, what weight
on the small piston will be required to
keep the pistons at the same height?
Through what distance must the large
piston be pushed down to raise the small
piston a distance of d1 = 3.5 m?
Demo: 5
19
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Hydraulic press
¤  Demonstration
of Pascal’s principle