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

• Average pressure exerted over time and area

Force

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. p1 = F1A1.

B. p1 = F1 + A1.

C. p1 = A1/F1.

D. p1 = 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

A1

F2

A2=

F1

F2

A1

A2=

• rearranges to

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 x1, is the distance x2 that the large piston moves more or less than that?

A. x2 = x1.

B. x2 < x1.

C. x2 > x1.

1 2

x1

x2 ?

Hydraulics are Simple Machines

• Volume changes V opposite: V = –V1 = V2

F1

A1

F2

A2=

F1x1 = F2x2

• System does same work as done on it

=VA1

F1

VA2

F2

• V = A1x1, so x1 = V/A1; x2 = –V/A2

F1, x1 same direction F2, x2 same direction

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. Decreases.

B. Increases.

C. It depends on the shape of the container.

D. 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 = hg

• p = pressure

• = density of liquid

• h = depth under top of liquid(Valid if is constant—liquid, not gas)

h

p = pressure here

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 = Vg

• = 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.