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Download Applications of modern hydrodynamics to aeronautics by Ludwig Prandtl PDF

By Ludwig Prandtl

The file supplies, fairly in brief, partly one an creation to hydrodynamics that is designed to offer those that haven't but been actively desirous about this technology this type of seize of the theoretical underlying ideas that they could persist with the following advancements. partially there follows a separate dialogue of different inquiries to be thought of, during which the speculation of aerofoils claims the best component to the distance. The final half is dedicated to the applying of the aerofoil idea to screw propellers. A desk giving crucial amounts is on the finish of the document. a quick reference record of the literature at the topic and in addition a desk of contents are added.

Translated from German by means of the employees of the nationwide Advisory Committee for Aeronautics.

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Let us remember that, by the overcoming of the drag, work is done, and that in a nonviscous fluid, such as we everywhere assume, this work can not vanish. Its equivalent is, in fact, the kinetic energy that remains behind in the vortex motions in the rear of the lifting system. This energy depends only upon the character of these 'vortices, not upon the way in which they are produced. If we neglect, as we have throughout, any change in shape of the vortex system, then, in fact, the staggering of the separate parts of the lifting system can not have any influence upon the total drag.

This effective angle of attack, according to our earlier considerations, is the angle of attack of the chord with reference to the resultant air current. It is therefore a'= a — 4,. If we substitute tan 0 = V for 0, and introduce in equation (39) again the lift coefficient, instead of using the lift, we obtain for the comparison of two wings, expressing the fact that the effective angle of attack s to be the same for two equal lift coefficients, the relation i c^ F, = C a F2 1 a1-7 F2 a2—Z L2, V which leads to the transformation formula Ca Flo.

Since in this, for the end r of the impulse phenomenon, 4^ = f (p,, — p) dt, P = const. , which, O indeed, was the original boundary condition for the free jet. 31. The conditions stated in the preceding section can be secured most easily for a jet, or tube, of a circular cross section. In this case the added motion is obtained very simply by assuming for every vortex flowing off an equally strong one outside the circle, at the point outside corresponding to the one inside according to the reciprocal radii.

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