notes fluid mechanics

8/13/2019 NOTES Fluid Mechanics

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Fluid Mechanics - Hydrostatics

AP Physics B


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States of Matter

Before we begin to understand the nature of a Fluidwe must understand the nature of all the states ofmatter:

The 3 primary states of matter

Special "states:


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Density

The 3 primary states have a distinct density,

which is defined as:


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What is a Fluid?By definition, a fluid is


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Why fluids are useful in physics?

Typically, liquids are considered to be incompressible.That is once you place a liquid in a sealed container youcan DO WORK on the FLUID as if it were an object. ThePRESSUREyou apply is transmitted throughout the

liquid and over the entire length of the fluid itself.


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Pressure

One of most important applications of a fluid is

it's pressure- defined as


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Example

A water bed is 2.0 m on a side and 30.0 cm deep.

(a) Find its weight if the density of water is 1000 kg/m3.

(b) Find the pressure that the water bed exerts on the floor. Assume that the

entire lower surface of the bed makes contact with the floor.


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Atmospheric Pressure

Pat is a direct result of the

weight of the air above

us.


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Hydrostatic PressureSuppose a Fluid (such as a liquid) is at REST, we call this

HYDROSTATIC PRESSURE

Two important points

A fluid will exert a pressure_________________________________

A fluid will exert a pressure_________________________________

Notice that the arrows on TOP of the objects are smaller than at the

BOTTOM. This is because pressure is greatly affected by the DEPTH of

the object. Since the bottom of each object is deeper than the top the

pressure is greater at the bottom.


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Pressure vs. DepthSuppose we had an object

submerged in water with the

top part touching theatmosphere. If we were todraw an FBD for this objectwe would have three forces


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Pressure vs. DepthBut recall, pressure is force per unit area. So if we

solve for force we can insert our new equation in.

Note:The initial

pressure in thiscase is atmospheric

pressure, which is a

CONSTANT.

Po=1x105N/m2


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Examplea) Calculate the absolute pressure at an ocean depth of

1000 m. Assume that the density of water is 1000kg/m3and that Po= 1.01 x 10

5Pa (N/m2).

b) Calculate the total force exerted on the outside of a30.0 cm diameter circular submarine window at this

depth.


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Pressure Gauges

Mercury Barometer:

measures atmospheric

pressure

Open Tube Manometer:

measures pressure in a

container

Po= 0

P = Patm

Patm= 0 + gh

Patm= gh

P = Patm+ gh

Example: blood pressure cuff


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A closed systemIf you take a liquid and place it in a

system that is CLOSED like plumbingfor example or a cars brake line, thePRESSURE is the same everywhere.

Since this is true, if you apply a force atone part of the system the pressure isthe same at the other end of the

system. The force, on the other handMAY or MAY NOT equal the initialforce applied. It depends on the AREA.

You can take advantage of the fact thatthe pressure is the same in a closed

system as it has MANY applications.

The idea behind this is called PASCALSPRINCIPLE


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Pascals Principle


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Example: Hydraulic Car Lift
http://images.google.com/imgres?imgurl=http://2.bp.blogspot.com/_2XJwgH8jhEc/Sa0kq7T7YsI/AAAAAAAAAuM/HkzSJV-pb1g/s400/hydralic%2Blift.png&imgrefurl=http://www.physicspractice.com/2009/03/hydraulic-lift.html&usg=__ifOTNKs64CeC6RIexzoffBLl1FQ=&h=300&w=400&sz=28&hl=en&start=1&um=1&tbnid=4hT6hrAZcAXZjM:&tbnh=93&tbnw=124&prev=/images%3Fq%3Dhydraulic%2Bcar%2Blift%2Bphysics%26hl%3Den%26safe%3Dactive%26um%3D1


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ExampleTo inspect a 14,000 N car, it is raised with a hydraulic lift. If the radius

of the small piston is 4.0 cm, and the radius of the large piston is17cm, find the force that must be exerted on the small piston to lift

the car.


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Buoyancy

When an object is immersed in a fluid, such as a liquid, it is buoyed______________ by a force called the ____________________________.


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Archimedes's Principle

*V = A (h2h1)


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ExampleA bargain hunter purchases a "gold" crown at a flea market. After she gets home,

she hangs it from a scale and finds its weight in air to be 7.84 N. She then

weighs the crown while it is immersed in water (density of water is 1000kg/m3) and now the scale reads 6.86 N. Is the crown made of pure gold if thedensity of gold is 19.3 x 103kg/m3?


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What if the magnitude

of the buoyant force

equals the weight of the

displaced fluid?

larger than?

less than?

T is the

apparent weight


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Example A piece of wood with a density o706 kg/m3is tied with a stringto the bottom of a water-filled

flask. The wood is completely

immersed, and has a volumeof 8.00 x 10-6 m3. What is the

tension in the string?

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