Transcript Pressure

Pressure and Fluids
§ 12.1–12.3
Density
Relating “how big” to “how much”
§ 12.1
Density
•
•
•
•
Mass per volume r = dm/dV; m = rdV
If r is constant, m = rV
SI units kg/m3; conventionally g/cm3
Intensive quantity
– Depends on substance, not amount
Densities
Substance
kg/m3
g/cm3
Air
1.20
0.0012
Plain water
1,000
1.000
Sea water
1,030
1.03
Lead
11,300
11.3
Pressure
One type of stress
§ 12.2
Pressure
• Force per unit area p = F/A
• F is component perpendicular to surface
• Scalar quantity
Units of Pressure
• SI Units: N/m2 = pascal = Pa
• Bar = 100,000 Pa; mbar = hPa = 100 Pa
• Atmosphere = atm = mean sea level
pressure = 101,325 Pa = 1.01 bar
• Torr: Height in mm of a mercury
barometer (760 torr = 1 atm)
• lb/in2 = psi (14.696 psi = 1 atm)
Gauge and Absolute Pressure
• Gauge: increase above surrounding
atmosphere
– e.g. tire pressure 32 psig
• Absolute: total
Poll Question
When a molecule bounces elastically off a surface,
what is the direction of its momentum change?
A.
C.
B.
D.
Poll Question
When a molecule bounces elastically off a surface,
what is the direction of the force on the surface?
A.
C.
B.
D.
Collisions
• Collision exerts a force into surface
Force
• Pressure from force averaged over time
and area
Pressure in a fluid
• Pascal’s Principle: pressure in a fluid is
exerted uniformly in all directions
throughout the fluid.
Hydraulics
just another simple machine
Quick Question
If a force F1 is applied to the small piston with
area A1, what is the pressure increase in the
fluid?
A.
B.
C.
D.
Dp = F1A1.
Dp = F1 + A1.
Dp = A1/F1.
Dp = F1/A1.
1
2
Poll Question
If a force F1 is applied to the narrow piston with
area A1, How does the magnitude of the force F2
exerted by the fluid on the wide piston compare
to F1?
A. F2 = F1.
B. F2 < F1.
C. F2 > F1.
1
2
Hydraulics
• Pistons have different areas
• Pressure p = F/A for both pistons
F1
F2
=
A1
A2
• rearranges to
F1
A1
=
F2
A2
Poll Question
If the narrow piston with area A1 is moved a
distance Dx1, How does the distance Dx2 that the
wide piston moves compare to Dx1?
A. Dx2 = Dx1.
B. Dx2 < Dx1.
C. Dx2 > Dx1.
Dx2 ?
Dx1
1
2
Hydraulics are Simple Machines
F1
F2
=
A1
A2
• Volume changes DV are opposites
• DV = A1Dx1, so Dx1 = DV/A1; Dx2 = –DV/A2
DV
DV
F1
= F2
A1
A2
F1Dx1 = –F2Dx2
• input, output work equal and opposite
Example Problem
In an auto shop a hydraulic jack is used to
lift vehicles for service. If the radius of the
cylinder below piston 1 is r1 = 0.02 m, and
the radius of the cylinder below the piston
holding the car is r2 = 0.1 m, what force F1
must be exerted on the small piston to lift a
1500-kg car?
Pressure with Depth
Pressure beneath a fluid
• Force comes from weight of fluid above
• Pressure increases with depth
Supports weight above
Pressure in a liquid
h
weight of fluid above
p = F/A =
cross-section
mass  g
=
A
density  volume  g
=
A
rAhg
=
= rgh
A
p = pressure here
Depth Pressure Formula
p = p0 + rgh
•
•
•
•
p0 = pressure here
p0 = pressure at depth 0
p = pressure at depth h
r = constant density of liquid
h = depth under top of liquid
p = pressure here
h
Buoyancy
How do things float?
§ 12.3
What forces are present?
What forces are present?
What forces are present?
What forces are present?
Pressure in a fluid
• Pressure increases with depth
• Greater pressure at bottom than top of an
immersed object
• Results in upward buoyancy force that is
the (vector) sum of all pA forces
F = A p dA
Buoyancy from Ug
Force = –dUg/dh
Ug = Ug obj + Ug displaced fluid
DUg = mg(Dh) + rVg(–Dh)
∑F = –dUg/dh = –mg + rVg
–mg = gravity force
rVg = buoyancy force
Dh
Quick example
The density of fresh water r = 1000 kg/m3.
a. What is the buoyancy force on a 1-m3 parcel
of water?
b. What is the buoyancy force on a 1-m3 rock
submerged under water?
c. What is the buoyancy force on a 1-m3 chunk
of Styrofoam submerged under water?
Quick Questions
All blocks are cubes with 1-m sides.
Which ones float?
Which one makes the water level change the most?
Which one makes the water level change the least?
Buoyancy and Density
• If an object is more dense than the surrounding fluid, it sinks
• If an object is less dense than the surrounding fluid, it rises
• A floating object displaces exactly enough fluid to support its weight
Quick Question
Which boat (with cargo) has the greatest volume?
A. The high boat (left).
B. The low boat (right).
C. Both have the same volume.
Quick Question
Which boat (with cargo) has the greatest volume under the
water line?
A. The high boat (left).
B. The low boat (right).
C. Both have the same volume under water.
Quick Question
Which boat (with cargo) experiences the greatest buoyancy
force?
A. The high boat (left).
B. The low boat (right).
C. Both experience the same buoyancy force.
Quick Question
Which boat (with cargo) has the greatest mass?
A. The high boat (left).
B. The low boat (right).
C. Both have the same mass.
Poll Question
After a boat sinks, it displaces
A. more water than when it floated.
B. less water than when it floated.
C. the same volume of water as when it
floated.