10_FluidDynamics

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AP Physics BFluid Dynamics


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College Board Objectives

II. FLUID MECHANICS AND THERMAL PHYSICSA. Fluid Mechanics1. Hydrostatic pressure

Students should understand the concept of

pressure as it applies to fluids, so they can:a) Apply the relationship between pressure, force,

and area.b) Apply the principle that a fluid exerts pressure in

all directions.

c) Apply the principle that a fluid at rest exertspressure perpendicular to any surface that itcontacts.


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d) Determine locations of equal pressure in a

fluid.

e) Determine the values of absolute and gaugepressure for a particular situation.

f) Apply the relationship between pressure and

depth in a liquid, DP =r g Dh

Fluid mechanics, cont.


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Fluid Mechanics, cont.

2. Buoyancy

Students should understand the concept ofbuoyancy, so they can:

a) Determine the forces on an objectimmersed partly or completely in a liquid.

b) Apply Archimedes principle to determine

buoyant forces and densities of solids andliquids.


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Fluid Mechanics, cont.

3. Fluid flow continuity

Students should understand the equation ofcontinuity so that they can apply it to

fluids in motion.

4. Bernoullis equation

Students should understand Bernoullisequation so that they can apply it to fluidsin motion.


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Unit Plan

Read Chapter 10.1-10 re FluidMechanics in Giancoli

Assignment: Q/4,7,11

P/5,6,11,12,14,16,25,33,35,

and 44,46,48


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10.1&2 Density &Specific Gravity

The mass density rof a substance isthe mass of the substance dividedby the volume it occupies:

unit: kg/m3

for aluminum 2700 kg/m3or 2.70 g/cm3

mass can be written as m = V and

weight as mg = Vg

Specific Gravity: substance / water

V

mr


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Problem 10.55. (II) A bottle has a mass of 35.00 g when empty

and 98.44 g when filled with water. When filledwith another fluid, the mass is 88.78 g. What isthe specific gravity of this other fluid?

5. Take the ratio of the density of the fluid to that

of water, noting that the same volume is usedfor both liquids.

fluid fluid fluid

fluid

water water water

88.78 g 35.00 g0.8477

98.44 g 35.00 g

m V mSJ

m V m

r

r

SGfluid


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A fluid- a substance that flows andconforms to the boundaries of its

container. A fluid could be a gas or a liquid;

however on the AP Physics B examfluids are typically liquids which areconstant in density.


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An ideal fluidis assumed

to be incompressible (so that itsdensity does not change),

to flow at a steady rate,

to be nonviscous (no friction betweenthe fluid and the container throughwhich it is flowing), and

flows irrotationally (no swirls oreddies).


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10.3 Pressure

Any fluid can exert a forceperpendicular to its surface on thewalls of its container. The force is

described in terms of the pressure itexerts, or force per unit area:

Units: N/m2or Pa (1 Pascal*)

dynes/cm2 or PSI (lb/in2)

1 atm = 1.013 x 105Pa or 15 lbs/in2

*One atmosphere is the pressure exerted on usevery day by the earths atmosphere.

A

Fp


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The pressure is the same in everydirection in a fluid at a given depth.

Pressure varies with depth.

P = F = Ahg so P = gh

A A


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A FLUID AT REST EXERTSPRESSURE PERPENDICULAR TOANY SURFACE THAT ITCONTACTS. THERE IS NOPARALLEL COMPONENT THATWOULD CAUSE A FLUID AT RESTTO FLOW.


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PROBLEM 10-99. (I) (a) Calculate the total force of the

atmosphere acting on the top of a table that

measures

(b) What is the total force acting upward on theunderside of the table?

9. (a) The total force of the atmosphere on

the table will be the air pressure times the areaof the table.

