By Ludwig Prandtl

The document offers, really in short, partially one an advent to hydrodynamics that's designed to provide those that haven't but been actively involved in this technology this type of snatch of the theoretical underlying rules that they could stick with the next advancements. partially there follows a separate dialogue of different inquiries to be thought of, within which the speculation of aerofoils claims the best component of the gap. The final half is dedicated to the appliance of the aerofoil conception to screw propellers. A desk giving an important amounts is on the finish of the document. a brief reference record of the literature at the topic and in addition a desk of contents are added.

Translated from German via the workers of the nationwide Advisory Committee for Aeronautics.

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**Extra resources for Applications of modern hydrodynamics to aeronautics**

**Sample text**

By the introduction of the factor Vt, c, and c 2 are made pure numbers. The numerical value of c l , which is the more important, can be expressed, if c a . is the lift coefficient for the infinitely long wing at the angle of attack a', by the relation 1 dc,^ In fact _A Cam p /y__ Fq rVl _2r _2 (c lt. ) 1 For a flat-plate theory proves that c1 = 7r, for curved wings it has a slightly greater value. ,write dx =f(x) and therefore r= f X f(x)dx 0 we obtain after a simple calculation the integral equation f X f(x)dx+ L' fx :x) x = Vt (c,a+c2) =const.

According to the results of section 22, the drag then is IN! r dx PI(,. —Velocity at a point A off the P o zwi2dx or, if the value of w1z as given by equation (50) is substituted, fblfb2 W1z= p 47r r,rz COS 2 a zdx,dx2 (51 lifting line, but in the transverse The double integral, as one sees, is perfectly symmetrical in the quantities assoplanA, due to the ciated with both wings 1 and 2. We conclude from this that the drag which vortex system. wing '1 experiences owing to the presence of wing 2 is of the same amount as the drag calculated here, that, therefore, Wiz = T21- 37 REPORT NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS.

The lifting line, if we do not take into account the change in shape of the vortex ribbon. We therefore have here, neglecting this change in shape, an illustration of a two-dimensional fluid flow (uniplanar flow), for which the vertical velocity components at the point where the wing is reached are specified. For the simple case that the vertical velocity w is constant, as was found to be true for the elliptical lift distribution, the shape of the flow that arises has been known for a long time.