By Maurice Holt

Easy advancements in Fluid Dynamics

summary: simple advancements in Fluid Dynamics

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Additional info for Basic Developments in Fluid Dynamics

Example text

The computation becomes somewhat more lengthy for small values of incident angle a and cavitation number o as the singularity at the point t0 becomes closer to the path of integration. 2), which is certainly satisfactory for practical pur­ poses. In any case, if a higher accuracy should be needed, one can always shift back to the first iteration method. 39) where the angle y is given by Eq. 8a). 3) becomes oM) = i0(£) = i cos 1 1, + 2 f1 s i , (l-e)mP(T)dr T2 - 2£T + 1 ( - ! 41) 48 T. 42b) where from Eq.

SlN, 8s j , . . 37) where the explicit expressions for dyjdy^ can be readily obtained by differen­ tiation of Eqs. 12) and sk = sk. 37) provided the Jacobian S(7i, • • •, y2N+ i ) / % i ' , • • • ? 38) From this it also follows that the relations 3y1 — . . = Sy2N+\ = 0 imply Sy{> = . . = 3y2N+ i = 0, and vice versa. This is the property of infinitesimal uniqueness. INVISCID CAVITY AND WAKE FLOWS 37 The proof of infinitesimal uniqueness is seen to be equivalent to the following variational problem.

0 V. 0 FIG. 16. Asymptotic width of the far wake. 6 Examples; Comparison with Experiments To exhibit some of the important physical effects of cavity flows past curved bodies, we consider the following typical examples. 1 Flat Plate with a Flap. As the simplest case of a polygonal obstacle in an asymmetrical flow, we treat a flat plate AP lying along the x axis, with an extended flap PB held at a flap angle sn with the x axis, positive in the clockwise sense (see Fig. 17). 45) where t = x is the image of point P.