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The tubes illustrated above are used only to demonstrate the principle of continuity and Bernoulli’s theorem and are of no practical use in making an aeroplane fly.
But an aerodynamic force to oppose the weight of an aircraft can be generated by using a specially shaped body called an aerofoil.
Basic Aerodynamic Theory 3
Figure 3.3 Typical aerofoil section
The airflow velocity over the top surface of a lifting aerofoil will be greater than that beneath, so the pressure differential that results will produce a force per unit area acting upwards. The larger the surface area, the bigger the force that can be generated.
In the next section we see that the flow over the top of the aerofoil looks very like the tube on the opposite page and the principle of continuity and Bernoulli’s theorem still apply.
Streamlines and the Streamtube
A streamline is the path traced by a particle of air in a steady airflow, and streamlines cannot cross. When streamlines are shown close together it illustrates increased velocity, and vice versa. Diverging streamlines illustrate a decelerating airflow and resultant increasing pressure, and converging streamlines illustrate an accelerating airflow, with resultant decreasing pressure.
Figure 3.4 Streamlines & a streamtube
A streamtube is an imaginary tube made of streamlines. There is no flow into or out of the streamtube through the “walls”, only a flow along the tube. With this concept it is possible to visualize the airflow around an aerofoil being within a tube made up of streamlines.
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Basic AerodynamicTheory |
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Theory Aerodynamic Basic 3
Summary
At flow speeds of less than about M 0.4, pressure changes will not affect air density.
Continuity:
•Air accelerates when the cross-sectional area of a streamline flow is reduced.
•Air decelerates when the cross-sectional area increases again.
Bernoulli:
•If a streamline flow of air accelerates, its kinetic energy will increase and its static pressure will decrease.
•When air decelerates, the kinetic energy will decrease and the static pressure will increase again.
By harnessing the principle of continuity and Bernoulli’s theorem an aerodynamic force can be generated.
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1. |
If the cross-sectional area of an airflow is mechanically reduced: |
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a. |
the velocity of the airflow remains constant and the kinetic energy increases. |
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b. |
the velocity of the airflow remains constant and the mass flow increases. |
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c. |
the mass flow remains constant and the static pressure increases. |
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d. |
the mass flow remains constant and the velocity of the airflow increases. |
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2. |
The statement, Pressure plus Kinetic energy equals constant, refers to: |
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a. |
Bernoulli’s theorem. |
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b. |
the principle of continuity. |
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c. |
Newton’s second law of motion. |
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d. |
the Magnus effect. |
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3. |
If the velocity of an air mass is increased: |
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a. |
the dynamic pressure will decrease and the static pressure will increase. |
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b. |
the static pressure will remain constant and the kinetic energy will increase. |
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c. |
the kinetic energy will increase, the dynamic pressure will increase and the |
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static pressure will decrease. |
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d. |
the mass flow will stay constant, the dynamic pressure will decrease and the |
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static pressure will increase. |
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4. |
When considering a streamlined airflow, which of the following statements is |
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correct? |
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1. |
A resultant decrease in static pressure is indicated by streamlines shown |
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close together. |
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2. |
An increase in velocity is indicated by streamlines shown close together. |
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3. |
Accelerating airflow with a resultant decreasing static pressure is indicated |
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by converging streamlines. |
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4. |
Diverging streamlines indicate decelerating airflow with a resultant |
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increasing static pressure. |
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a. |
2 and 4. |
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b. |
1, 3 and 4. |
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c. |
2, 3 and 4. |
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d. |
1, 2, 3 and 4. |
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5. |
If the pressure on one side of a surface is lower than on the other side: |
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a force per unit area will exist, acting in the direction of the lower pressure. |
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b. |
no force will be generated, other than drag. |
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c. |
a force will be generated, acting in the direction of the higher pressure. |
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d. |
the pressure will leak around the sides of the surface, cancelling out any |
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pressure differential. |
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6. |
When considering a streamtube, which of the following statements is correct? |
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1. |
Different sizes of stream tube are manufactured to match the wingspan of |
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the aircraft to which they will be fitted. |
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2. |
A streamtube is a concept to aid understanding of aerodynamic force |
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generation. |
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3. |
There is no flow into or out of the streamtube through the “walls”, only |
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4. |
A streamtube is an imaginary tube made up of streamlines. |
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flow along the tube. |
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a.1 only.
b.1 and 3.
c.2, 3 and 4.
d.1, 2 and 3.
7.In accordance with the principle of continuity:
1.air accelerates when the cross-sectional area of a streamline flow is reduced.
2.when air accelerates the density of air in a streamline flow is increased.
3.air decelerates when the cross-sectional area of a streamline flow is increased.
4.changes in cross-sectional area of a streamline flow will affect the air velocity.
Which of the preceding statements are true?
a.1, 2, 3 and 4.
b.1 and 4.
c.3 and 4.
d.1, 3 and 4.
8.In accordance with Bernoulli’s theorem:
1.if a streamline flow of air decelerates, its kinetic energy will decrease and the static pressure will increase.
2.if a streamline flow of air accelerates, its kinetic energy will increase and the static pressure will decrease.
3.if a streamline flow of air is accelerated, the dynamic pressure will increase and the static pressure will increase.
4.if a streamline flow of air is decelerated, its dynamic pressure will decrease and the static pressure will increase.
The combination of correct statements is:
a.1, 2, 3 and 4.
b.3 only.
c.1, 2 and 4.
d.3 and 4.
9.The statement, “Energy and mass can neither be created nor destroyed, only changed from one form to another”, refers to:
a.Bernoulli’s theorem.
b.the equation of kinetic energy.
c.the principle of continuity.
d.Bernoulli’s principle of continuity.
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Questions 3
Questions 3
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