Fluids Chapter 13 & 14 Liquids &...

Fluids Chapter 13 & 14 Liquids & Gases

Liquids like solids are difficult to compress.

Both liquids and gases can flow, so both are

called fluids.

• The pressure you feel is due to the weight of water (or air) above you

• The pressure a liquid exerts depends on depth.

• Also depends on density.

• Liquid pressure = weight density X depth + pressure of atm.

• Except for small changes produced by temp., the density of a

liquids is practically the same at all depths.

Pressure does not depend on the amount of liquid Volume is not the key- depth is

• Pressure is depth dependent, not volume dependent.

Figure 13.5

• All vases are filled to equal depths, so the water pressure is the same at the bottom, regardless of its shape or volume

Once believed that you had to move water at a

slow drop in gradient to move it.

• Now know water

can flow uphill in a closed system if there is pressure behind it.

• Pipes in the ground can follow the natural slope of the land

• Garden hose full of water with one end dropped will spill water, but it will flow up hill

The force exerted by a fluid

on a smooth surface is

always at right angles to the

surface

• Liquid pressure is exerted equally in all directions

• The pressure isn’t only downward

• When liquid presses against a surface, there is a net force that is perpendicular to the surface.

• While pressure does not have a specific direction, force does.

Figure 13.2

• Raising the water increases the pressure in all parts of the system

3-Dec-13 Physics 1 (Garcia) SJSU

Pressure

Pressure is defined as

Pressure =

Metric unit of pressure is Pascal.

1 Pascal = 1 Newtons per square meter

Atmospheric pressure is about 100,000 Pascals

( Force )

( Area )


Pressure in Liquids

Pressure in a liquid depends on depth.

As with bricks, weight of what’s above determines pressure.

High

Medium

Low

High

Medium

Low

• As you move up & down in the

atm & in water, the pressure changes

• Pressure is greatest the farther down you go

• Altitude is the most important factor in surface air pressure.

The strength of the stream of water coming out of the holes in the jug depends on the water pressure at each level.

At which hole is the pressure greatest?


Sample Problem

“Gold” brick is roughly:

12 kilograms [Mass]

120 Newtons [Weight]

(0.2 m)x(0.1 m) =

(0.02 m2) [Area]

Pressure on surface is

(120)/(0.02)

= 6000 Pascals

Note: Atmospheric pressure is about 100,000 Pascals so much more than pressure due to the “gold” brick.


Check Yourself In which case is the pressure

greatest?

Although the weight of both blocks is the same, the upright block exerts greater pressure against the table

A B

A B


Check Yourself

In which case is the pressure greatest? A B

A

B


Demo: Bed of Nails

One may safely lay or sit on a bed of nails, as long as there are enough nails so that the pressure, measured as force per nail, is small.

Weight of 150 pounds is distributed over 300 nails. Force per nail is ½ lb. Need 5 lb per nail to pierce skin.


Demo: Pressure & Weight

A can full of water has holes in the sides through which water comes out.

What happens when you drop the can?

The can is now in freefall and weightless. Water stops flowing as the can falls since the pressure was due to the water’s weight.

Pressure

• P = force/area The force of all the collisions Force-Measured in Newtons, N Area- m2

• Pascal- SI unit of pressure = pascal, Pa, 1 N/m2

Fluid pressure in the Environment

• The atm. Pushes downward due to gravity causing atm pressure = 100 000 Pa

Buoyant Force Why do things sink or float?

• If the weight of the

submerged object is greater than the buoyant force= sink

• If the weight is less than buoyant= float

• When the eight is = to buoyant force = remain at same level (won’t sink or rise)

• Rising motion of balloons are caused by

unbalanced forces.

• The air beneath exerts more force than

the air above.

• When it reaches an altitude where the

forces are equal, it stops rising.


Buoyancy

Since pressure depends on depth, a submerged object has more force due to pressure below it than above it.

Net effect is to have a net upward force, which we call buoyancy.

Buoyancy

Weight

If weight exceeds buoyancy force then object sinks, otherwise it floats.

Pressure Pressure

Pressure


Buoyancy & Depth

For a fully submerged object the buoyancy force does not depend on depth, even though pressure depends on depth.

1

2

3

4

5

6

Buoyancy

Buoyancy

Buoyancy

Figure 13.15

To control how high they float in the water

Crocs swallow stones

Fish use air bladders

Figure 13.10

Figure 13.18

Two solid blocks of identical size are submerged in water. One block is lead and the other is aluminum. Upon which is the

buoyant force greater?

The buoyant force is the same on each, for both blocks displace the same volume of water. For submerged objects, only the volume of water displaced, not the object’s weight, determines

the buoyant force.

Only in the special case of floating does the buoyant force acting on an object equal the object’s weight.

principle of flotation:

A floating object displaces a weight of fluid equal to its own weight.

