6.1 laminar and turbulent flow - mr findlay's website - textbook pages.pdf · 278 chapter 6...

278 Chapter 6 NEL

6.16.1 Laminar and Turbulent Flow

A log ride is smooth as long as the water flows evenly. However, the flow and

the ride can become rough where there are dips and sharp curves (Figure 1).

The factors that affect the smooth or rough flow of a fluid are part of the

study of fluids in motion, called fluid dynamics.

As a fluid flows, the forces of attraction between the molecules cause

internal friction, or resistance to the flow. The fluid’s viscosity is a measure of

this resistance to flow. A fluid with a high viscosity, such as liquid honey, has a

large amount of internal resistance and does not flow readily. A fluid with a

low viscosity, such as water, has low internal resistance and flows easily.

Viscosity depends not only on the nature of the fluid, but also on the fluid’s

temperature. As the temperature of a liquid increases, the viscosity generally

decreases because the particles of the liquid have more energy and flow more

easily. As the temperature of a gas increases, however, the viscosity generally

increases because the particles of the gas collide with each other more often,

making it more difficult for them to flow in one direction.Figure 1

The design of a log ride determines

its smoothness.

fluid dynamics the study of the

factors that affect fluids in motion

viscosity the property of a fluid

that determines its resistance to

flow; a high viscosity means a high

resistance to flow

TRYTHIS activity Viscosity

Observe the effect of temperature changes

on the viscosity of various products from

your home (e.g., vegetable oil, honey, clear

shampoo, syrup) when placed in stoppered

test tubes provided by your teacher

(Figure 2). Each tube should also contain

a marble. Obtain a test tube that has been

placed in a cold water bath, invert it, and

measure the time it takes for the marble to

travel through the liquid. Compare your

results with the time it takes for the marble

to travel through the liquid in a test tube

that has been placed in a hot water bath.

Wear gloves when handling the

liquids. Exercise care when using

hot water.

vegetable oil

in test tube

marble

stopper

Figure 2

After you invert the test tube, the

marble moves slowly downward

through the oil.

As a fluid flows, the fluid particles interact with their surroundings and

experience external friction. For example, as water flows through a pipe, the

water molecules closest to the walls of the pipe experience a frictional

resistance that reduces their speed to nearly zero. Measurements show that the

water speed varies from the wall of the pipe (minimum speed) to the centre of

the pipe (maximum speed). If the speed of a fluid is slow and the adjacent

regions flow smoothly over one another, the flow is called a laminar flow

laminar flow fluid flow in which

adjacent regions of fluid flow

smoothly over one another

Fluid Dynamics 279NEL

(Figure 3(a)). The flow of a fluid such as air passing around a smooth object is

also called laminar flow (Figure 3(b)).

Laminar flow is usually difficult to achieve because, as the fluid flows

through or past an object, the flow becomes irregular, resulting in whirls

called eddies (Figure 4). Eddies are common in turbulent flow, a fluid flow

with a disturbance that resists the fluid’s motion (e.g., water encountering

boulders in a river). A fluid undergoing turbulent flow loses kinetic energy as

some of the energy is transformed into thermal energy and sound energy. The

likelihood of turbulence increases as the velocity of the fluid relative to its

surroundings increases.

Section 6.1

low velocity

eddies

high velocity

eddies

(a) (b) (c)

Figure 4

(a) Low turbulence at a low velocity

(b) Higher turbulence at a higher velocity

(c) You can see examples of turbulent flow in this view of Jupiter’s atmosphere.

The Benefits of Turbulence

In some cases, air turbulence is

beneficial, for example, in the

coach’s whistle mentioned on

page 277. When you blow the

whistle, the bead gets knocked

around and increases the

turbulence, which improves the

quality of the sound and increases

its loudness. Air entering the

mouthpiece of a wind instrument

also needs some turbulence in

order to vibrate easily.

DID YOU KNOW??

turbulent flow fluid flow in which

a disturbance resists the fluid’s

motion; it results when fluids cannot

move smoothly around or through

objects

(a) (b)

Figure 3

The length of each vector represents the magnitude of the fluid velocity at that point.

The longer the arrow, the greater the velocity.

