Problem 1 In a lab experiment, it has been found that the velocity profile in a pipe where the flow is turbulent (this will be defined in the next module) is: V = Vmax (1-7)" و where Vmax is the maximum velocity in the centerline of the pipe; r is the radial distance from the pipe centroid; ro is the radius; and n is an exponent that depends on the flow condition and that varies between 1/6 to 1/8. Derive a formula for the kinetic energy correction coefficient a for the given velocity profile. What is a if n = 1/6?

Fig: 1