By Hermann Schlichting (Deceased), Klaus Gersten

This re-creation of the near-legendary textbook via Schlichting and revised via Gersten provides a finished evaluate of boundary-layer concept and its software to all parts of fluid mechanics, with specific emphasis at the circulation previous our bodies (e.g. airplane aerodynamics). the hot variation positive factors an up to date reference checklist and over a hundred extra adjustments during the booklet, reflecting the most recent advances at the topic.

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8) c where c is the speed of sound, is an important additional dimensionless coefﬁcient. There is great importance for all of theoretical and experimental ﬂuid mechanics attached to the similarity law given by Eq. 6). First of all, the dimensionless coeﬃcients cL , cD and Re are independent of the system of units used. Calculating the functions f1 (Re) and f2 (Re) is, in many cases, impossible theoretically, and we have to turn to experiments to determine 10 1. Some Features of Viscous Flows them.

Fig. 1. Flow along a thin ﬂat plate, after L. Prandtl; O. Tietjens (1931) Fig. 2. 2 Laminar Boundary Layer on a Flat Plate 31 Estimation of the boundary–layer thickness. For laminar plate boundary layers the boundary–layer thickness can easily be estimated as follows: in the boundary layer the inertial forces and the friction forces are in equilibrium. As was explained in Sect. 3, the inertial force per unit volume is equal to u ∂u/∂x. For a plate of length x, ∂u/∂x is proportional to U∞ /x, where U∞ is the velocity of the outer ﬂow.

The dependence of the lift coeﬃcient cL on the the angle of attack α is shown for the same NACA airfoil at the same Reynolds number in Fig. 10. Whereas the limiting solution Re = ∞ leads to vanishing drag (D’Alembert’s paradox), the lift curve shows good approximation to the ﬂow at Re = 3 · 106 . The pressure distribution on an airfoil in a transonic ﬂow is shown in Fig. 11. Both the measurements and the limiting solution show a sudden increase in the pressure on the upper side. This is due to a shock wave which occurs there.