(a) Water in a pipe

(b) Air around a cone

Turbulence in fluids moving in tubes or pipes can be reduced in various

ways. For example, in a sewage system, small amounts of liquid plastic can be

injected into the system. The plastic particles are slippery and mix with the

sewage particles, reducing the liquid’s viscosity and preventing the sewage

from sticking to the sewer pipe and walls. The plastic particles make it easier

for the pumps to transfer the sewage. A similar method can be used to reduce

the turbulence of water ejected from fire hoses, allowing the water-jet to

stream farther. This is especially advantageous for fighting fires in tall

buildings. Liquid plastic can also be added to the bloodstreams of people who

have problems with blood flow. This treatment helps reduce turbulence in the

blood, which reduces the chance that the blood will stop flowing.

Studies of large structures, such as bridges and submarines, can be

conducted using models in a wind tunnel or a water tank. These studies can

then be used to create computer simulations for further analysis. Large

quantities of data on flow patterns can be stored and analyzed. Then

CAREER CONNECTION

Practical nurses have a

background in physiology,

anatomy, and computer

applications. Employment

opportunities exist in a variety

of areas, for example, hospitals,

retirement homes, doctors’

offices, and in industry.

GO www.science.nelson.com

280 Chapter 6 NEL

modifications to the model can be made and tested before construction

begins. An example of a model is shown in Figure 5.

Turbulence is often created by high-rise buildings in urban areas. When

high-speed winds encounter tall buildings, the buildings direct the fast-

moving air from near the roof downward to street level. At street level,

gusts of wind can have devastating effects on pedestrians. To help overcome

this problem, scientists build models of proposed structures and their

surroundings and test the models in a wind tunnel. After analyzing observed

problems, they may make alterations to the lower part of the building or add

wind barriers (trees and shrubs).

For example, when the new city hall in Toronto, Ontario, was designed,

wind tunnel testing of the design revealed that a circular podium between the

two towers was necessary to reduce the wind gusts at street level (Figure 6).

Several years after the structure was built, the city decided to add a jogging

path around the podium, probably without realizing how gusty the winds

would be there. Unfortunately, on one occasion, a gust of wind picked up a

portion of the track and injured a family on the track.

Figure 5

A model of a bridge is tested in the

National Research Council’s

Aerodynamics Laboratory in Ottawa.

Figure 6

Toronto City Hall Practice

Understanding Concepts

1. For each of the following liquids, state whether the viscosity is high or low:

(a) skim milk (c) whipping cream

(b) liquid honey (d) methyl alcohol (antifreeze)

2. Compare the speeds of the top and bottom of the bulge where the viscous

fluid in Figure 7 leaves the beaker. Relate this pattern to laminar flow.

3. Give an example of how turbulence is reduced in each of the following:

(a) medicine

(b) firefighting

(c) construction of high-rise buildings

Applying Inquiry Skills

4. Describe how you would use common household items to safely test

different shapes or structures to determine the turbulence around them in

windy conditions.

bottom of

bulge

top of

bulge

Figure 7

For question 2


• Fluid dynamics is the study of the factors affecting fluid motion.

• Laminar fluid flow is smooth; it results when both the internal resistance

(viscosity) and external resistance (caused by contact with the

surroundings) are low.

• Turbulent flow is a disturbance in fluid flow that causes irregularities.

• Wind tunnel or water tank tests on models of structures, as well as

analysis using computer simulations, help improve the factors that affect

fluid flow, thus reducing unwanted turbulence.

Section 6.1

Making Connections

5. If you were installing small wind turbines at Toronto’s City Hall (shown in

Figure 6, page 280), where would you place them? Explain your answer.

6. Explain why pilots wait a fixed period of time before taking off after another

plane has taken off.

7. Shelters for livestock are built to control snowdrifts. Research the design of

these shelters.

(a) Draw a diagram of the shelter design. On your diagram, show the

predominant wind direction and the snowdrift patterns likely to develop.

(b) What must the livestock owner be aware of when using this type of

shelter?


Section 6.1 Questions


1. Name four liquids of differing viscosity, and arrange

them in a list from lowest to highest viscosity. (Do not

include liquids mentioned so far in this chapter.)

