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Fluids

Fluids

• Pressure• Fluids at rest• Archimedes’ principle• Fluids in motion• Bernoulli’s principle

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Fluids

Demonstration: Cups and Balloons

Fluids

Fluid –•Water•Oil•Air•Jellybeans?

Anything that flows

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Fluids

Fluids can be:

Static

Dynamic

Fluids can not be directly pushed or pulled. They can only be moved by PRESSURE

Static Fluids

Density (ρ)

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( )( )

Mass kgVolume m

⇒mv

ρ =

ρwater=1000 kg/m3To convert from g/cm3

to kg/m3 you must multiply by 1000

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Static Fluids

Pressure=Force/Area

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( )( )

Force NPArea m

=

Pascal (Pa) is the unit of pressure

The smaller the area the greater the

pressure

Can you think of other common units???

Static Fluids

A cube and a spherical ball are made of the same material and have

the same mass. Which exerts the larger pressure on the floor?

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Static Fluids

Describe how a gas exerts pressure on the walls of its container.

Static Fluids

Why does the pressure in a tire increase as you add more air?

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Static Fluids

Demonstration: Dixie Cups

Static Fluids

Some Perspective on Pressure

Air Pressure= 14.7or PSI51.01 10 Pa⋅

Tire Pressure= 53.03 10 Pa⋅ 45or PSI

Full SCUBA TANK= 72.06 10 Pa⋅ 3000or PSI

Ocean Bottom= 81.1 10 Pa⋅ >16000or PSI

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Static Fluids

Example: The “foot print” of a car tire is approx. 150 cm2. The pressure in each tire is 3.03x105 Pa. What is the weight of the car?

Static Fluids

Day 1 HW:

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Static Fluids

Demonstration: Vacuum Cannon

Static Fluids

Vacuum Cannon…how it works

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Static Fluids

Demonstrations

•Suction Cups•Magdeburg Hemispheres•Balloon in Bell Jar•Alarm in Bell Jar

Static Fluids

Pascal's Principle (hydraulic principle)

Any INCREASE (or decrease) in pressure to a confined fluid is transmitted

undiminished throughout the fluid

Assume the fluid is

quasistatic

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Static Fluids

Pascal's Principle examples:

•Hydraulic Jacks•Squeezing Toothpaste•Bulldozers and Backhoes•Automotive Breaks

Large Area=large output force

Small Area= small input force

F PA=

Static Fluids

Pascal's Principle Equation

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Static Fluids

Example: A Hydraulic jack for a car has an output piston diameter of 5.0 cm and an input piston diameter of 1.0 cm. You want to lift a 8000 N car. How much force must be applied to the input piston?

Pressure Measurement

The change in height relates directly to the gauge pressure using P hgρ=

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Pressure Measurement

Static Fluids

Q: Which container has the greatest fluid pressure at the bottom of the container?

h

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Static Fluids

Q: Which container has the greatest fluid pressure at the bottom of the container?

Static Fluids

Example: You are driving on a rainy day and hydroplane into a puddle that is barely deep enough to cover the roof of your car (approx. 1.6 meters). Determine the minimum force necessary to open your car door. The door has an area of approximately 1 square meter.

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Static Fluids

Homework:

Static Fluids – Buoyant Force

Buoyant Force -An upward pointing force exerted on a body immersed in a fluid.

-Caused by the increasing pressure with increasing depth

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Static Fluids – Buoyant Force

Buoyant Force

Static Fluids – Buoyant Force

Example: Determine the apparent weight of a 3000 N treasure chest filled with gold coin. The chest is airtight and 40 cm on a side.

Fg

FbuoyN

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Static Fluids – Buoyant Force

Example: What volume of helium is needed if a balloon is to lift a load of 180 kg (including the weight of the empty balloon)

FgHe

Fbuoy

Fgload

Static Fluids – Archimedes’ Principle

Archimedes’ Principle

The buoyant force is equal to the weight of the displaced fluid.

Eureka!!

If you want something to float in water you must

make its effective density less than the density of

water.

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Static Fluids – Archimedes’ Principle

Archimedes’ Principle

Lab: Buoyant Force w/ force sensor

Static Fluids – Archimedes’ Principle

Activity – Penny Barge

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Fluids in Motion

Fluid Dynamics

•The study of moving fluids

•Only consider Laminar flow

Laminar – Layers

Turbulent –Mixing of layers

Equation of Continuity

The equation of continuity is really a statement of conservation of matter…what

goes in must come out!

Av is another way of expressing volume/time

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Equation of Continuity

Moving Fluids – Bernoulli’s Equation

Bernoulli’s Equation is just another restatement of conservation of energy.

2 21 11 1 1 2 2 22 2P v gy P v gyρ ρ ρ ρ+ + = + +

Pressure at location 1

Kinetic Energy location 1

GPE at location 1

More accurately, work done as a result of a pressure difference P1-P2

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Example 1: Heating Duct – Eqtn of Continuity

What area must a heating duct have if air moving 3.0 m/s along it can replenish the air every 15 minutes in a room of volume 300 m3? Assume the air’s density remains constant.

Example 2: Blood Flow – Eqtn of Continuity

In humans, blood flows from the heart into the aorta, from which it passes into the major arteries. These branch into arterioles, which in turn branch into capillaries. The blood returns to the heart via the veins. The radius of the aorta is about 1.2 cm, and the blood passing through it has a speed of about 40 cm/s. A typical capillary has a radius of about 4 x 10-4 cm, and blood flows through it at a speed of about 5x10-4

m/s. Estimate the number of capillaries that are in the body.

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Example 2: Blood Flow – Eqtn of Continuity (continued)

Example 3: Bernoulli’s Equation

Water circulates throughout a house in a hot-water heating system. If the water is pumped at a speed of 0.50 m/s through a 4.0 cm diameter pipe in the basement under a pressure of 3 atm, what will be the flow speed and pressure in a 2.6 cm diameter pipe on the second floor 5.0 m above? Assume the pipes do not divide into branches.

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Example 3: Bernoulli’s Equation

Example 3: Bernoulli’s Equation

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Torricelli’s Theorem

Predicts the speed a fluid will shoot come out of a pipeAssumes the height of the water doesn’t change appreciably ie. V2=0The pressure at the top and bottom of the container is the same (1 atm)

Moving Fluids – Bernoulli’s Principle

Bernoulli’s Principle

Where fluid flow is fast, pressure is lowWhere fluid flow is slow, pressure is high

Activities: Dime in cupPing Pong Ball and coffee stir“two sheets to the wind”Ball in stream of water

Bernoulli, Mexican and movies??

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Fluids in Motion

Physics of FlightPhysics of baseball Physics of Chimneys Physics of Sailboats

Fluids in Motion

Where is the pressure the greatest, at point A, B or C?

AB

C