Physics 215 – Fall 2014 Lecture 15-1 1

Welcome back to Physics 215

Today’s agenda:

• Pressure• Pressure as a function of depth• Forces exerted on and by liquids• Buoyancy

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Current homework assignment

• HW11:– Knight Textbook Ch.13: 30, 32, 66– Knight Textbook Ch.15: 32, 40, 56– due Friday, Dec. 5th in recitation

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Fluid mechanics

• Fluid = substance which is unable to support a shear stress

• liquids, gases

• Apply Newton’s laws to study statics of fluids...

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Definition of pressure:

where |N| is the magnitude of the (normal) force exerted on one object by another and A is the area of the surface at which the two objects are in contact.

also, 1 atm = 1.01 x 105 Pa

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Pressure in liquids (and gases):

• Pressure is not a vector (does not have a direction).

• Normal force (N) is between two “objects” which can be adjacent regions of water in the same container.

• Pressure in liquids is associated with a geometric point, not with an object or pair of objects.

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Pressure as a function of depth in a liquid

The pressure in a liquid increases linearly with depth from its value P0 at the surface that is open to the atmosphere or from some other reference point.

The increase in pressure for every one meter increase in depth is proportional to the density of the liquid.

= density = mass/volume

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The difference in pressure between two points in a liquid depends on the difference of their depths below the open surface (i.e. below the points where P = P0).

Comparing pressures at different points

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Rank the pressures at the three points

1. PA < PB = PC

2. PA < PB < PC

3. PA < PC < PB

4. PC < PA < PB

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1. A

2. B

3. C

4. The weight of the water is the same in all three containers.

Three containers of different shape but with bases of equal area (or equal “footprints”) are filled with water to the same height.

The weight of the water is the greatest in container…

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1. A

2. B

3. C

4. The pressure at the bottom is the same in all three containers.

Three containers of different shape but with bases of equal area (or equal “footprints”) are filled with water to the same height.

The pressure at the bottom of the container is the greatest in container…

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For differently shaped containers that have the same bottom surface and are filled with the same liquid up to the same height

• the weights of the contents are

• the pressures at the bottom are

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Free-body diagrams for liquids*consider fluid in equilibrium

Fy = 0

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Pascal’s principle

A change in pressure applied to a fluid at rest is transmitted undiminished to every point of the fluid and to the walls of the container.

*Pascal’s principle does not state that the pressure is the same at every point in the fluid.

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Principle of hydraulic lift

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Mercury barometer

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Another barometer is placed next to the one discussed previously. The second barometer uses a wider glass tube but is otherwise the same.

The top of the column in the second barometer is1. higher than

2. lower than

3. at the same height as

4. Don’t know.

the height in the narrow barometer.

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Mercury has a density that is about 14 times greater than that of water. If you were to build a barometer that uses water instead of mercury, how would the height of the column of water needed compare to that of the mercury?

1. higher than

2. lower than

3. equal to

4. Can’t tell.

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Two disks that make a tight seal contain a small space that is initially filled with air. The space is then evacuated, so that atmospheric pressure holds the two disks together.

1. A one-kilogram mass

2. Two physics text books

3. A three-gallon bucket of water

4. Two (physics) students

Atmospheric pressure is about 15 psi (pounds per square inch), or 100 000 N/m2. The radius of the disks is about 6 inches, or 15 cm.

If the evacuated disks are hung from the ceiling, what objects can they support?

How big is atmospheric pressure?

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Archimedes’ principle

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

The buoyant force is the total upward force exerted on an object by the surrounding fluid.

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A cubical block made of a certain type of plastic has a density of 0.75 g/cm3. The density of water is 1.0 g/cm3. If the block is allowed to float in water, what fraction of the volume of the block would be below the water level?

1. one quarter

2. one half

3. three quarters

4. some other fraction

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How do boats float?• If the density of an object is less than that

of water, an object floats in water.

• If the density of an object is greater than that of water, an object sinks in water.

• …but boats can be made of metal, e.g., aluminum (Al / W ~ 2.7)…

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A glass beaker is filled with water and placed on a balance. A person holds a finger into the water. The reading on the balance will

1. go up

2. go down

3. stay the same

4. Can’t tell.

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Reading assignment

• Chapter 15 in textbook

• Fluid dynamics