Flow coefficient and reynolds number

[Tezzador]

Homework Statement

I don't understand why flow coefficient increases with Re and why it becomes independent after a certain Re number for orifice plates and venturi meter!

Homework Equations

The Attempt at a Solution

It seems than when the flow becomes turbulent, the flow coefficient becomes independent of Re but I still don't get it. Is it something to do with friction, velocity or viscosity?

 

[edgepflow]

The dependence of flow coefficient and Reynold's Number is strong when the flow is layared (i.e. laminar) and in the "transition" region between Re of 2000 to 4000. In the laminar region, the Darcy friction factor is determined exactly to be 64 / Re.

For turbulant flow, the dependence of flow coefficient on Reynolds number is still there but decays slowly. Thus, flow coefficients are approximated as constant for large Re.