<< Chapter < Page Chapter >> Page >
  • Express mathematically the drag force.
  • Discuss the applications of drag force.
  • Define terminal velocity.
  • Determine the terminal velocity given mass.

Another interesting force in everyday life is the force of drag on an object when it is moving in a fluid (either a gas or a liquid). You feel the drag force when you move your hand through water. You might also feel it if you move your hand during a strong wind. The faster you move your hand, the harder it is to move. You feel a smaller drag force when you tilt your hand so only the side goes through the air—you have decreased the area of your hand that faces the direction of motion. Like friction, the drag force    always opposes the motion of an object. Unlike simple friction, the drag force is proportional to some function of the velocity of the object in that fluid. This functionality is complicated and depends upon the shape of the object, its size, its velocity, and the fluid it is in. For most large objects such as bicyclists, cars, and baseballs not moving too slowly, the magnitude of the drag force F D size 12{F rSub { size 8{D} } } {} is found to be proportional to the square of the speed of the object. We can write this relationship mathematically as F D v 2 size 12{F rSub { size 8{D} } α`v rSup { size 8{2} } } {} . When taking into account other factors, this relationship becomes

F D = 1 2 Av 2 , size 12{F rSub { size 8{D} } =0 "." 5Cρ ital "Av" rSup { size 8{2} } } {}

where C size 12{C} {} is the drag coefficient, A size 12{A} {} is the area of the object facing the fluid, and ρ size 12{ρ} {} is the density of the fluid. (Recall that density is mass per unit volume.) This equation can also be written in a more generalized fashion as F D = bv 2 , where b is a constant equivalent to 0 .5 CρA . We have set the exponent for these equations as 2 because, when an object is moving at high velocity through air, the magnitude of the drag force is proportional to the square of the speed. As we shall see in a few pages on fluid dynamics, for small particles moving at low speeds in a fluid, the exponent is equal to 1.

Drag force

Drag force F D size 12{F rSub { size 8{D} } } {} is found to be proportional to the square of the speed of the object. Mathematically

F D v 2 size 12{F rSub { size 8{D} } α`v rSup { size 8{2} } } {}
F D = 1 2 Av 2 , size 12{F rSub { size 8{D} } =0 "." 5Cρ ital "Av" rSup { size 8{2} } } {}

where C size 12{C} {} is the drag coefficient, A size 12{A} {} is the area of the object facing the fluid, and ρ size 12{ρ} {} is the density of the fluid.

Athletes as well as car designers seek to reduce the drag force to lower their race times. (See [link] ). “Aerodynamic” shaping of an automobile can reduce the drag force and so increase a car’s gas mileage.

A two-person team in a bobsled race. The bobsled has an aerodynamic design and smooth runners so it can go as fast as possible.
From racing cars to bobsled racers, aerodynamic shaping is crucial to achieving top speeds. Bobsleds are designed for speed. They are shaped like a bullet with tapered fins. (credit: U.S. Army, via Wikimedia Commons)

The value of the drag coefficient, C size 12{C} {} , is determined empirically, usually with the use of a wind tunnel. (See [link] ).

A model plane is can be seen being tested in a wind tunnel.
NASA researchers test a model plane in a wind tunnel. (credit: NASA/Ames)

The drag coefficient can depend upon velocity, but we will assume that it is a constant here. [link] lists some typical drag coefficients for a variety of objects. Notice that the drag coefficient is a dimensionless quantity. At highway speeds, over 50% of the power of a car is used to overcome air drag. The most fuel-efficient cruising speed is about 70–80 km/h (about 45–50 mi/h). For this reason, during the 1970s oil crisis in the United States, maximum speeds on highways were set at about 90 km/h (55 mi/h).

