Question: The following table is an actual velocity profile measured through a turbulent boundary layer on a rough surface made up of 1.27mm balls packed in a dense, regular pattern. There is no pressure
gradient or transpiration. The fluid is air at 1 atm and 19°C; and u∞ = 39.7 m/s, = 0.376 cm, = 9974, cf/2 = 0.00243. The distance y is measured from the plane of the tops of the balls. The objective of this problem is to analyze these data in the framework of the rough-surface theory developed in the text. What is the apparent value of ks? Of Res? What is the roughness regime? What is the apparent value of K? How does the wake compare with that of a smooth surface? Do the data support the theory? The use of the plane of the tops of the balls as the origin for y is purely arbitrary. Feel free to move the origin if this will provide a more coherent theory.