Please show step by step works Engineering Fluid Mechanics

Please show step by step works ( Engineering Fluid Mechanics )

Above what Reynolds number is the flow through a 3 m diameter riveted steel pipe (k_s = 3 mm) independent of the viscosity of the fluid?

Solution

Relative roughness = Absolute roughness / Pipe dia

= 3*10^-3 / 3

= 0.001

From Moody diagram, for rel roughness = 0.001, we notice that it intersects the Transition zone curve at Re = 1.5*10⁶

Hence, flow becomes independednt of viscosity at Re > 1.5*10⁶