2. Is fluid flow more likely to be laminar in a pipe with a

smooth interior or a corroded interior? Explain your

answer.

3. Is the viscosity of syrup higher at 5 °C or at 55 °C?

Use the particle theory of matter to explain why.


4. Shortly after a snowstorm with high winds, you notice

snowdrifts that display a variety of shapes.

(a) Where would you look for examples of eddies in

the snow?

(b) Where would you look for examples of laminar

flow of the blowing snow?

(c) If possible, create a photographic portfolio of

examples of turbulent and laminar flow in snow,

sand, or dust.

Making Connections

5. Explain why parachute instructors and hot-air balloon

pilots always check the wind conditions before a

flight.

6. Why are compressor stations required at regular

intervals along the cross-Canada natural gas

pipeline? (These stations are located approximately

200 km apart; they do not add any gas to the

pipeline.)

7. Motor oils are made with different viscosities (e.g.,

SAE 20 and SAE 50) and sometimes with a range of

viscosities (e.g., SAE 10W40).

(a) Which oils are used in the summer? in the

winter?

(b) What is the advantage of 10W40 oil?

Laminar and Turbulent FlowSUMMARY

282 Chapter 6 NEL

6.26.2 Streamlining

At speeds that often exceed 50 km/h, speed skaters can encounter air resistance

and turbulence. One way to reduce this resistance and turbulence is to crouch;

another is to wear low-friction clothing (Figure 1).

The forces that act against an object’s motion through a fluid are called

drag. Drag is a form of frictional resistance. The importance of drag forces can

be observed in sports activities and the transportation industry, as well as in

nature. The main technique used to reduce drag is streamlining. Streamlining

is the process of reducing turbulence by altering the design, which includes

shape and surface features, of an object that moves rapidly relative to a fluid.

Streamlined flow is the same as laminar flow.Figure 1

Speed skating is an example of a

sport that requires high-tech designs

to maximize the speed.

drag the forces that act against an

object’s motion through a fluid

streamlining the process

of reducing the turbulence

experienced by an object

moving rapidly relative to

a fluid

TRYTHIS activityThe Effects of AlteringShapes

To study an example of the effect of streamlining, you can use a tea light in a

sand tray and a piece of paper about 15 cm 3 20 cm.

(a) Predict what will happen to the flame of the tea light when air is blown

toward the paper, as illustrated in Figure 2.

(b) Keeping the paper a safe distance from the flame, verify your prediction and

explain what occurs.

Place the tea light in a sand tray before lighting it. Keep the paper

at least 20 cm from the candle.

airflow

streamlinedshape

(b)

airflow

flat piece ofpaper or cardboard

(a)

Figure 2

Testing streamlining

Fish, birds, and many other animals that move quickly in water or air

provide excellent examples of streamlining. In fact, scientists study animal

streamlining closely and try to apply their findings to technology. The

transportation industry in particular devotes much research to trying to

improve streamlining to reduce drag on cars, trucks, motorcycles, trains,

boats, submarines, airplanes, spacecraft, and other vehicles. Although

streamlining often enhances the appearance of a vehicle, its more important

functions are to improve safety in windy or turbulent conditions and reduce

fuel consumption.

Try a computer simulation to help

visualize drag.

LEARNING TIP



Streamlining is an experimental science that relies heavily on large wind

tunnels, water tanks, and computer simulations for its research. Figure 3(a)

shows a series of fans that propel air in a wind tunnel used to research the

streamlining of automobiles. Figure 3(b) shows how a fan directs air along a

tunnel, around two corners, then through a smaller tunnel. As the air moves

into the smaller tunnel it accelerates, reaching speeds up to 100 km/h, and

flows past the test automobile or model. It then returns to the fan to be

recirculated. Researchers view the action from behind an adjacent glass wall

(shown in the diagram) and analyze the turbulence around the model.

Pressure-sensitive beams, electronic sensors, drops of coloured water, small

flags, and plumes of smoke are among the devices used to detect turbulence.

