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It is quite true that MacMillan gave corrections for both the wall effect and the shear effect. I did not say that MacMillan gave no results for the wall effect but it appears, however, that Patel took notice of a correction which did not include the wall effect.
Thus Patel puts the effective centre of the pitot tube at a distance from the wall y=½Kd and by consideration of a model consisting of a linear sublayer, a transition zone and a fully turbulent region derives a value for K of 1·30 and values for the constants in the logarithmic law profile, A= 5·5 and B=5·45.