Drag coefficient for a flat plate with wholly turbulent boundary layer

The local friction coefficient Q may now be expressed in terms of x by substituting from Eqn (7.81) in Eqn (7.80). Thus

Drag coefficient for a flat plate with wholly turbulent boundary layer

Fig. 7.25 Two-dimensional surface friction drag coefficients for a flat plate. Here Re = plate Reynolds number, i. e. UxL/v, Ret = transition Reynolds number, i. e. U^xt/v-, C> = F/^pU^L] F = skin friction force per surface (unit width)

These expressions are shown plotted in Fig. 7.25 (upper curve). It should be clearly understood that these last two coefficients refer to the case of a flat plate for which the boundary layer is turbulent over the entire streamwise length.

In practice, for Reynolds numbers (Re) up to at least 3 x 105, the boundary layer will be entirely laminar. If the Reynolds number is increased further (by increasing the flow speed) transition to turbulence in the boundary layer may be initiated (depending on free-stream and surface conditions) at the trailing edge, the transition point moving forward with increasing Re (such that Rex at transition remains approximately constant at a specific value, Reu say). However large the value of Re there will inevitably be a short length of boundary layer near the leading edge that will remain laminar to as far back on the plate as the point corresponding to Rex = Ret. Thus, for a large range of practical Reynolds numbers, the boundary – layer flow on the plate will be partly laminar and partly turbulent. The next stage is to investigate the conditions at transition in order to evaluate the overall drag coeffi­cient for the plate with mixed boundary layers.