Section 6.2

test chambertest car

control

booth

corner vanes (direct the air around corners)

fan

air speed

increases

air speed

decreases

(a)

(b)

Figure 3

(a) Fans in a wind tunnel. Testing large

objects rather than small models

requires more airflow, which is

provided by a series of large fans.

(b) A typical wind tunnel arrangement

used to analyze the streamlining of

automobiles


Unique Wind Tunnels

Imagine an enclosed tunnel built

for cyclists who simply sit on their

bikes and let the wind in the

tunnel carry them along for several

kilometres. This type of tunnel is

proposed for linking cities in

Holland, a country where 80% of

the population own bikes. Fans

above the tunnel would provide a

tailwind for the cyclists. Of course,

two tunnels would be needed to

allow two-way traffic. If you were

on a bike in such a tunnel, what

posture would give you maximum

speed?

DID YOU KNOW??

284 Chapter 6 NEL

The best streamlining features discovered through research are applied to

the design of cars, like the one illustrated in Figure 4. Similar features are

found on other vehicles.

low-profile

windshield

flush

pillars

concealed

windshield

wipers

low,

tapered

hood

tapered

light

covers

air

dam

flush wheel

openings

flush wheel

openings

aerodynamic mirrors

flush door

handles

tapered

rear

Figure 4

Some streamlining features

on an automobile

5 mm

grooved coating

metal

(a) (b)Figure 5

(a) Sharkskin, showing the

grooves. This patch of skin is

magnified to about 30003.

(b) A thin plastic coating with

three grooves per millimetre

reduces the drag of a metal

surface passing through water.

Designing Better Golf Balls

At one time, golf balls were smooth.

Then it was discovered that a ball

with scratches travels farther than a

smooth ball. Now, the surfaces of

golf balls are dimpled. Experiments

verify that a golfer can drive a

dimpled ball up to 25% farther than

a smooth ball of equal mass! As a

smooth ball travels through the air,

laminar flow produces a high

pressure at the front of the ball and

a low pressure at the rear, creating

a large drag. As a dimpled ball

travels through the air, however,

there is just enough turbulence to

cause the pressure difference

between front and rear to be

minimal, thereby reducing drag.

DID YOU KNOW??


It has long been assumed that perfectly smooth surfaces and hidden joints

are the best means of reducing drag. However, nature has provided a clue that

this is not necessarily so. Sharks are obviously well adapted to moving through

water with reduced drag. A microscopic view of the skin of some species of

fast-moving sharks reveals that the skin has tiny grooves parallel to the flow of

water (Figure 5(a)). This feature reduces the tendency of the water to stick to

the skin, thus reducing drag. Based on this finding, the surfaces of submarines

are now covered with a thin, plastic coating with fine grooves (Figure 5(b)).

This coating reduces drag and increases the submarine’s maximum speed.

Competitive swimmers wear suits with similar technology; the suits reduce

drag even though they are not smooth.

Researchers have found another way to streamline submarines: To reduce

the tendency of water particles to stick to a submarine’s hull, compressed air

is forced out from a thin layer between the hull and its porous outer skin.

Millions of air bubbles then pass along the submarine, preventing sticking and

thus reducing the drag. Some of the discoveries applied to submarines can

also be used for boats, ships, and aircraft.


CAREER CONNECTION

Sailboard designer entrepreneurs

not only understand the principles

of streamlining, but must also be

familiar with material textures as

well as construction and laminating

procedures.


To communicate the results of their research in a simple fashion, scientists

determine a number, called the drag coefficient (symbol Cd), for each vehicle

tested. To understand the range of values of this coefficient, consider the

following two extremes: For a highly streamlined airplane wing, Cd 5 0.050.

For an open parachute, which is designed for maximum drag, Cd 5 1.35.

Most other Cd values lie between these extremes.

During the 1930s, when cars were not streamlined and gasoline was less

expensive, the average Cd for cars was about 0.70. Today, the average value has

dropped to less than 0.40, although some test models have Cd values reported

to be as low as 0.15.

Section 6.2

Practice


1. Imagine you are driving a motorcycle travelling around 60 km/h. You extend

your left arm to signal a turn, and you feel the drag caused by air resistance.

(a) Sketch your hand in the position in which it feels maximum drag.

