Aerodynamics

Lecture 2

Chapter 2

Review from last class

• Balloons

• Cayley

• Wright Brothers

• Aerodynamics

• Da Vinci

• Montgolifer

LIFT

What is lift?

What opposes Lift?

• Gravity– The force that opposes lift is the pull of

gravity.– Gravity acts on all bodies on or near the

surface of the Earth.– The resulting force that gravity causes on

some mass is referred to as weight.

The Force called Lift

• In order to rise into the air, a force must be created that is equal to or greater than the weight acting in the opposite direction.

Back to the Balloon

– In the balloon example last class, the lift force was caused by an imbalance between pressure over the surface of the balloon and the weight of the balloon.

– With the balloon and its contents being lighter than the surrounding air, the imbalanced resulted in a net force in the upward direction.

Airplanes

• Airplanes are heavier than the air that they displace and must rely on other means to develop lift.

– What device is employed to develop lift on an airplane?

The Physics of Lift

The principle of lift discovered by a Swiss mathematician is?????

Daniel Bernoulli

• He never heard of an airplane.

• His work had nothing to do with flight.

• He was trying to explain mathematically, the variation in pressure exerted by a moving mass of fluid ( a stream of water)

Bernoulli’s Principle

• His equation says that the pressure plus ½ times the density times the velocity squared must always equal a constant value.

• Pressure + ½ x density x velocity squared = constant.

In other words

• Static pressure + dynamic pressure = constant.– Static means still (last lecture)– Static pressure is used to describe the pressure

exerted by a static, or still, air mass.– Dynamic pressure is the pressure that would

be exerted if the fluid were brought to rest.

Bernoulli’s Point

• That fluid only contains so much pressure.

• If a fluid is a rest, all of the pressure is static pressure,

• however, if the fluid is in motion, then some static pressure is traded off for dynamic pressure.

Bernoulli’s principle

• As the air flow speeds up, there is an increase in dynamic pressure,

• the static pressure must be reduced because the sum of the two pressures must be the same.

Example

• Static pressure + dynamic pressure= total constant.

• 6+6 =12– Now suppose the fluid speeded up.– SP DP= TC– 4+ 8 = 12– Dynamic pressure increased so static pressure

must decrease so the end result is constant (p.14).

Continuity

• The law of continuity or continuity equation called the Law of Conservation of Matter.

• Applied to a moving stream,it states that in a moving stream of fluid, the density times the cross sectional area of the flow times the velocity must be a constant.– Q x A V= constant.

Venturi Tube

• A venturi tube is a good example for Bernoulli’s principle because it has a restricted area of flow.

– Think about canoeing down a river. When is the water static?

– When is the water moving rapidly?

Venturi

• A flow coming into a venturi tube will have an increased velocity, due to a reduced area, by the continuity law.

– If the velocity is increased, the pressure will be decreased by Bernoulli’s principle.

• A tube connected at the reduced area will create a suction. (principle behind gyro instruments, p. 16)

How airfoils create lift

Ahead of the airfoil, the air has a uniform velocity associated with it across the entire stream.

• When it reaches the airfoil, it must divide, with part of the stream flowing over the top surface and part over the bottom surface.

How an airfoil creates lift

• At this point the cross-sectional area of the stream is reduced by the amount of space the airfoil takes.

– According the the law of continuity, this reduction must cause an increase in velocity.

– The end result is a greater lowering of pressure on the top surface than the bottom, even though the pressure is lowered somewhat over the bottom surface.

Next Time

• We will begin on airfoil terminology.

• If you have not read all of chapter 2 please do so for next time.

Quiz on Lecture 2

Please take out a sheet of paper.

Include today’s date and your name.

Quiz on Lecture 2

• Please explain Bernoulli’s principle.

• What is the difference in static pressure and dynamic pressure?

• Explain the Law of Continuity.

• How can a venturi tube create lowered pressure?

• How does an airfoil create lift?