Pressure and Fluids
What’s the point?
• What principles govern hydraulic and
pneumatic machines?
• Why do some things float on water?
Objectives
• Relate pressure, force, and area.
• Explain the effect of depth on the pressure
within a fluid.
• Explain and calculate the buoyant force on
an object in a fluid.
Pressure
• Force per unit area p = F/A
• Force is component perpendicular to
surface
• Scalar quantity
Units of Pressure
• SI Units: N/m2 = pascal = Pa
• Bar = 100,000 Pa; mbar = 100 Pa
• torr: Height in mm of a mercury barometer
(760 torr = 1 atm)
• Atmosphere = atm = mean sea level
pressure = 101,325 Pa = 1.01 bar
• lb/in2 = psi (14.696 psi = 1 atm)
Fluids
Gases and liquids
Origin of Fluid Pressure
• Collision exerts a force perpendicular to surface
Force
• Average pressure exerted 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
Poll Question
If a force F1 is applied to piston 1 with area
A1, what is the pressure increase in
cylinder 1?
A.
B.
C.
D.
Dp1 = F1A1.
Dp1 = F1 + A1.
Dp1 = A1/F1.
Dp1 = F1/A1.
1
2
Poll Question
If a force F1 is applied to piston 1 with area
A1, How does force F2 compare to F1?
A. F2 = F1.
B. F2 < F1.
C. F2 > F1.
1
2
Hydraulics
• Pistons have different areas
• Pressure p = F/A = same for both pistons
F1
F2
=
A1
A2
• rearranges to
F1
A1
=
F2
A2
Group Whiteboard Work
If a force F1 = 50 N is applied to the small
piston with area A1 = 100 cm2, what
upward force F2 does the liquid apply to the
large piston with area A2 = 1000 cm2?
Remember: Pressure is the same everywhere.
Poll Question
If the small piston with area A1 is moved a
distance Dx1, is the distance Dx2 that the
large piston moves more or less than that?
A. Dx2 = Dx1.
B. Dx2 < Dx1.
C. Dx2 > Dx1.
Dx2 ?
Dx1
1
2
Hydraulics are Simple Machines
F1
F2
=
A1
A2
DV
DV
F1
= F2
A1
A2
• Volume changes DV opposite: DV = –DV1 = DV2
• DV = A1Dx1, so Dx1 = DV/A1; Dx2 = –DV/A2
F1Dx1 = F2Dx2
F1, Dx1 same direction
F2, Dx2 same direction
• System does same work as done on it
Example Problem
If the small piston with area A1 = 100 cm2 moves
10 cm, how far does the large piston with A2 =
1000 cm2 move?
Remember: Volume leaving piston 1 equals volume
entering piston 2.
Pressure with Depth
Poll Question
As the depth beneath the surface of a fluid
increases, the pressure within the fluid
A.
B.
C.
D.
Decreases.
Increases.
It depends on the shape of the container.
Fluids are incompressible, so the pressure
does not change.
Pressure in a fluid
• Force comes from weight of fluid above
• Pressure increases with depth
Supports weight above
Liquid Pressure Formula
p = rhg
• p = pressure
• r = density of liquid
• h = depth under top of liquid
(Valid if r is constant—liquid, not gas)
p = pressure here
h
Buoyancy
How do things float?
Submerged in a liquid
Why does it sink or float?
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
Buoyancy Force
• Buoyancy force = weight of fluid displaced
F = rVg
•
•
•
r = density of fluid
V = volume of fluid displaced
= submerged volume of object
g = 9.8 N/kg
Whiteboard Work
What is the water pressure at the bottom at the deepest
point of Lake Superior? Lake depth = 406 m, density of
water = 1000 kg/m3.
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
(Why? What happens if it’s too high or too low?)
Think Question
Which boat (with cargo) has the greatest total volume?
A. The high boat (left).
B. The low boat (right).
C. Both have the same total volume.
Think 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 submerged volume.
Poll 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.
Think 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 and weight of water as
when it floated.