(b) Sketch your hand in the position in which it experiences maximum

streamlining.

2. Figure 6 shows the test of a scale model of a truck with its trailer attached.

(a) Describe the design features that cause turbulent flow.

(b) What improvements would provide better streamlining?


3. Students are asked to design and test a way to prevent snowdrifts from

piling up in an airport runway. Two designs are shown in Figure 7.

(a) From which direction in the diagrams do the predominant winds come?

(b) How would you test the designs to see how effective they are?

(c) Based on your observations in the Try This Activity titled The Effects of

Altering Shapes, page 282, which design do you think would work

better? Explain your answer.

(d) Sketch another design that you would submit for testing.

Making Connections

4. (a) Name three animals (not named so far) that are streamlined.

(b) Name a human-made technology (not described so far) that is shaped

like each animal you named in (a).

5. Sketch a conifer tree and a deciduous tree.

(a) In the winter, which tree is more streamlined?

(b) Use your sketches to show why a winter storm with heavy wet snow and

high winds would be devastating to a deciduous tree if it kept its leaves

all winter.

Figure 6

This model was tested in the

National Research Council’s wind

tunnel in Ottawa. In this test, smoke

plumes show airflow patterns.

runway

(a)

(b)

runway

Figure 7

(a) Single fence design

(b) Double fence design

Case Study Drag CoefficientsCase Study

286 Chapter 6 NEL

Consider the difference made by the way the rider sits on a bicycle

(Figure 8). When the rider is sitting in an upright position, the drag

coefficient of the bicycle and rider can be as high as 1.1. However, when the

rider is in the crouched, racing position on a streamlined racing bicycle, the Cd

is reduced to about 0.83. The Cd can be further reduced by following another

cyclist closely. The lower air resistance in this case allows a Cd as low as 0.50.

(Refer to Figure 4(a) in section 6.1, page 279, to see how fluid flow behind an

object doubles back. This produces a zone where a closely following object

experiences less air resistance.) Some cycling enthusiasts use a lightweight

shielding, called fairing, which creates a streamlined envelope around cycle

and cyclist and reduces the Cd to an amazing 0.10.

(a)

(b)

(c)

(d)

(e)

Figure 8

(a) Commuter bicycle, upright

position, Cd 5 1.1

(b) Aerodynamic components,

crouched position, Cd 5 0.83

(c) Partial fairing, crouched

position, Cd 5 0.70

(d) Closely following another

bicycle (drafting), Cd 5 0.50

(e) Vector single (three wheels),

complete fairing, Cd 5 0.10

Practice


6. (a) Draw a diagram of an egg so that its drag coefficient is lowest when it is

moving to the right.

(b) At what location in a ski jump run would a competitive ski jumper use

the “egg position?” Why?

7. In which sports, besides speed skating and ski jumping, do the athletes try

to reduce the drag coefficient to a minimum?

8. Figure 9 shows a cyclist in a wind tunnel.

(a) What is revealed by the smoke

streamer seen above the cyclist?

(b) Describe features in the photograph

that reduce drag.

(c) Estimate the cyclist’s drag coefficient

in this case using the values given in

Figure 8.

Making Connections

9. Small cars and motorcycles can get

better gasoline consumption by following

a transport truck relatively closely.

(a) Explain why the gasoline

consumption improves.

(b) Explain the dangers of this practice.

10. Using the Internet or another resource, research drag for Formula 1 racing

cars.

(a) How is the drag coefficient calculated?

(b) Why do the drag coefficients of these cars tend to be so much higher

than the coefficients of passenger cars?


Figure 9

How can you tell that this cyclist is

in a wind tunnel?


Section 6.2

Every Bit Counts

Researchers do everything they

can to reduce drag, even if the

gain is as little as 1% or 2%. For

example, when shaved heads are

compared with heads covered with

low-friction material, they find that

the material provides slightly less

drag. In comparing wheel designs,

researchers find that spoke shape

has a measurable effect. For front

wheels, oval spokes are slightly

better than round and flat spokes

in most situations. However, flat

spokes provide the least drag for

straight-line racing (such as in

triathlon racing). For the rear

wheels, the disk design provides

the least drag.

