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Reference Temperature Method for Turbulent Flow
The reference temperature method discussed in Section 18.4 for laminar boundary layers can be applied to turbulent boundary layers as well. With the reference temperature T* given by Equation (18.53), the incompressible turbulent flat plate result for C f given by Equation (19.2) can be modified for compressible turbulent flow as
0.074 (Re*)1/5
and we will assume that the reference temperature for this case is the same as given in Example
18.2. Hence, from Example 18.2, we have
Re* = 3.754 x 107 and p* = 0.574 kg/m3
From Equation (19.3) we have
_ 0.074 0.074
f ~ (Rer*)‘/5 (3.754 x 107)1’5 “ 226 X 10
From Equation (19.4),
Df = p*u)SC*f = |(0.574)( 1000)2(40)(2.26 x КГ3) = 25,945 N
Comparing this answer with that obtained in Example 19.1ft, we find a 27 percent discrepancy between the two methods of calculations. This is not surprising. It simply points out the great uncertainty in making calculations of turbulent skin friction.
