# AP Physics B

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24 Οκτ 2013 (πριν από 4 χρόνια και 8 μήνες)

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AP Physics B

Fluid Dynamics

2

College Board Objectives

II. FLUID MECHANICS AND THERMAL PHYSICS

A. Fluid Mechanics

1. 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 exerts
pressure perpendicular to any surface that it
contacts.

3

d) Determine locations of equal pressure in a
fluid.

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

f) Apply the relationship between pressure and
depth in a liquid,
D
P =
r
g
D
h

Fluid mechanics, cont.

4

Fluid Mechanics, cont.

2. Buoyancy

Students should understand the concept of
buoyancy, so they can:

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

b) Apply Archimedes’ principle to determine
buoyant forces and densities of solids and
liquids.

5

Fluid Mechanics, cont.

3. Fluid flow continuity

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

fluids in motion.

4. Bernoulli’s equation

Students should understand Bernoulli’s
equation so that they can apply it to fluids
in motion.

6

Unit Plan

-
10 re Fluid
Mechanics in Giancoli

Assignment:

Q/4,7,11

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

and
44,46,48

7

10.1&2 Density &

Specific Gravity

The mass density
r

of a substance is
the mass of the substance divided
by the volume it occupies:

unit: kg/m
3

r

fralminm2700歧/m
3

or 2.70 g/cm
3

mass can be written as
m =
r
V

and



mg㴠
r

pecific䝲a癩t示
r

sbstance/
r

8

Problem 10.5

5.

(II) A bottle has a mass of 35.00 g when empty
and 98.44 g when filled with water. When filled
with another fluid, the mass is 88.78 g. What is
the 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 used
for both liquids.

SG
fluid

9

A
fluid

-

a substance that flows and
conforms to the boundaries of its
container.

A fluid could be a gas or a liquid;
however on the AP Physics B exam
fluids are typically liquids which are
constant in density.

10

An
ideal fluid

is assumed

to be incompressible (so that its
density does not change),

to flow at a steady rate,

to be nonviscous (no friction between
the fluid and the container through
which it is flowing), and

flows irrotationally (no swirls or
eddies).

11

10.3 Pressure

Any fluid can exert a force
perpendicular to its surface on the
walls of its container. The force is
described in terms of the pressure it
exerts, or force per unit area:

Units: N/m
2

or Pa (1 Pascal*)

dynes/cm
2

or PSI (lb/in
2)

1 atm = 1.013 x 10
5

Pa or 15 lbs/in
2

*One atmosphere is the pressure exerted on us
every day by the earth’s atmosphere.

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

Pressure varies with depth.

P =
F

=
r
Ahg

sP=
r


AA

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A FLUID AT REST EXERTS
PRESSURE PERPENDICULAR TO
ANY SURFACE THAT IT
CONTACTS. THERE IS NO
PARALLEL COMPONENT THAT
WOULD CAUSE A FLUID AT REST
TO FLOW.

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PROBLEM 10
-
9

9.
(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 the
underside of the table?

9.

(
a
)

The total force of the atmosphere on
the table will be the air pressure times the area
of the table.

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

15

10.4 Atmospheric Pressure and Gauge
Pressure

The pressure
p1

on the surface of the water is 1
atm, or 1.013 x 105 Pa. If we go down to a depth
h

below the surface, the pressure becomes
greater by the product of the density of the water
r
, the acceleration due to gravity
g
, and the
depth
h
. Thus the pressure
p2

at this depth is

h

h

h

p
2

p
2

p
2

p
1

p
1

p
1

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In this case,
p2

is called the
absolute
pressure

--

the total static pressure at a certain depth in a
fluid, including the pressure at the surface of the
fluid

The difference in pressure between the surface and
the depth
h

is
gauge pressure

Note that the pressure at any depth does not
depend of the shape of the container, only the
pressure at some reference level (like the surface)
and the vertical distance below that level.

h

h

h

p
2

p
2

p
2

p
1

p
1

p
1

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14.
(II) (
a
) What are the total force and the
absolute pressure on the bottom of a swimming
pool 22.0 m by 8.5 m whose uniform depth is 2.0
m? (
b
) What will be the pressure against the
side

of the pool near the bottom?