Figure 13.17

The weight of a floating object equals the

weight of the water displaced by the

submerged part.


Check Yourself

?

Place block of wood in the water. Scale reading goes up, down, or stays the same?

50 N

10 N Block

10 N Water

40 N Water

A floating

object

displaces a

weight of fluid

equal to its

own weight.


Check Yourself Use similar block of petrified wood. Scale reading goes up, down, or stays the same?

?

50 N

30 N Block

10 N Water

40 N Water

Figure 13.19

The same ship empty and loaded. How does the weight of

its load compare with the weight of extra water displaced?

Floating Mountains

• when mountains erode, they are lighter, and they are pushed up from below to float to nearly their original heights. So, when a kilometer of mountain erodes away, some 85% of a kilometer of mountain thrusts up from below. That’s why it takes so long for mountains to weather away.

The tip of a floating iceberg above the ocean’s

surface is approximately 10% of the whole

iceberg.

That’s because ice is 0.9 times the density of

water, so 90% of it submerges in water.

Similarly, a mountain floats on the Earth’s

semiliquid mantle with only its tip showing.

That’s because Earth’s continental crust is about

0.85 times the density of the mantle it floats

upon; thus, about 85% of a mountain extends

beneath the Earth’s surface. So, like floating

icebergs, mountains are appreciably deeper

than they are high.

Gravity is less at the top of a mountain because

of the greater distance to Earth’s center.


Archimedes’ Principle Weight of liquid displaced by floating or submerged

object equals the buoyant force on the object.


Density & Floating

By Archimede’s principle, a solid object will float if the density of the object is less than the density of the liquid.

Billiard ball (4.0 g/cm3) floating in a cup of mercury (13.6 g/cm3)


Demo: Diet or Regular?

What can you say about the density of diet cola as compared with regular cola?


Demo: Take a Dip

A 1 kg mass (1000 g) submerged in water displaces 150 cm3.

Water has density of 1 g/cm3 so displaced water has mass of 150 grams.

Buoyant force equals weight of 150 grams.

1000 g

1000 g

850 g

150 cc displaced

Beaker of Water


Demo: Floating in the Tub

Buoyant force depends only on the volume of fluid displaced, not on the volume of fluid in which the object is immersed.

Rubber duck floats the same in a little water or in a full beaker of water


Check Yourself

Did the designers of this “water bridge” have to account for the weight of ships or just the water?


Floating & Liquid Density

The greater the density of a liquid, the greater the buoyant force on objects floating or immersed in the liquid. Floating in Great Salt Lake, Utah is easy

because the lake water is dense due to high concentration of salt.

Pascal’s principle:

• A change in pressure at any point in an enclosed fluid at rest is transmitted undiminished to all points in the fluid.

Pressure exerted against the

left piston will be transmitted

throughout the liquid and

against the bottom of the right

piston.

The pressure that the left

piston exerts against the water

will be exactly equal to the

pressure the water exerts

against the right piston

Pascal’s Principle

• When force applied to a confined fluid, an increase in pressure is transmitted equally to all parts of the fluid A liquid completely filling a bottle exerts pressure in all directions

Figure 13.22 • The additional pressure is exerted against every square centimeter of the larger piston. Since there is 50 times the area, 50 times as much force is exerted on the larger piston. Thus, the larger piston will support a 500-kg load—fifty times the load on the smaller piston!

the piston on the right

has 50 times the area of

the piston on the left

(let’s say that the left

piston has a cross-

sectional area of 100

square centimeters and

that the right piston has

a cross-sectional area of

5000 square

centimeters).

Figure 13.23

• Pascal’s principle in a service station Increased air pressure

produced by an air

compressor is transmitted

through the air to the surface

of oil in an underground

reservoir. The oil, in turn,

transmits the pressure to a

piston, which lifts the

automobile. The relatively

low pressure that exerts the

lifting force against the piston

is about the same as the air

pressure in automobile tires

Figure 13.24

Surface Tension

• When the bent wire is lowered into the water

and then raised, the spring will stretch because

of surface tension.

•

contractive tendency of the

surface of liquids

Figure 13.27

• Small blobs of water are drawn by surface tension into sphere-like shapes.

Raindrops, drops of oil,

and falling drops of molten

metal are all spherical

because their surfaces

tend to contract and force

each drop into the shape

having the least surface

area. This is a sphere

• These molecular attractions thus tend to pull the molecule from the surface into the liquid, and this tendency minimizes the surface area.

Surface tension is caused by molecular

attractions.

Beneath the surface, each molecule is

attracted in every direction by neighboring

molecules, resulting in no tendency to be

pulled in any specific direction.

A molecule on the surface of a liquid,

however, is pulled only by neighbors on

each side and downward from below;

there is no pull upward.

The water surface sags like a piece of

plastic wrap, which allows certain insects,

such as water striders, to run across the

surface of a pond.

