Question: Flow in a long straight pipe is turbulent. The average velocity, v, at a distance, y, from the pipe wall depends on roughness height of the pipe, k, the pipe diameter, D, the kinematic viscosity v(v = μ/ρ), the mass density of the flowing fluid, p, and the shear stress at the pipe wall, 
a. Write down the functional relation for these variables.
b. Show the dimensional matrix for these variables in an M, L, t system
c. If the functional relation in a is reduced to a complete set of dimensionless products, how many products are there?
d. Determine the dimensionless products using the systematic algorithm (use v, y, p as the subset of Qs).