Forces in Fluids
Thought Questions
Why is the electricity produced at the
bottom of dams?
When you catch a deep-sea fish, why
does its eyes pop-out?
Why do your ears pop on an airplane or up
in the mountains?
How did DENVER manage to get to the
divisional playoffs – just to be blown out by
NEW ENGLAND ? …...
Pressure
•
Pressure is equal to the force applied
to a surface, divided by the area.
Pressure in Fluids
P=F/A
Units of pressure in the SI
system are pascals:
1 Pa = 1 N/m2
Pressure is a scalar – It is the
same in every direction in a
fluid at a given depth; if it
were not, the fluid would flow.
Pressure in Fluids
The pressure at a depth h below the surface of
the liquid is due to the weight of the liquid above
it. We can quickly calculate:
At rest ⇒ ∑Fy = 0
F - mg = 0 ⇒ F = mg
F = mg = ρVg, V =Ah
⇒ F = ρAhg
⇒ P ≡ F/A = ρgh
Pressure at depth h (fluid at rest)
P = ρgh
This relation is valid for any liquid whose density
does not change with depth.
Absolute and Gauge Pressure
●
P = ρgh is often called gauge pressure:
–
●
●
Does not include the effect of atmospheric
pressure on top of the fluid
If the fluid is water, this is referred to as
hydrostatic pressure.
Absolute pressure includes the effect of
atmospheric pressure PAbsolute = Patm + ρgh
Barometers
P2 = P1 + ρ gh
Patm = ρ gh
Patm
h=
ρ g
(1.01× 10
5
)
Pa
h=
13.6 × 103 kg m 3 9.80 m s 2
(
)(
h = 0.760 m = 760 mm
)
Manometers
P2 = PB = PA
PA = P1 + ρ gh
Measurement of Pressure
Here are two more devices for
measuring pressure: the
aneroid gauge and the tire
pressure gauge.
Pressure and Elevation
•
•
Air Pressure decreases as elevation
increases.
Astronomical telescopes are placed on mountain tops because the thinner air
means less interference with the stars
Mauna Kea at 13,700 feet
Is above 40% of the atmosphere
Atmospheric Pressure
• Earth’s atmosphere: A fluid.
• Pressure at any height in a fluid → Weight of fluid
above (P = ρgh)
• Sea level: PA ≡ 1.013 × 105 N/m2
= 101.3 kPa ≡ 1 atm
⇒ Change in pressure:
∆P = ρg∆h
• Pressure at height h above sea level = P - ∆P
Water Pressure
Marianas Trench = 10,911 m (35,800 ft) or 1,100
atmospheres.
That is the equivalent of an average-sized person holding
up 48 jumbo jets or 400 times the pressure in automobile
tires.
Pressure in a Liquid
●
Practice – Holt Problem B
Pascal's Principle
Any change in the pressure applied to a
completely enclosed fluid is transmitted
undiminished to all parts of the fluid and
enclosing walls.
P2 = P1 + ρ g ( 0 m )
F2 F1
=
A2 A1
 A2 

F2 = F1 
 A1 
Hydraulic Devices
•
In a hydraulic device, a
force applied to one piston
increases the fluid pressure
equally throughout the fluid.
Hydraulic Devices
•
By changing the size of the
pistons, the force can be
multiplied.
Hydraulic Brakes
•
The hydraulic brake system of a
car multiplies the force exerted
on the brake pedal.
Pascal's Principle
●
Practice – Holt Physics Problem C