Figure 13.29

The large bubble is elongated due to blowing, but it will quickly settle

to a spherical shape due to surface tension.

Figure 13.30

. The attraction between unlike substances such as water and

glass is called adhesion.

The attraction between like substances, molecular

stickiness, is called cohesion. When a glass tube is dipped

into water, the adhesion between the glass and water causes a thin film of water to be drawn up over the inner

and outer surfaces of the tube

Surface tension causes • a thin film of water to be drawn up over the inner and outer surfaces of the tube (Figure 13.31a).It causes this film to contract (Figure 13.31b).

• The film on the outer surface contracts enough to make a rounded edge.

• The film on the inner surface contracts more and raises water with it until the adhesive force is balanced by the weight of the water lifted (Figure 13.31c

What happens to a can that is leaking water, when it is dropped?

Will it continue to lose water?

How would moving up or down in an elevator affect it?

Capillary Action

• If your hair is long, and you let it hang into the sink or bathtub, water will seep up to your scalp.

• This is how oil soaks upward in a lamp wick and water soaks into a bath towel when one end hangs in water.

• Capillary action is essential for plant growth. It brings water to the roots of plants and carries sap and nourishment to high branches

12. Which will hold the most ?

Unnumbered Figure 13.5

• 34. A piece of iron placed on a block of wood makes it float lower in the water. If the iron were instead suspended beneath the wood, would it float as low, lower, or higher? Defend your answer


• 41. A balloon is weighted so that it is barely able to float in water. If it is pushed beneath the surface, will it return to the surface, stay at the depth to which it is pushed, or sink? Explain. (Hint: Does the balloon’s density change?)

Unnumbered Figure

13.7

• 49. When the wooden block is placed in the beaker, what happens to the scale reading? Answer the same question for an iron block.


• 51. The weight of the container of water, as shown in a, is equal to the weight of the stand and the suspended solid iron ball. When the suspended ball is lowered into the water, as shown in b, the balance is upset. Will the additional weight needed on the right side to restore balance be greater than, equal to, or less than the weight of the solid iron ball?

Unnumbered Figure 13.8A

Unnumbered Figure 13.8B


• 57. In the hydraulic arrangement shown, the larger piston has an area that is fifty times that of the smaller piston. The strong man hopes to exert enough force on the large piston to raise the 10 kg that rest on the small piston. Do you think he will be successful? Defend your answer.

The pressure at the bottom of a submerged object is greater than the pressure at the top. The result is a net force in the upward direction.

What is this upward force called?

Force Pumps-

• Causes a fluid to move from one place to another by increasing the pressure on a pump (A medicine dropper) Heimlich maneuver- increases lung pressure & forces object out of windpipe

Hydraulic devise

• Multiplies a force by applying the force to a small surface area.

• The increase in pressure is then transmitted to another part of a confined fluid, which pushes on a larger surface area

Hydraulic pressure

• Force applied to one piston

increases the pressure in the fluid

• Pressure from a small piston acts over a larger area to produce a greater force in a hydraulic car lift.

• Used by seastars

Gases & Plasmas

The atmosphere.

• Air is more compressed at sea level than at higher altitudes.

• atmospheric pressure is caused by the weight of the air.

• The reason we don’t feel this weight crushing against our bodies is that the pressure inside our bodies equals that of the surrounding air. There is no net force for us to sense.

The pressure of the atmosphere is not uniform. Besides altitude variations, there are variations in atmospheric pressure at any one locality due to moving

weather fronts and storms.

• average atmospheric pressure at sea level is 101.3 kilopascals (101.3 kPa). 1

Barometer

• A common instrument used for measuring the pressure of the atmosphere

• If the atmospheric pressure increases, then the atmosphere pushes down harder on the mercury and the column of mercury is pushed higher than 76 centimeters. The mercury is literally pushed up into the tube of a barometer by the weight of the atmosphere. Could water be used to make a barometer? The answer is yes, but the glass tube would have to be much longer—13.6 times as long

• there is a 10.3-meter limit on the height that water can be lifted with vacuum pumps.

aneroid barometer

• measures atmospheric pressure

• A metal box that is partially exhausted of air and has a slightly flexible lid that bends in or out with changes in atmospheric pressure.

• Since the atmospheric pressure

decreases with increasing

altitude, a barometer can be

used to determine elevation.

• An aneroid barometer calibrated

for altitude is called an altimeter

(altitude meter).

• Some altimeters are sensitive

enough to indicate a change in

elevation of less than a meter.

“hard vacuum” can reach 10−13 Pa. In space

• A vacuum pump simply provides a region of lower pressure into which fast-moving gas molecules randomly move

Boyle’s Law

• Boyle’s law applies to ideal gases. An ideal gas is one in which the disturbing effects of the forces between molecules and the finite size of the individual molecules can be neglected. Air and other gases under normal pressures approach ideal-gas conditions.

• the product of pressure and volume for a given mass of gas is a constant as long as the temperature doesn’t change

• pressure and volume are inversely proportional;

Archimedes’ principle

• holds for air just as it does for water: An object surrounded by air is buoyed up by a force equal to the weight of the air displaced.

• any object less dense than air will rise in air

• (Left) At ground level, the balloon is partially inflated. (Right) The same balloon is fully inflated at high altitudes where surrounding pressure is less

Bernoulli’s Principle

• fluids in motion—fluid dynamics.

• True for liquids and gases

• The pressure exerted by a

moving stream of fluid is

less than the pressure of

the surrounding fluid

Blow on paper?

• When the speed of a fluid increases, internal pressure in the fluid decreases. pressure at the walls of the pipes decreases when the speed of the water increases.

Bernoulli’s principle is consistent with the conservation of energy

• .For a steady flow of an ideal fluid free of internal friction, there are three kinds of energy: kinetic energy due to motion, work associated with pressure forces, and gravitational potential energy due to elevation

• In a steady fluid flow where no energy is added or taken away, whatever work is done by one part of the fluid on another part makes its appearance as kinetic and potential energy. Then the sum of the three energy terms remains constant.

Bernoulli’s Demo Blow over a piece of

paper

Air pressure above the roof is less than air pressure beneath the roof.

• Consider wind blowing across a peaked roof.

The wind speeds up as it flows over the top,

as the crowding of streamlines in Figure

14.20 indicates.

• Pressure along the streamlines is reduced

where they are closer together.

• Unless the building is well vented, greater

pressure inside and beneath the roof can

push it off.

• .

Even a small pressure difference over a large roof area can produce a large upward “lifting” force

Curving may be increased by threads or fuzz, which help to drag a thin layer of air with the ball and to produce further crowding

of streamlines on one side.

• a) The streamlines are the same on either side of a nonspinning baseball.

• (b) A spinning ball produces a crowding of streamlines. The resulting “lift” (red arrow) causes the ball to curve, as shown by the blue arrow.

• The vertical vector represents the net upward force (lift) that results from more air pressure below the wing than above the wing. The horizontal vector represents air drag.

Bernoulli’s principle

• Pressure is greater in the stationary fluid (air) than in the moving fluid (water stream). The atmosphere pushes the ball into the region of reduced pressure.

Bernoulli’s principle explains why trucks and boats passing closely on are drawn to each other

• passing ships run the risk of a sideways collision. Water flowing between the ships travels faster than water flowing past the outer sides

• . Streamlines are closer together between the ships than outside. Hence, water pressure acting against the hulls is reduced between the ships.

• the greater pressure against the outer sides of the ships forces them together.

• On a windy day, waves in a lake or the ocean are higher than their average height. How does Bernoulli’s principle contribute to the increased height?

plasma

• a fourth phase of matter

• the least common phase -but it is the most prevalent phase of matter in the universe as a whole. The Sun and other stars are largely plasma.

• A plasma is an electrified gas.

• The atoms that make it up are ionized, stripped of one or more electrons, with a corresponding number of free electrons

plasma

• Plasmas on Earth are created in laboratories by heating gases to very high temperatures, making them so hot that electrons are “boiled” off the atoms. Plasmas may also be created at lower temperatures by bombarding atoms with high-energy particles or radiation.

• Ex. Fluorescent tubes

• Neon signs & street lights

• Plasma TV screens

• Auroras

• Exhaust of jet engine

• MHD power- Magnetohydrodynamic interaction between plasma & magnetic field

Plasma= future?

• Fusion power

• Fusion power may not only make electrical energy abundant, but it may also provide the energy and means to recycle and even synthesize elements.

• Air flowing over the top of the wing travels farther than the air on the bottom in the same amount of time.

This means the

speed of the air

above the wing is

much faster than

the speed below.

• The difference in speed leads

to a greater pressure over the

top of the wing and a lower

pressure below the wing.

• This pressure difference is what causes the lift.

Steamlined shape of plane reduces drag

• Thrust - force which pushes the plane forward

provided by plane’s propeller/jet

• To land a plane increases its area and drag by

using flaps to change the shape of the wing

Fluid Pressure

P = Force /area

measured in Pascals


•Explains hydraulic systems

•Pressure is exerted equally throughout a closed container

•Hydraulic systems multiply force (over a greater distance)

Bernoulli’s Principle

Pressure exerted on a moving steam of fluid is less than the pressure of the surrounding fluid

•Explains Flight

Archimedes’ Principle

(Sinks) Buoyant force on an object is equal to the weight

of the fluid displaced

If an object floats- the volume of displaced water = volume of the portion of the object that is submerged.

Fluids Chapter 13 & 14 Liquids &...

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