5 2 51.013 10 N m 1.6 m 2.9 m 4.7 10 NF PA

(b) Since the atmospheric pressure is the same on the underside of thetable (the height difference is minimal), the upward force of air pressure isthe same as the downward force of air on the top of the table,

54.7 10 N

m.2.9m6.1


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10.4 Atmospheric Pressure and GaugePressure

The pressurep1on the surface of the water is 1

atm, or 1.013 x 105 Pa. If we go down to a depthhbelow the surface, the pressure becomesgreater by the product of the density of the water

r, the acceleration due to gravity g, and the

depth h. Thus the pressurep2at this depth is

h h hp2 p2 p2

p1 p1p1

ghpp r 12


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In this case,p2is called the absolute pressure--the total static pressure at a certain depth in afluid, including the pressure at the surface of the

fluidThe difference in pressure between the surface and

the depth his gauge pressure

ghpp r12

Note that the pressure at any depth does notdepend of the shape of the container, only thepressure at some reference level (like the surface)

and the vertical distance below that level.

h h hp2 p2 p2

p1 p1p1


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14.(II) (a) What are the total force and theabsolute pressure on the bottom of a swimmingpool 22.0 m by 8.5 m whose uniform depth is 2.0

m? (b) What will be the pressure against the sideof the pool near the bottom?

(a)The absolute pressure is given by Eq. 10-3c, andthe total force is the absolute pressure times thearea of the bottom of the pool.

5 2 3 3 2

0

5 2

5 2 7

1.013 10 N m 1.00 10 kg m 9.80 m s 2.0 m

1.21 10 N m

1.21 10 N m 22.0 m 8.5 m 2.3 10 N

P P gh

F PA

r


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(b) The pressure against the side ofthe pool, near the bottom, will be thesame as the pressure at the

bottom,

5 2

1.21 10 N mP


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10.5 Pascals Principle

Pascals Principle - if an external pressureis applied to a confined fluid, the pressure atevery point within the fluid increases by thatamount. Applications: hydraulic lift and brakes

Pout = Pin

And since P = F/a

Fout = Fin

Aout Ain

Mechanical Advantage:

Fout = Aout

Fin Ain


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Problem 10-10

10.(II) In a movie, Tarzan evades his captors byhiding underwater for many minutes whilebreathing through a long, thin reed. Assumingthe maximum pressure difference his lungs canmanage and still breathe is calculate the deepesthe could have been. (See page 261.)

10.The pressure difference on the lungs is thepressure change from the depth of water

2

3 3 2

133 N m85mm-Hg

1 mm-Hg 1.154 m 1.2 m

1.00 10 kg m 9.80 m s

PP g h h

gr

r

DD D D

10 7 B d A hi d P i i l


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10-7 Buoyancy and Archimedes Principle

This is an object submergedin a fluid. There is a

net forceon the object because the pressuresatthe top and bottom of it are different.

The buoyant forceis

found to be the upward

force on the samevolume

of water:



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The net force onthe object is then the difference

between the buoyant forceand the gravitationalforce.



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If the objects densityis lessthan that of water,

there will be an upwardnet force on it, and it willrise until it is partially outof the water.



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For a floatingobject, the fraction that is

submergedis given by the ratio of the objectsdensityto that of the fluid.



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This principle also works in

the air; this is why hot-airand

heliumballoons rise.


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22. (I) A geologist finds that a Moon rock

whose mass is 9.28 kg has an apparent

mass of 6.18 kg when submerged inwater. What is the density of the rock?

22. The difference in the actual mass and the apparent mass is the

mass of the water displaced by the rock. The mass of the water

displaced is the volume of the rock times the density of water, andthe volume of the rock is the mass of the rock divided by its density.

Combining these relationships yields an expression for the density

of the rock.

rock

actual apparent water rock water rock

3 3 3 3rock

rock water

9.28kg1.00 10 kg m 2.99 10 kg m

9.28 kg 6.18 kg

mm m m V

m

m

r rr

r r

D

D


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24. (b)When the hull is completely out of the

water, the tension in the cranes cable

must be equal to the weight of the hull.

4 2 5 51.8 10 kg 9.80m s 1.764 10 N 1.8 10 NT mg


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34.(III) A 5.25-kg piece of wood

floats on water. What minimum mass of lead, hung from

the wood by a string, will cause it to sink?

34.For the combination to just barely sink, the total weightof the wood and lead must be equal to the total buoyant

force on the wood and the lead.

