A New Integral Method for Analyzing the Turbulent Boundary Layer With Arbitrary Pressure Gradient

A. S. Mujumdar. Professor White is to be complimented for developing an ingenious slide-rule technique for routine boundary layer calculations. I would like to make the following observations in connection with his comments on the conventional integral techniques. First of all, his technique is essentially a Von Karman integral technique as pointed out by Mr. P. S. Granville in his discussion of the paper. Secondly, the author feels tha t Professor White is overly critical of existing computational techniques based on the Karman method. The empiricism contained in the Karman method is no greater than that contained in Professor White's method. As long as the number of empirical inputs is not inconveniently large, the accuracy of the method does not depend on the number of empirical inputs but on their validity or otherwise. A single empiricism far from reality would clearly lead to wrong results. I t is the author's opinion that the shape factor is still a good criterion for determining separation. Although there can be a large variation in the shape factor, H, near separation, this is not a serious drawback of the Karman method since H increases rapidly around separation. An analogous situation is encountered when the skin friction coefficient, cf) is chosen as the pertinent parameter. I t may be seen from Figs. 4 and 5 of Professor White's paper that cf drops rather abruptly around separation. Since the measurement of skin friction beomes progressively inaccurate as Cf becomes small, use of cf as a criterion for separation would involve about the same degree of uncertainty as the shape factor.