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How is electricity generated
at the bottom of dams?
When you catch a deep-sea
fish, why does its eyes popout?
Why do your ears pop on an
airplane or while climbing up
mountains?
Pressure
• Pressure is equal to the force
applied to a surface, divided
by the area.
Equations for Pressure
• Pressure = Force/surface area
•Pressure = Newtons (Kg x m/s/s)
side x side
•Units are in Pascals or N/m²
• A substance that can easily
change its shape, such as liquids
and gases.
•The molecules in a fluid have
a certain amount of force (mass
and acceleration) and exert
pressure on surfaces they
touch.
•All the molecules add
up together to make up
the force exerted by the
fluid.
•Air has a
mass of
1Kg/m³
•Gravity creates an air pressure
of 10.13N/m³ at sea level.
1 atmosphere = 760 mmHg = 29.92 inHg = 14.7 lb/in2 = 101.3 KPa
•Air Pressure
decreases as
elevation
increases.
Very Low
pressure
Higher Pressure
The whole system
is a low pressure,
but it dramatically
decreases towards
the eye of the
hurricane.
Pressure always
flows from high to
low, which creates
the high velocity
winds.
Barometric Pressure
• The barometer is used to forecast
weather.
• Decreasing barometer means
stormy weather and an
increasing barometer means
warmer weather.
Measuring Pressure
•
A manometer is a U-shaped
tube that is partially filled with
liquid.
•
Both ends of the tube are open
to the atmosphere.
•
A container of gas is connected
to one end of the U-tube.
•
If there is a pressure difference
between the gas and the
atmosphere, a force will be
exerted on the fluid in the Utube. This changes the
equilibrium position of the fluid
in the tube.
From the figure:
At point C
Also
Pc  Patm
PB  PB'
The pressure at point B is the pressure
of the gas.
let d  h
PB  PB '  PC  h  D  g
PB  PC  PB  Patm  h  D  g
Pgauge  h  D  g
Pgauge easily remembered as “hot dog”
A Barometer
The atmosphere pushes on the
container of mercury which forces
mercury up the closed, inverted tube.
The distance d is called the barometric
pressure.
From the figure:
and
PA  PB  Patm
let d  h
PA  h  D  g
Atmospheric pressure is equivalent to a column of mercury
76.0 cm tall.
P = ρgh
where
P = Pressure
ρ = density of fluid
g = gravity
h = height of fluid
•Water pressure
increases with
depth.
• When the liquid is pressing
against a surface there is a
net force directed
perpendicular to the surface.
• If there is a hole in the
surface, the liquid initially
moves perpendicular to the
surface.
• At greater depths, the net
force is greater and the
horizontal velocity of the
escaping liquid is greater.
• At any point within
a liquid, the forces
that produce
pressure are
exerted equally in
all directions.
• Pressure increases
vertically
downward.
• Pressure constant
horizontally.
Columnar Fluid Pressure
(sometimes called gauge pressure)
• pressure due to a
column of fluid of height
h and mass density D;
P  hDg
• The pressure of a liquid at
rest depends on the
density and depth of the
liquid.
• Liquids are practically
incompressible, so except
for changes in the
temperature, the density
of a liquid is normally the
same at all depths.
Columnar Fluid Pressure
• At a given depth, a given liquid
exerts the same pressure against
any surface - the bottom or sides of
its container, or even the surface
of an object submerged in the
liquid to that depth.
• Pressure a liquid exerts depends
only on its density and depth.
• Total pressure (or absolute
pressure) Pabsolute on a submerged
surface equals the pressure the
liquid exerts plus the atmospheric
pressure Po (1 atm = 1.013 x 105
Pa) .
Pabsolute  Po  h  D  g
( peanut  hot dog )
Fluid Pressure
• Pressure of a liquid does not
depend on the amount of liquid.
• Neither the volume or total
weight of the liquid matters.
• If you sampled water pressure
at 1 m beneath a large lake
surface and 1 m beneath a small
pool surface, the pressure would
be the same.
• The fact that water pressure
depends on depth and not on
volume is illustrated by Pascal
vases.
• Water surface in each of the
connected vases is at the same
level.
• Occurs because the pressures at
equal depths beneath the
surface are the same.
Forces Exerted By a
Fluid
• When the liquid is pressing
against a surface there is a
net force directed
perpendicular to the
surface.
• If there is a hole in the
surface, the liquid initially
moves perpendicular to the
surface.
• At greater depths, the net
force is greater and the
horizontal velocity of the
escaping liquid is greater.
Pascal’s Principle
• When force is applied to a confined fluid,
the change in pressure is transmitted equally
to all parts of the fluid.
Transmission of Pressure:
Pascal’s Principle.
• Pascal’s Principle: A CHANGE
IN PRESSURE IN A CONFINED
FLUID IS TRANSMITTED
WITHOUT CHANGE TO ALL
POINTS IN THE FLUID.
• Ex. Hydraulic lift.
• Hydraulic piston apparatus
uses an incompressible fluid to
transmit pressure from a small
cylinder to a large cylinder.
• According to Pascal’s Principle,
the pressure in the small
cylinder resulting from the
application of F1 to a
frictionless piston is
transmitted undiminished to
the larger piston.
Transmission of pressure:
Pascal’s Principle.
P1 = P 2
F2
F1

A1 A 2
• A2 is larger than A1, so
the force exerted by the
large piston is greater
than the force exerted on
the small piston.
• AMA (actual mechanical
advantage) for hydraulic
lift:
F
AMA  2
F1
Hydraulic Devices
• By changing the size of
the pistons, the force
can be multiplied.
4N
3. What is the total force of
the right Piston?
F=P A= 2000 N/m2 x 20m2 = 40,000N
20 m2
.002m2
1. What is the pressure of the left P= F/A = 4 N/.002 m2=
piston?
2000 Pa
2. What is the pressure of the right 2000Pa
Piston?
Hydraulic Brakes
• The hydraulic
brake system of a
car multiplies the
force exerted on
the brake pedal.