AERODYNAMICS - FLUID MOTION The forms taken by the flow of air past a solid body can in general be classified as belonging to one of two characteristic types. Fig. I is typical of the flow around the majority of bodies not specially shaped to move easily through fluids. The motion, which in this figure is from left to right, is characterized by a dead region a, of small velocity and low pressure, followed by a turbulent wake b. Such a flow exerts a powerful drag upon the body, and much energy will be required to force the body rapidly through the fluid. Fig. 2 is typical of the flow around bodies which move easily through fluids, the dead region a is- absent, whilst the wake has become very small. Flows of this type are generally called streamline flows, and bodies which generate them are called streamline bodies. The turbulent flow, as in fig. 1, is not yet susceptible to precise mathematical analysis, but stream line flows, as in fig. 2, approximate, when the Reynolds number is large, to the flow of a hypothetical inviscid fluid, the analysis of which has been thoroughly studied.
In most aeronautical problems the air at all points far from the body is assumed to be undisturbed, so that its velocity relative to the body and its pressure are uniform ; if these are called V and P respectively, then Bernoulli's equation leads easily to: flow has the remarkable property that, although it may cause variations of pressure which tend to rotate the body, it exerts no resultant force upon the body, no matter what the shape of the body may be. The actual air flow about a streamline body, such as an airship (fig. 2) is a very close approximation to this theo retical flow, and hence the resultant of the pressures upon the surface of the body is almost zero—the small remaining drag, or resistance to motion, being nearly all due to skin friction, i.e., the tangential forces on the surface due to the friction of the air. When the Reynolds number is large, as in aeronautics, the fluid mechanism which exerts these skin friction forces is confined to a very thin sheath, or layer, enveloping the body. This is called the boundary layer; the motions within it are very complex and are known to provide the determining factor which decides whether the flow will be streamline or turbulent. Outside this very thin boundary layer the flow, if streamline, behaves very closely as though the fluid were absolutely inviscid.
A wing may be loosely described as a flattened streamline body. Its cross section in one plane containing the direction of motion has a typical streamline form, as in fig. 3 (see also AEROPLANE) which shows a modern wing section. So long as the incidence, or inclination of this section to the direction of motion is not too great, the flow about the wing will be streamline, the drag will be small and the wing will exert a lift perpendicular to the direction of motion which increases progressively with the incidence. If the incidence becomes too large the flow changes, more or less from which the pressure at any point can be deduced from the velocity at that point, or vice versa. The maximum pressure will thus occur where v is zero, and will have the value of this maximum pressure occurs on the surface of the solid body at the point where the streamlines divide. (See figs. r and 2.) This fact is used to measure the velocity of air in aeronautical experi ments. If a tube, closed at one end and open at the other, is placed with the open end facing the air stream, the pressure within it will have the maximum value If the difference between this pressure and the pressure P of the undisturbed stream can be measured and if the density is known, the velocity V can be determined. The undisturbed, or static pressure P can be obtained within a closed tube placed with its axis parallel to the wind and having small holes punctured in its sides at some dis tance from the closed end. These two tubes are known respec tively as the pitot and static pressure tubes; and together with some form of manometer, for measuring the difference between the pressures within them, they provide the standard speed meas uring unit both in the laboratory and on aeroplanes in flight.
Below the stalling angle the flow, though streamline, differs from that unique flow which could be generated from rest in an in viscid fluid, and approximates more nearly to one of a series of flows, which are possible to the inviscid fluid, but which could not be generated in it without the action of some additional agency. The way in which these flows are generated is still somewhat 613 scure, but it is known that their development is made possible by the slight trace of viscosity in the air, which allows eddies to be shed from the trailing edge of the wing, and that as these eddies are shed the flow about the wing changes until the appropriate flow has developed. When these changes have ceased and the flow has become steady the viscosity plays no further appreciable part in the motion, except in the boundary layer. Theoretically there are, for each wing at each incidence, a series of such flows which could exist steadily in the inviscid fluid but could not be generated in it, and a question arises as to which one of them will occur in any given instance. Unlike the flows which could arise from rest in an inviscid fluid, these flows give theoretically, a lift upon the wing, and if th .! actual lift of the wing can be measured, the particular flow of this series which is occurring can be identi fied as that one which theoretically gives the measured lift. It is thus possible, by merely measuring the total lift of a wing, to calculate, with considerable accuracy, the direction and velocity of the flow at all points in its neighbourhood and from Bernoulli's equation the distribution of pressure over its surface. If the lift cannot be measured, the flow can be approximately identified as that one of the series in which the streams flow smoothly off the trailing edge of the wing without sharp changes of direction. This method of identification is not so accurate as the former.
For a given wing arrangement, the induced drag is proportional to the ratio, weight supported/span ; this ratio is now called the span loading. The induced drag varies in inverse proportion to the air density and the square of the speed. The profile drag, for a given incidence and profile, depends upon the total wing area and varies in direct proportion to the density and the square of the speed. When calculating the drag of an aeroplane wing, it is now normal practice to divide the drag into these two parts and to study them separately. Induced drag can be calcu lated, not only for single wings, but for multiple wings, as in a bi plane, or for wings in the presence of plane boundaries, such as the walls of a wind tunnel or the surface of the earth. Such cal culations are used extensively in all modern laboratories and de sign offices.