Lesson 3: Properties of Fluids
Section 3 - Air in Motion
The invisibility of air can make it difficult to understand its motion. We can touch and set a watch, break open a bottle of champagne, or weigh fruit in a market, but although we can feel the wind and see its effects, we can rarely actually see it at work in nature.
However, there are ways to show motion of air. Smoke streams can be introduced to indicate the flow direction and whether it is smooth or disturbed.
Shafts of light in a wind tunnel can pick out the wake of a wing or body. We have modern technology to determine the flow of air.
Flow visualization can help explain some of the phenomena involved in addition to instruments which measure the speed and direction of the steady air current, the pressure, turbulence, and the temperature. At high speeds, there are also instruments to explain the flow of electrified particles. At extremely high speeds, very high altitudes or very high temperatures, it is sometimes necessary to measure the magnetic field of the flow.
STREAMLINES
This introduces the concept of streamlines. In a steady airflow, you can draw an imaginary smooth line which indicates the direction of flow at all points along it. This is referred to as a streamline.
Since the flow direction is parallel to a streamline, no air crosses it. This leads to the idea of a streamtube with walls or streamlines which confine a known current of air.
If the velocity increases along a streamtube as it passes around an obstruction, the streamline changes its cross-sectional area. If the flow becomes unsteady, the streamlines indicated by the flow visualization methods will disappear. The term “streamlining” refers to the shaping of bodies to promote a smooth airflow which has the low air-resistance required for moving bodies.
Although we know air moves freely, it does behave according to some direct rules and there are several patterns of flow which occur very frequently.
Vision air passing around an obstacle such as mountain or hill, or a projectile traveling rapidly through the air.
PATTERNS OF AIRFLOW
There are patterns of airflow that may be in effect.
These include:
- A main, streamlined flow.
- A vortex or large circulatory flow.
- A boundary layer with rapid changes of fluid speed near to surfaces.
- A wake or ragged disturbed flow left downstream of an object.
- Shock waves, which occur if the flow exceeds the speed of sound.
FLUID ELEMENTS
Fluid elements can have three kinds of motion:
- Translation – here, elements move but do not change their direction.
- Rotation – elements rotate about their centers.
- Distortion – the shape of elements is altered.
MAIN FLOW
Main flow is the simplest type of continuum flow. It has constant density and no particle rotation. This is very close to moving air, provided that the speed is less than the speed of sound and does not go too close to the surface of a body.
Its pattern can be indicated by streamlines, and velocity, V, and pressure, p, changes are given by Bernoulli’s equation:
ρ + ½ ρV*2 = constant, H (the total Head)
where p is the constant density and ½ ρV*2 is called the dynamic pressure, also referred to as q.
In this case, as the velocity increases, the pressure decreases. The reverse of this is also true. This is basically what happens with a lifting aeroplane wing. The air flowing over the curved top surface is forced to speed up, giving a reduced pressure, while the flow deflecting below is slightly slowed, giving a higher pressure. Bernoulli’s equation is important in enabling the air pressure on a body to be calculated once the air velocity near the surface is known.
For circulation, if an ideal flow is created around, not past, a cylinder, so that the streamlines are all concentric circles, the motion is defined as a circulation.
This is measured as the integral of the velocity taken around a curve through the air enclosing the cylinder and is represented by:
K = 2πV
Where V is the tangential velocity to the radius r. This is constant throughout the area in an ideal flow. Therefore, the velocity is inversely proportional to the radius.
A vortex is a portion of air in a rotational motion. This type of motion occurs in a spinning golf ball. A vortex may be free and persist in the air by itself. A tornado is a good example of this, as is a vortex shed from an airplane wing.
In a boundary layer, the air in motion divides itself very neatly into the main flow. The actual “boundary layer” is confined to a region very close to a surface.
Air particles very close to a solid surface encounter molecular forces and stick to it so that the air speed at the surface is zero. The air speed increases rapidly away from this adhered layer until the main flow is reached.
A wake is the disturbed flow downstream of an object. If the body is streamlined and the boundary layer is laminar, the wake will be thin.
If a pressure disturbance moves through the air breaking the speed of sound, roughly 740 mph equivalent to a Mach, a shock wave is created. It arises because when air is compressed, its temperature rises. Since the velocity of sound increases with temperature, strong waves travel faster than weaker ones and overtake them.
Bibiliography
Aerodynamics and G. Forces. www.voodoo.cz/falcon/agf.html.
Allen, John E. Aerodynamics: A Space Age Survey. New York: Harper & Row, 1963.
Wegener, Peter P. What Makes Airplanes Fly? New York: Springer-Verlag, 1991.