DID YOU KNOW??StreamliningSUMMARY

• Drag on an object moving in a fluid results from frictional resistance and

turbulence acting on the object.

• Streamlining reduces drag by allowing the fluid to flow smoothly around

an object.

• Applications of streamlining are found in many areas, for example, in

nature and in the fields of transportation and sports.



1. Discuss the types of features used on each of the

following vehicles to reduce drag:

(a) sport motorcycle

(b) large passenger airplane

(c) locomotive

(d) bobsled

(e) racing car

2. Describe three ways in which drag can be reduced in

bicycle racing.


3. Small flags, smoke plumes, and other methods can

be used to study an object in a wind tunnel.

(a) How could you experimentally observe the flow

of air into or out of the air vents in your

classroom?

(b) How might you benefit from knowing about the

airflow in a room?

Making Connections

4. The solar collectors on the International Space Station

are rectangular in shape and are about the size of a

football field. Explain why they do not need to be

streamlined.

5. Describe three instances where drag is intentionally

increased. (You can use Figure 10 as your first

example.)

Figure 10

For question 5


6.46.4Bernoulli’s Principle

The speed of a moving fluid has an effect on the pressure exerted by the

fluid. Consider water flowing under pressure through the pipe illustrated in

Figure 1. As the water flows from the wide section to the narrow section, its

speed increases. This effect is also seen in rivers that flow slowly through

widely spaced banks but speed up when passing through a narrow gorge.

The effect can be verified experimentally, as you discovered in

Investigation 6.3.

The water flow in Figure 1 accelerates as the water molecules travel from

region A into region B. The acceleration is caused by an unbalanced force,

but what is the source of the acceleration? The answer lies in the pressure

difference between the two regions. The pressure (or force per unit area) must

be greater in region A than in region B in order to accelerate the molecules as

they pass into B.

These concepts were analyzed in detail by the Swiss scientist Daniel

Bernoulli (1700–1782). His conclusions became known as Bernoulli’s

principle.

A device used to demonstrate pressure differences in a fluid at various

speeds is shown in Figure 2. The same conclusions can be drawn from

viewing this apparatus. By comparing the liquid level in the three vertical

columns, we can compare the different speeds of the liquid in the different

parts of the horizontal pipe. (In the diagram, the base of each vertical column

is located at the same level so that the effect of gravity need not be

considered.)

There are many applications of Bernoulli’s principle in technology,

transportation, sports, and other fields. As you read about the examples that

follow, think about how they relate to the activities in Investigation 6.3.

water moves

slowlywater moves

quickly

direction

of flow

A B

Figure 1

The speed of water flowing under

pressure in a pipe depends on the

pipe’s diameter.

Bernoulli’s Principle

Where the speed of a fluid is low, the pressure is high. Where the speed of a fluid

is high, the pressure is low.

slow slow

high pressurehigh pressure

low pressure

pressure indicators

fast

direction of flow

Figure 2

The pressure of the water depends on its speed.

292 Chapter 6 NEL

Consider a paint sprayer (Figure 3). Air from a pump moves rapidly across

the top end of a tube, reducing the pressure in the tube. Atmospheric pressure

forces the paint up the tube to be mixed with the flowing air, creating a spray.

The upward force, or lift, on an airplane wing can be explained by applying

Newton’s third law of motion and Bernoulli’s principle. An airplane wing

(Figure 4) is flatter on the bottom and more curved on the top. As the wing

moves forward, air deflects off the bottom of the wing. The wing thus exerts a

downward action force on the air, and the air exerts an upward reaction force

on the wing. Furthermore, the speed of the air near the deflection is less than

the speed of the streamlined flow of air over the wing. Thus, the pressure

above the wing is low, and the pressure below the wing is high. The pressure

difference adds to the lift on the wing.

reduced pressureair

reduced pressure

air

deflection of

air off wing

Figure 3

A paint sprayer

Figure 4

An airplane wing

The Physics of Flight

There is more to airplane flight than

lift, as explained by Newton’s third

law of motion and Bernoulli’s

principle. Control components such

as flaps are also needed. These

components are examples of

hydraulic systems; they aid in

takeoff, landing, changing altitude,

and steering the plane.

