10-98 For the linear approximation of Prob. 10-97, use the definition of local skin friction coefficient and theKármán integral equation to generate an expression for 8/x. Compare your result to the Blasius expression for 8/x.(Note: You will need the results of Prob. 10-97 to do this problem.) 10-97 The streamwise velocity component of a steady, incompressible, laminar, flat plate boundary layer of boundary layerthickness 8 is approximated by the simple linear expression, u = Uy/8 for y<8, and u = U for y> 8 (Fig. P10-97).Generate expressions for displacement thickness and momentum thickness as functions of 8, based on this linear approximation.Compare the approximate values of 8/8 and 8/8 to the values of 8*/8 and 9/8 obtained from the Blasius solution.Answers: 0.500, 0.167000) = V(10-97 provided as context for 10-98 only)

Given:Write the equation for skin friction coefficient using Karman's integral equation for plate boundary layer as shown:Here, momentum thickness is and x is the location on the flat plate.Write the expression for the momentum thickness:Substitute for and U for in equation (2):Write the equation for local skin friction coefficient for a laminar boundary layer:Substitute all the values in equation (1):The Blasius solution for boundary layer thickness for a laminar flow over a flat plate is: