introducing fluids

8/2/2019 Introducing Fluids

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Pressure

Hydrostatic Pressure


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Fluids

Fluids are substances that can flow,, such asliquids and gases, and even a few solids.

In Physics B, we will limit our discussion of fluidsto substances that can easily flow, such as liquidsand gases.


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Review: Density

r = m/V since w=mg wfluid= Vg r (rho):density (kg/m3)

m: mass (kg)

V: volume (m3)

It is useful to know the density of water 1000kg/m3

When we want to determine if it is likely thatsomething will sink in water, it is useful to compare the

density of a substance to the density of water. We call this comparison Specific Gravity.

For example lead has a density of 11,000 kg/m3 thereforeit has a specific gravity of 11


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Pressure P = F/A

P: pressure (Pa)

F: force (N)

A: area (m2)

Pressure unit: Pascal ( 1 Pa = 1 N//m2)

!atm = 760mm of Hg = 1x105 Pa

NOTE Hg = 13.5 H2O

The force on a surface caused by pressure is alwaysnormal (or perpendicular) to the surface. This meansthat the pressure of a fluid is exerted in alldirections, and is perpendicular to the surface at

every location.

Balloon


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Sample Problem Calculate the net force on an airplane window if

cabin pressure is 90% of the pressure at sealevel, and the external pressure is only 50% ofthat at sea level. Assume the window is 0.43 m talland 0.30 m wide.


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Atmospheric Pressure

Atmospheric pressureis normally about100,000 Pascals.

Differences in

atmospheric pressurecause winds to blow.

Low atmosphericpressure inside a

hurricanes eyecontributes to thesevere winds and thedevelopment of the

storm surge.


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The Pressure of a Liquid

P = gh P: pressure (Pa)

: density (kg/m3

) g: acceleration constant (9.8 m/s2)

h: height of liquid column (m)

This type of pressure is often calledgauge

pressure. If the liquid is water, this is referred to as

hydrostatic pressure.


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Absolute Pressure Absolute pressure is obtained by addingthe

atmospheric pressure to the hydrostaticpressure.

Pabs = Patm+ gh


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Hydrostatic Pressure in Dam

Design The depth of Lake

Mead at the HooverDam is 600ft. What isthe hydrostaticpressure and what isthe absolute pressureat the base of thedam?

115 miles to the end of lake Mead

Hoover Dam


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Hydrostatic Pressurein Levee DesignHurricane Katrina, August 2005

A hurricanes stormsurge can overtop levees,but a bigger problem canbe increasing thehydrostatic pressure atthe base of the levee.


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Floating is a type of equilibrium An upward force counteracts the

force of gravity for theseobjects. This upward force iscalled the buoyant force.

mg

Fbouy


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Archimedes Principle Archimedes Principle: a body immersed in a fluid

is buoyed up by a force that is equal to the weightof the fluid it displaces.


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The Buoyant Force Fbuoy= Vg

Fbuoy: the buoyant force exerted on a submerged orpartially submerged object.

V: the volume of displaced liquid.

: the density of the displaced liquid.

When an object floats, the upward buoyant forceequals the downward pull of gravity.

The buoyant force can float very heavy objects,and acts upon objects in the water whether theyare floating, submerged, or even sitting on thebottom.


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A sharks body is not neutrally buoyant, and so ashark must swim continuously or he will sinkdeeper.

Buoyant force on submerged

object

mg

Fbouy = Vg


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object SCUBA divers use a buoyancy control system to

maintain neutral buoyancy (equilibrium!).

mg

Vg


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object If the diver wants to rise, he inflates his vest,

which increases the amount of water he displaces,and he accelerates upward.

mg

Vg


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Buoyant force Buoyant force on

floating object

If the object floats on the surface, we know for afact Fbuoy = mg! The volume of displaced waterequals the volume of the submerged portion ofthe ship.

mg

Vg


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Sample problem Assume a wooden raft has 80.0% of the density

of water. The dimensions of the raft are 6.0 mlong by 3.0 m wide by 0.10 m tall. How much of theraft rises above the level of the water when itfloats?


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Buoyant Force The buoyant force can be extremely strong.