DID YOU KNOW??

GO www.science.nelson.comTRYTHIS activity Paper Airplanes

You can learn a lot about lift and control in airplane flight by designing and

testing paper airplanes. With your teacher’s permission, create and safely test a

paper airplane.

(a) Compare your design and flight distance with those of other students.

(b) Compare your flight distance with the maximum distance in public, indoor

competitions, which can be greater than 40 m!

Perform the tests in an empty space, aiming the planes away from

observers.

Turbine blades in jet engines, windmills, fans, and so on, apply Bernoulli’s

principle (Figure 5). The blade shape resembles an airplane wing. As the fan

rotates, the air above the more curved part of each blade moves faster than the

air above the flatter part. Thus, the pressure is higher on the flatter side of the

blade, and air is forced to move through the fan in the direction from higher

pressure to lower pressure.Figure 5

Jet engine fan


Some skis used in ski-jumping competitions have flexible rubber extensions

at their rear. As the skier glides through the air, the air above the skis travels

faster than the air below. The result is a higher pressure below the skis than

above, which creates an upward lift on the skis (Figure 6).

Section 6.4

reduced pressure

Figure 6

Ski-jumping

direction of throw

airair

original direction

of throw

curved path

of ball

airair

(a) (b) (c)

Figure 7

(a) A ball thrown without spin is not deflected.

(b) Air is dragged around the surface of a baseball thrown with a spin. In this case, the spin is

clockwise when viewed from above the ball.

(c) Because the speed around a spinning ball is not equal on both sides, the pressure is not

equal. The ball is deflected in the direction of the lower pressure.

Throwing a curveball is also an application of Bernoulli’s principle. In

Figure 7(a), a baseball is thrown in the direction shown. Relative to the ball,

the air is moving backward. When the ball is thrown with a clockwise spin, as

viewed from above, the air near the ball’s surface on the left is dragged along

with the ball in the opposite direction to the main airflow (Figure 7(b)). To

the left of the moving ball, the speed of the air is slow, so the pressure is high.

The ball is forced to curve to the right, following the path shown in

Figure 7(c). Most of the ball’s curve takes place in the last few metres of its

path. This last-minute curve tricks the batter, which is the object of throwing

a curveball.

Curveball Simulation

You can pitch a curveball online

and see the airflow around the

baseball. You can choose from a

few locations, including Mars!

LEARNING TIP


294 Chapter 6 NEL

TRYTHIS activityMeasuring the Speed ofWater

(a) Design and perform an experiment to measure the linear speed of water as it

leaves a horizontal hose of known diameter, as shown in Figure 9(a). (Hint:

Time the collection of a measured volume of water to determine the volume

flow rate, qv, then divide that value by the area of the nozzle. This will give

you the speed. Recall from section 5.2, page 231, that v = }

q

Av}.

(b) Extend the experiment to find the speed of the water jet when the original

fluid pressure is constant but the area of the end of the nozzle is halved, as

shown in Figure 9(b).

(c) Relate what you observed in this activity to Bernoulli’s principle.

Perform this activity outdoors where spills will not cause damage.

(a)

(b)

gasoline

mixture of air

and gasoline

(to engine)

air

reduced

pressure

Figure 8

A carburetor used in a small engine

A carburetor is a device that applies Bernoulli’s principle to control the

air–fuel mixture fed to small engines, like those used in snow blowers and

lawnmowers. (It serves the same function as fuel injectors in cars.) A

carburetor has a barrel in which airflow controls the amount of gasoline sent

to the engine. Figure 8 shows air flowing by the gasoline intake. The fast-

moving air has reduced pressure, so the gasoline, which is under atmospheric

pressure, is forced into the carburetor. There it mixes with the air and goes to

the engine.

Figure 9

(a) Water flow with a low pressure (b) Water flow with a high pressure


Section 6.4

Practice


1. Explain the following statements in terms of Bernoulli’s principle:

(a) A tarp, which covers a dumpster with no top, bulges outward as the

dumpster is towed along a highway.

(b) A fire in a fireplace burns better when the wind is blowing outside.

