ISO 5167 talks about the measurement of flow rate using a venturimeter. It provides us an expression for the discharge coefficient as a function of Reynolds Number and ratio of diameters of throat and inlet. Can anybody elaborate on how such expressions are obtained? There are many expressions of that kind in Turbulence, with stuff like raising to the power of 0.7 and then multiplying it by 0.0##. It might be the case that formulae of that kind are usually a result of data fitting, but a counterexample is the thickness of the laminar boundary layer due to Blasius. Even if it is due to data fitting, I would be happy if anyone describe the exact procedure for deriving.