0.50SG

weight buoyant wood Pb wood water Pb water

wood Pb water water

wood Pb water water Pb wood

wood Pb Pb wood

1 1

F F m g m g V g V g

m mm m m m

r r

r rr r

r r r r

water

wood wood

Pb wood wood

water

Pb Pb

1 11 1 10.50

5.25kg 5.76kg11

11 111.3

SGm m m

SG

r

r

r

r

10 8 Fluids in Motion; Flow Rate and the


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10-8 Fluids in Motion; Flow Rate and the

Equation of Continuity

If the flow of a fluid is smooth, it is called streamlineor

laminarflow (a).

Above a certain speed, the flow becomes turbulent(b).

Turbulent flow has eddies; the viscosityof the fluid is much

greater when eddies are present.



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We will deal with laminarflow.The mass flow rateis the mass that passes a

given point per unit time. The flow rates at any

two points must be equal, as long as no fluid is

being added or taken away.

This gives us the equation of continuity:



(10-4a)



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If the density doesnt change typical forliquidsthis simplifies to .

Where the pipe is wider, the flow is slower.

10 9 Bernoullis Equation


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10-9 Bernoullis Equation

A fluid can also change itsheight. By looking at the

work done as it moves, we

find:

This is Bernoullisequation. One thing it

tells us is that as the

speedgoes up, the

pressuregoes down.


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36. (I) A 15-cm-radius air duct is used to replenish the

air of a room every 16 min. How

fast does air flow in the duct?

36. We apply the equation of continuity at constant

density, Eq. 10-4b. Flow rate out of duct = Flow rate into

room

.cm0.22

2 room room

duct duct duct duct 22

to fill to fill

room room

9.2 m 5.0 m 4.5 m 3.1m s

60 s0.15 m 16 min

1 min

V VA v r v v

t r t

m4.5m5.0m2.9


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39. (II) A (inside) diameter garden hose is used to

fill a round swimming pool 6.1 m in diameter. How long

will it take to fill the pool to a depth of 1.2 m if water

issues from the hose at a speed of 39. The volume flow rate of water from the hose,

multiplied times the time of filling, must equal the volume

of the pool.

inch-8

5

?sm40.0

2

pool pool 5

2hose

"hose hose 51

2 8 "

5

3.05m 1.2m 4.429 10 s

1m0.40m s

39.37

1day

4.429 10 s 5.1 days60 60 24s

V VAv t

t A v


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40. (II) What gauge pressure in the water mains is

necessary if a firehose is to spray water to a height of

15 m?

40. Apply Bernoullis equation with point 1 being the watermain, and point 2 being the top of the spray. The

velocity of the water will be zero at both points. The

pressure at point 2 will be atmospheric pressure.

Measure heights from the level of point 1.

2 21 1

1 1 1 2 2 22 2

3 3 2 5 2

1 atm 2

1.00 10 kg m 9.8m s 15 m 1.5 10 N m

P v gy P v gy

P P gy

r r r r

r

Vi it th f ll b it f


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Visit the follow website fromBoston University

http://physics.bu.edu/~duffy/py105.html

For more information about (choose

from left panel)

Pressure; Fluid Statics

Fluid Dynamics

Viscosity
http://physics.bu.edu/~duffy/py105.htmlhttp://physics.bu.edu/~duffy/py105.htmlhttp://physics.bu.edu/~duffy/py105.htmlhttp://physics.bu.edu/~duffy/py105.html


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At the website complete thefollowing:

1. Read and record important

equations and facts.2. For each equation write the

quantity for each symbol

3. Write the unit for eachquantity (symbol ok)


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Demonstrations to View

http://www.csupomona.edu/~physics/oldsite/demo/fluidmech.html
http://www.csupomona.edu/~physics/oldsite/demo/fluidmech.htmlhttp://www.csupomona.edu/~physics/oldsite/demo/fluidmech.htmlhttp://www.csupomona.edu/~physics/oldsite/demo/fluidmech.htmlhttp://www.csupomona.edu/~physics/oldsite/demo/fluidmech.html

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