STAGNATION POINT

What is stagnation point ?

A point in the field a flow about a body where the fluid particles have zero velocity with respect to the body.

In fluid mechanics a stagnation point is a point in a flow field where the local velocity of the fluid is zero.Stagnation points exist at the surface of objects in the flow field, where the fluid is brought to rest by the object. The Bernoulli's equation shows that the static pressure is highest when the velocity is zero and hence static pressure is at its maximum value at stagnation points. This static pressure is called the stagnation pressure.

Therefore, P(static) + Kinetic Energy = constant

                       P(static) + 0 = constant

Therefore  P(static) = Maximum= stagnation pressure

KUTTA CONDITION :

On a streamlined body fully immersed in a potential flow there are two stagnation points — one near the leading edge and one near the trailing edge. On a body with a sharp point such as the trailing edge of a wing , the kutta condition specifies that a stagnation point is located at that point. The streamline at a stagnation point is perpendicular to the surface of the body.

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BERNOULLIS THEOREM AND ITS APPLICATION

BERNOULLI'S THEOREM :

In a streamline flow of an idle fluid (which is not viscous) the sum of potential energy ( energy due to its position) , pressure energy and kinetic energy ( energy due to its speed ) will remain constant.

As per Bernoulli's theorem ,

                          P.E + Pr.E + K.E = Constant 

 When considering the flow of air the potential energy can be ignored; the statement can therefore be modified ; for all practical aerodynamic purposes, by saying that "the sum of kinetic energy and pressure energy of smooth flow of air is always constant." 

Therefore, Pr.E + K.E = Constant

It means that , the pressure is low where the velocity is high and vice versa to keep the energy constant during flow.

VENTURI TUBE:

One of the most simplest and burning example of Bernoulli's theorem is venturi tube.

"For a flow of air to remain stremlined the volume passing a given point in unit time (the mass flow) must remain constant." If a venturi tube is positioned in such an air stream it obeys the above law. In obeying this law,the flow increase speed while flowing through the throat and in consequence the pressure drops at the throat. This increase or decrease is gradual as the tube slopes. So, at the narrowest portion of the tube the speed of the flow is maximum and the pressure in minimum.

AIR RESISTANCE:

The flat plate produces most drag , the cylinder about 50% drag (due to its shape) and streamlined shape produces only 5%(due to its position).

AEROFOILS:   

The performance of aerofoil is governed by its contour(area of the aerofoil).Generally aerofoils can be divided into three classes:

High lift aerofoils:

Features- 1. Smooth leading edge.

                     2. Lift is the prime factor, not the speed.

                     3. Thickness/chord is more.

                     4. Thickness is almost 15% of the chord. 

General purpose aerofoils: 

Features- 1. Sharp leading edge in respect of high lift aerofoil.

                     2. Lift as well as the speed is the important factor.

                     3. Thickness/chord is less than high lift aerofoil.

                     4.  Thickness is almost 10% of the chord. 

High speed aerofoils: 

Features- 1. Sharp leading edge.

                     2. Speed is the prime factor.

                     3. Thickness/chord is very less.

                     4.  Thickness is almost 7% of the chord.

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ATMOSPHERE

The atmosphere is an ocean of air surrounding the earth and extending upwards for about 500 miles. The flight of all objects using fixed or moving wings to sustain them is confined  to the lower layers of the atmosphere. The ability of the body to fly successfully is therefore closely associated with the atmosphere , its properties and peculiarities.

Composition of air :

Since air is a fluid having a very low internal friction between its molecules, it can be considered within limits as an ideal fluid. Air is a physical mixture of a number of separate gases They are Nitrogen, Oxygen, Argon, Carbon dioxide,Hydrogen,Neon and Helium. For all practical purposes the atmosphere can be regarded as consisting of 21% oxygen and 79% Nitrogen.

Density of air :

The weight of air is usually considered negligible for all practical purposes. It is true that the density of air i.e. mass per unit volume is comparatively low, yet it is the very important property which makes all flight possible. 

Pressure of the atmosphere:

The average pressure at sea level is about 14.7psi/sq.in. The higher we ascend the less will be the the air above and hence less will be the pressure.

Temerature changes in the atmosphere:

An important factor that affecting the atmosphere is the temperature . The air in contact with the earth is heated by conduction and radiation, As a result the density becomes less and the air therefore rises. In rising the pressure drop allows the air to expand and the expansion in turn causes the drop in temperature. Both on account of expansion and because of the greater distance from the heating effect of the earth, the temperature is lower at high altitude than at sea level. the rate of fall  in temperature  is about one degree fahrenheit for every 300 ft. This rate of fall in temperature continues up to a height 36000 ft and then suddenly constant. The portion of the atmosphere where the temperature drops is known as the "TROPOSPHERE" and the portion where the the temperature remain constant is called the "STRATOSPHERE".

Adiabatic lapse rate of temperature in troposphere is 6.5 degree C/Km or 1.98 degree fahrenheit/1000Ft.At standard sea level condition the temperature at sea level is 15 degree C or 59 degree F and the temperature at tropopause , at an average height of  36000 ft is -56.5 degree C or -70 degree F approx.

Humidity and its effect:

Humidity is a conditions of moistures and dampness. The amount of water vapor that the air can holds depends upon on the temperature . Higher the temperature of the air , more the water vapor that it can absorb. Weight of the water vapor is approximately 5/8 of that dry air and hence the air containing water vapour is not as heavy as dry air.  On damp days the density is less than that on the dry days. For this reason the aircraft requires a longer run way for take-off or landing on a damp day than it does on a dry day.

Invertion of temperature :

It often happens that as we begin to climb, the temperature rises instead of falling , this is called an "inversion of temperature'.

The instrument which indicates the speed of an aeroplane is known as "air speed indicator" and the instrument which is used to measure the height of an aeroplane is called "altimeter."

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INTRODUCTION

Theory of flight is simplified aerodynamics which means the study of the aircraft in motion, through the air and the forces that produce and change such motion. It is indeed easy to understand in short " how an aircraft flies "? But to make that flight a success , we should know about the problems that the flight presents and how these problems are getting solved by and by. The man is not contented with only an aircraft that flies , he becomes crazy to fly at more speeds, and higher and higher in altitudes , with utmost safety for himself as well as for the machine . At the present day , the space flights and reaching moon is not a news to us.But to understand the theory behind these flights for a lay man it requires the understanding of the basic theory first. The aim of this notes is to start from the basic principles of flight and to finish with the modern developments on this subjects within the scope of the available data.

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