2. Apply Bernoulli’s principle to explain what you observed in Investigation 6.3,

page 288, Figures 1, 3, 4, 5, and 6.

3. Animals that live underground, such as prairie dogs and gophers, require air

circulation in their burrows. To provide enough circulation, these creatures

make one burrow entrance higher than the other, as shown in Figure 10.

Explain how this design helps increase air circulation.

4. Devices described in the text that apply Bernoulli’s principle to turbine blades

are used in air. List devices with turbine blades that are used in water.


5. (a) In a storm with extremely high winds, what might happen to windows if

all windows and doors are closed tightly? Explain your answer.

(b) How would you test your answer to (a) in a laboratory situation?

Making Connections

6. (a) A baseball (viewed from above) is thrown as indicated in Figure 11.

If the ball is spinning counterclockwise, determine the approximate

direction of the ball’s path. Use diagrams in your explanation.

(b) Research the spit ball. What is it, and why was it banned from baseball?

7. Research the meanings of the golfing terms “slice” and “hook.” What causes

slices and hooks, and what should a golfer do to prevent them?

8. During winter, airplane components are carefully checked for ice buildup

before takeoff. If necessary, de-icing procedures are used (Figure 12).

Explain the dangers of ice buildup on aircraft.

Extension

9. (a) If you performed the Try This Activity titled Measuring the Speed of

Water, page 294, relate your calculations in (a) and (b) from the activity

to the equation of continuity, illustrated in Figure 13. This equation

states that the volume flow rate remains constant or continuous for a

particular flow. Thus,

q1 5 q2 or A1v1 5 A2v2

where A1 is the cross-sectional area of the first pipe or opening,

v1 is the speed of the water in the first pipe or through the first

opening,

A2 is the cross-sectional area of the second pipe or opening, and

v2 is the speed of the water in the second pipe or through the

second opening.

(equation applies to incompressible fluids with constant density only)

(b) Water in a garden hose with a cross-sectional area of 3.4 cm2 is

travelling at 4.5 m/s. Determine the speed of the water coming from

a nozzle with a cross-sectional area of 1.2 cm2 attached to the hose.

(Apply the equation of continuity.)

A1 v1 v2A2

Figure 10

Figure 11

Figure 12

De-icing an airplane

Figure 13

Where the area is large, the speed

is slow; where the area is small, the

speed is fast.

Answer

9. (b) 13 m/s

296 Chapter 6 NEL

• Bernoulli’s principle states that where the speed of a fluid is low, the

pressure is high, and where the speed of a fluid is high, the pressure is

low. This principle is applied in throwing a curveball and in many other

situations.

Bernoulli’s PrincipleSUMMARY



1. It is unwise to stand close to a fast-moving

subway train. Explain why in terms of

Bernoulli’s principle.

2. Figure 14 shows a device called a Venturi

flowmeter, used to measure the speed of

gas flowing through a tube. Explain how

its design relates to Bernoulli’s principle.

3. Imagine you are able to test your

throwing skills in a large laboratory

with all its air removed. You are given a

table-tennis ball and a Frisbee to throw.

You find that the table-tennis ball goes much farther

than it does in a room with air, but the Frisbee flies

comparatively poorly. Explain these observations.


4. Explain how you would use a manometer as a meter

to measure the flow rate of moving air. (The mano-

meter was described in section 5.3, page 241.)

Making Connections

5. A spoiler on the rear of a car (Figure 15) has a

cross-sectional shape that resembles an airplane

wing.

(a) Does the spoiler shown result in an upward or

downward force on the rear of the moving car?

Explain your answer.

(b) To help keep a car stable when travelling around

curves, which way should the spoiler be

installed? Explain your answer.

(c) Some spoilers are designed just for appearance

(i.e., they provide none of the advantages that

spoilers on racing cars provide). Describe the

disadvantage of having this type of spoiler.

6. Windsurfing boards are designed for maximum

speed and stability in a variety of wind conditions.

However, the problems created by high winds are

different from problems created by low winds.

Research windsurfing boards, and find out how the

vented nose on the board reduces the tendency of

the board to lift off and “tail walk” in high winds.

flow of gas

mercury

Figure 14

A Venturi flowmeter

Figure 15


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