Solids & Fluids

Relating Pressure to Solid & Fluid systems

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What is a “FLUID”?

• A fluid is a nonsolid state of matter in which the atoms or molecules are free to move past each other, as in a gas or a liquid.

• Both liquids and gases are considered fluids because they can flow and change shape.

• Liquids have a definite volume; gases do not.

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Recall the definition of Density

• “How much matter there is in an amount of space.”

• In other words… Density = Mass / Volume

or… ρ=m/V (Greek letter “rho” is given for

density)

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Buoyancy…what is it and how is it applied?

• The buoyant force is the upward force exerted by a liquid on an object immersed in or floating on the liquid.

• Buoyant forces can keep objects afloat if they are great enough. It really depends on the density of the object and the density of the fluid it is in.– Ex’s: ice in liquid water, helium balloon in air, brick

in air, stone in pool water, etc.

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Archimedes’ Principle

• Archimedes’ principle describes the magnitude of a buoyant force.

• Archimedes’ principle: Any object completely orpartially submerged in a fluid experiences anupward buoyant force equal in magnitude to theweight of the fluid displaced by the object.• FB = Fg (displaced fluid) = mfg• magnitude of buoyant force = weight of fluid

displaced

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For example…

The Brick, when added, will cause the water tobe displaced and fill the smaller container. What will the volume be inside the smallercontainer? The same volume as the brick!

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Another example…

The raft and cargoare floatingbecause theirweight andbuoyant force arebalanced.

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Another example…

Now imagine a small holeis put in the raft. The raft and cargo sinkbecause their overall density is now greater than the density ofthe water.

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More about Buoyancy…

• For a floating object, the buoyant force equals the object’s weight (they would be BALANCED).

• The apparent weight (actual weight minus buoyant force experienced) of a submerged object depends on the density of the object.

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More about Buoyancy…

For an object with density ρo which is submerged in a fluid ρf, the following relationship is true:

Weight / Buoyant Force = Object’s Density / Fluid’s Density

Or…

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Example:

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Example:

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Example:

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Pressure

• The SI unit for pressure is the pascal, Pa.• It is the same as a N/m2.• The pressure at sea level is about 101,000 Pa.• This gives us another unit for pressure, theatmosphere, where 1 atm = 101,000 N/m2

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A woman’s high heels sink into the soft ground, but the larger shoes of the much bigger man do not.

Pressure = force / area

Definition of Pressure

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Solid Applications

• We often relate this Force-to-Area ratio to the idea of “stress” felt by an object.

• In 1-Dimension, the change in Length due to stress is determined by Young’s Modulus.

• In 2-Dimensions, the change in Area due to stress is determined by the Shear Modulus.

• In 3-Dimensions, the change in Volume due to stress is determined by the Bulk Modulus.

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Solid Applications

• “strain” is defined as the measure of the amount of deformation (the EFFECT of the STRESS on the material)– Examples: tension on a suspension bridge cable, applying a

horizontal force to the top of a textbook, submerging a block of plastic in a tank of water.

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NOW for some FLUID applications…

Pascal’s Principle:

Any change in the pressure of a fluid is transmitted uniformly in all directions throughout the fluid.

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Some visuals…

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Here’s a common application:

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Here’s a common application:

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Here’s a common application:

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A small force F1 applied to a piston with a small area produces a much larger force F2 on the larger

piston. This allows a hydraulic jack to lift heavy objects.

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Example:

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Example:

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More on Pressure…Pressure varies with depth in a fluid. The pressure in a fluid increases withdepth.

It is also important to know that “Absolute Pressure” takes fluid Atmospheric Pressure into account ALONG with Fluid Pressure.

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Fluid FLOW

• Viscosity is related to the “thickness” (internal resistance) of a fluid. The higher the viscosity, the slower a fluid will flow.

• There is a Continuity Equation which is important for ideal fluids:

Think: Pinching a water-hose

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Bernoulli’s Principle

• The speed of fluid flow depends on cross-sectional area.

• Bernoulli’s principle states that the pressure in a fluid decreases as the fluid’s velocity increases.Think: “Is this true”? What’s happening inside of a DRINKING STRAW, for instance?

Think: “How does this relate to Lift”?

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To Sum it all Up

• “TOTAL ENERGY is ________”– Because of this, we can show that the following is

valid for these fluid-flow systems:• “The sum of the Pressure, Kinetic Energy per unit

Volume, and the Potential Energy per unit Volume has the same value at all points along a streamline.”

Think: “Can you tell from where each term comes”?

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The END!

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