Fig.J-5
The two examples in Fig.J-2, the flat plate in perpendicular and in parallel position relative to fluid flow, are exceptional cases in which pressure drag or friction drag act practically alone. In most other cases, the two drag components are acting simultaneously - we refer to frictional drag component and pressure drag component of the total drag. Yet it is useful to discriminate between them, because each one behaves differently. The more difficult to evaluate is


- or the frictional component of drag, mainly caused by friction effect in the boundary layer, which forms on the surface of the body. In the laminar flat plate case the drag coefficient is dependent upon the length Reynolds number. The dependence results, according to Fig.J-5, from integration of infinitesimal

Fig.J-6
elementary forces, calculated from the friction formula derived in chapter [I]. Of common interest in applications are flows at higher Reynolds numbers, at which flow and the drag are influenced by transition to turbulence. In contrast to transition occurring simultaneously everywhere in pipe flow, in boundary layer flow there is usually a length of laminar boundary layer - starting from the leading edge - followed by the turbulent boundary layer further downstream. The rather complicated resultant dependence of the drag coefficient in Fig.J-7 is described by the Prandtl-Gebers formula.
Fig.J-7


This is obtained from the surprisingly simple model according to Fig.J-6, based upon the fifth-root approximation to skin friction dependence in the turbulent regime and on
Fig.J-8



addition and subtraction of the boundary layer segments of critical length. This are determined by the valueof the critical Reynolds number. In this case, there is no universal value of the critical Reynolds number, as it depends strongly upon the degree of turbulence in the outer flow (outside the boundary layer). This is characterised by the turbulence level parameter . Dependence between the critical Reynolds number and this parameter evalkuated from experimental data accumulated in various aerodynamic facilities is shown plotted in Fig.J-8. Prandtl in his original publication of the formula, which has shown an excellent agreement with Gebers' experimental data, used value of the constant A = 1 700. This reveals that both Gebers and Blasius (Fig.J-7) used a facility, according to Fig. J-8, with turbulence level slightly more then 1 %. It should be perhaps mentioned that there seems to be a limiting minimum value of critical Reynolds number below which it is not possible to get even with vitually zero turbulence level.


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This is page Nr. J02 from textbook Vaclav TESAR : "BASIC FLUID MECHANICS"
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