The Moody Chart is often used to estimate friction factor as a function of Re for the purpose of calculating pressure drop as to fully developed fluid flowing in a circular pipe. Why could two fluid flows be similar in flow pattern with the same Re ?

 

The reason can be derived from the Navier-Stokes equation specifically applying the conditions of constant viscosity and incompressible Newtonian fluid, which is shown as follows

(Ref. : Hinze, J.O. " Turbulence, 2nd edition", Equations (1-4)-(1-16), pp 17-20 (1975).