Questions & Answers

what are the important of economic to accounting students with references
salihu Reply
Economics is important because it helps people understand how a variety of factors work with and against each other to control how resources such as labor and capital get used, and how inflation, supply, demand, interest rates and other factors determine how much you pay for goods and services.
Muhammad
explain the steps taken by the government in developing rural market?
Azeem Reply
contribution of Adam smith in economics
abel Reply
I will join
Dexter
I will join
Patrick
Hey
Fatima
Hey
Amir
Hello
AS
hey
Umarou
I love this book and i need extra Economic book
Amir
Hey
Amir
what's happening here
AS
I love this book and i need extra Economic book
Amir
what is the meaning of function in economics
Effah Reply
Pls, I need more explanation on price Elasticity of Supply
Isaac Reply
Is the degree to the degree of responsiveness of a change in quantity supplied of goods to a change in price
Afran
Discuss the short-term and long-term balance positions of the firm in the monopoly market?
Rabindranath Reply
hey
Soumya
hi
Mitiku
how are you?
Mitiku
can you tell how can i economics honurs(BSC) in reputed college?
Soumya
through hard study and performing well than expected from you
Mitiku
what should i prepare for it?
Soumya
prepare first, in psychologically as well as potentially to sacrifice what's expected from you, when I say this I mean that you have to be ready, for every thing and to accept failure as a good and you need to change them to potential for achievement of ur goals
Mitiku
parna kya hai behencho?
Soumya
Hallo
Rabindranath
Hello, dear what's up?
Mitiku
cool
Momoh
good morning
Isaac
pls, is anyone here from Ghana?
Isaac
Hw s every one please
Afran
Ys please I'm in Ghana
Afran
Hello
OLANIYI
pls anyone from Nigeria
OLANIYI
am a new candidate here, can someone put me 2ru
OLANIYI
hello
OLANIYI
Pls economic A level exam tomorrow pls help me
akinwale
am from Ghana
Jacob
hi
Charles
Pls economic A level exam tomorrow pls help me
akinwale
Hi
Dev
bol Diya discuss ab krega v
Dev
hello Mr. Rabindranath
Dev
what do you want Dimlare
Dev
yes tell me your desire to have it
Dev
to have what?
OLANIYI
Good luck
JOSEPH
I want to know about economic A level tomorrow pls help
Lerato
okay
Umarou
okay
Umarou
what is firms
Anteyi Reply
A firm is a business entity which engages in the production of goods and aimed at making profit.
Avuwada
What is autarky in Economics.
Avuwada
what is choice
Tia Reply
So how is the perfect competition different from others
Rev Reply
what is choice
Tia
please what type of commodity is 1.Beaf 2.Suagr 3.Bread
Alfred Reply
1
Naziru
what is the difference between short run and long run?
Ukpen Reply
It just depends on how far you would like to run!!!🤣🤣🤣
Anna
meaning? You guys need not to be playing here; if you don't know a question, leave it for he that knows.
Ukpen
pls is question from which subject or which course
Ada
Is this not economics?
Ukpen
This place is meant to be for serious educational matters n not playing ground so pls let's make it a serious place.
Docky
Is there an economics expert here?
Docky
Okay and I was being serous
Anna
The short run is a period of time in which the quantity of at least one inputs is fixed...
Anna
that is the answer that I found online and in my text book
Anna
Elacisity
salihu
Meaning of economics
Suraj Reply
It will creates rooms for an effective demands.
Chinedum Reply
different between production and supply
babsnof
Hii
Suraj
hlo
eshita
What is the economic?
Suraj
Economics is a science which study human behavior as a relationship between ends and scarce means which has an alternative use.
Mr
what is supply
babsnof
what is different between demand and supply
Debless Reply
Demand refers to the quantity of products that consumers are willing to purchase at various prices per time while Supply has to do with the quantity of products suppliers are willing to supply at various prices per time. find the difference in between
Saye
Please what are the effects of rationing Effect of black market Effects of hoarding
Atty Reply
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
Practice Key Terms 2

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, College physics: physics of california. OpenStax CNX. Sep 30, 2013 Download for free at http://legacy.cnx.org/content/col11577/1.1
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College physics: physics of california' conversation and receive update notifications?

Ask