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

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(
b
)

The pressure against the side of
the pool, near the bottom, will be the
same as the pressure at the

bottom,

19

10.5 Pascal’s Principle

Pascal’s Principle
-

if an external pressure
is applied to a confined fluid, the pressure at
every point within the fluid increases by that
amount. Applications: hydraulic lift and brakes

Pout = Pin

And since P = F/a

Fout = Fin

Aout Ain

Fout = Aout

Fin Ain

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Problem 10
-
10

10.
(II) In a movie, Tarzan evades his captors by
hiding underwater for many minutes while
breathing through a long, thin reed. Assuming
the maximum pressure difference his lungs can
manage and still breathe is calculate the deepest
he could have been. (See page 261.)

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

21

10
-
7 Buoyancy and Archimedes’ Principle

This is an object
submerged

in a fluid. There is a
net
force

on the object because the
pressures

at
the top and bottom of it are different.

The
buoyant force

is
found to be the
upward

force on the
same

volume
of water:

22

10
-
7 Buoyancy and Archimedes’ Principle

The
net force on

the object is then the difference
between the
buoyant force

and the
gravitational

force.

23

10
-
7 Buoyancy and Archimedes’ Principle

If the object’s
density

is
less

than that of water,
there will be an
upward

net force on it, and it will
rise until it is partially
out

of the water.

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10
-
7 Buoyancy and Archimedes’ Principle

For a
floating

object, the fraction that is
submerged

is given by the ratio of the object’s
density

to that of the fluid.

25

10
-
7 Buoyancy and Archimedes’ Principle

This principle also works in
the air; this is why
hot
-
air

and
helium

balloons 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 in
water. 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, and
the 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.

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24.
(II) A crane lifts the 18,000
-
kg steel hull of a ship out of
the water. Determine (
a
) the tension in the crane’s cable
when the hull is submerged in the water, and (
b
) the
tension when the hull is completely out of the water.

24.(
a
)

When the hull is submerged, both the buoyant force
and the tension force act upward on the hull, and so their
sum is equal to the weight of the hull. The buoyant force
is the weight of the water displaced.

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24. (
b
)When the hull is completely out of the
water, the tension in the crane’s cable
must be equal to the weight of the hull.

29

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 weight
of the wood and lead must be equal to the total buoyant
force on the wood and the lead.

30

10
-
8 Fluids in Motion; Flow Rate and the
Equation of Continuity

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

or
laminar

flow (a).

Above a certain speed, the flow becomes
turbulent

(b).
Turbulent flow has
eddies
; the
viscosity

of the fluid is much
greater when eddies are present.

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We will deal with
laminar

flow.

The
mass flow rate

is 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
-
8 Fluids in Motion; Flow Rate and the
Equation of Continuity

(10
-
4a)

32

10
-
8 Fluids in Motion; Flow Rate and the
Equation of Continuity

If the density doesn’t change

typical for
liquids

this simplifies to

.
Where the pipe is
wider
, the flow is
slower
.

33

10
-
9 Bernoulli’s Equation

A fluid can also change its
height
. By looking at the
work done as it moves, we
find:

This is
Bernoulli’s

equation. One thing it
tells us is that as the
speed

goes up, the
pressure

goes down.

34

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

35

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.

36

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 Bernoulli’s equation with point 1 being the water
main, 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.

37

Visit the follow website from
Boston University

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

from left panel)

Pressure; Fluid Statics

Fluid Dynamics

Viscosity

38

At the website complete the
following:

1. Read and record important
equations and facts.

2. For each equation write the
quantity for each symbol

3. Write the unit for each
quantity (symbol ok)

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Demonstrations to View

http://www.csupomona.edu/~physic
s/oldsite/demo/fluidmech.html