Incredibly massive objects can float, even when

they are not intended to


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St. Bernard Parish after

Hurricane Katrina


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St. Bernard Parish after

Hurricane Katrina


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When a Fluid Flows mass is conserved..

Provided there are no inlets our outlets in a

stream of flowing fluid, the same mass per unittime must flow everywhere in the stream.

http://library.thinkquest.org/27948/bernoulli.html

http://home.earthlink.net/~mmc1919/venturi.html
http://library.thinkquest.org/27948/bernoulli.htmlhttp://library.thinkquest.org/27948/bernoulli.htmlhttp://home.earthlink.net/~mmc1919/venturi.htmlhttp://home.earthlink.net/~mmc1919/venturi.htmlhttp://library.thinkquest.org/27948/bernoulli.htmlhttp://library.thinkquest.org/27948/bernoulli.html


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Fluid Flow Continuity The volume per unit time of a liquid flowing ina pipe is constant throughout the pipe.

We can say this because liquids are notcompressible, so mass conservation is also volumeconservation for a liquid.


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Fluid Flow Continuity V = Avt

V: volume of fluid (m3)

A: cross sectional areas at a point in the pipe (m2

) v: speed of fluid flow at a point in the pipe (m/s)

t: time (s)


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A1v1 = A2v2 A1, A2: cross sectional areas at points 1 and 2

v1, v2: speed of fluid flow at points 1 and 2

Fluid Flow Continuity


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A pipe of diameter 6.0 cm has fluid flowing throughit at 1.6 m/s. How fast is the fluid flowing in anarea of the pipe in which the diameter is 3.0 cm?How much water per second flows through thepipe?

Sample problem


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Sample problem The water in a canal flows 0.10 m/s where the

canal is 12 m deep and 10 m across. If the depthof the canal is reduced to 6.5 meters at an areawhere the canal narrows to 5.0 m, how fast willthe water be moving through this narrowerregion?


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Question What will happen to the water in an open

waterway if it cannot flow as fast as it wants tothrough a narrow region in a channel?


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Natural Waterways Flash floodingcan be explainedby fluid flow

continuity.


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Fluid Flow Continuity

in WaterwaysMississippi River GulfOutlet levees areovertopped by Katrinas

storm surge.

A hurricanesstorm surge can

be amplified bywaterways thatbecome narroweror shallower asthey move inland.


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Bernoullis Theorem The sum of the pressure, the potential energy per

unit volume, and the kinetic energy per unit volumeat any one location in the fluid is equal to the sumof the pressure, the potential energy per unit

volume, and the kinetic energy per unit volume atany other location in the fluid for a non-viscousincompressible fluid in streamline flow.

All other considerations being equal, when fluidmoves faster, the pressure drops.

http://library.thinkquest.org/27948/bernoulli.html
http://library.thinkquest.org/27948/bernoulli.htmlhttp://library.thinkquest.org/27948/bernoulli.html


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Bernoullis Theorem P + g h + v2 = Constant

P : pressure (Pa)

: density of fluid (kg/m3)

g: gravitational acceleration constant (9.8 m/s2)

h: height above lowest point (m)

v: speed of fluid flow at a point in the pipe (m/s)


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Sample Problem Knowiing what youknow about Bernouillisprinciple, design an

airplane wing that youthink will keep anairplane aloft.

Draw a cross sectionof the wing.


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Virtual

Windtunnel Fluid flow

researcher atwork in virtual

windtunnelprovidinginteractive 3-dimensional

environment. Date taken:

1992


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Bernoullis Principle and

Hurricanes In a hurricane or tornado, the high winds travelingacross the roof of a building can actually lift theroof off the building.

http://video.google.com/videoplay?docid=6649024923387081294&q=Hurricane+Roof&hl=en
http://video.google.com/videoplay?docid=6649024923387081294&q=Hurricane+Roof&hl=enhttp://video.google.com/videoplay?docid=6649024923387081294&q=Hurricane+Roof&hl=enhttp://video.google.com/videoplay?docid=6649024923387081294&q=Hurricane+Roof&hl=enhttp://video.google.com/videoplay?docid=6649024923387081294&q=Hurricane+Roof&hl=en

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