Expression for calculating friction velocity
 

In one of the research papers whose work I want to replicate, a hydraulically smooth turbulent velocity profile is specified at the inlet.

The expressions mentioned contain the term friction velocity in them. But how can I know the value of the friction velocity without any prior computation. And how will I do any prior computation without specifying the velocity inlet?

The paper doesn't provide any information regarding the expression used for calculating the friction velocity. Although I have found the expression for it in some other papers, but they use a term of bed surface roughness in calculating the friction velocity. But in my case the bed is smooth. What value of bed roughness can I use?