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, ![1070_t.png](https://secure.tutorsglobe.com/CMSImages/1070_t.png)
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).