5.15. in the turbulent flow of a fluid through a smooth pipe, the frictional force on the fluid is represented in terms of a friction factor f which is positive and less than 0.1. the equation for fis 78-2 log, o(refi/2)-0.8 where re is a constant, termed the reynolds number, which varies with the fluid properties, flow rate, and tube diameter. obtain the approxi- mate value of the friction factor by the search method, and then use the newton-raphson method to converge to the root for re = 104 and 106.