Deriving the Expression for Discharge Coefficient of a Venturimeter in ISO 5167

[gpavanb]

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.

 

[Navin A S]

The expression for the discharge coefficient of a venturimeter as given in ISO 5167 is based on the work of Prandtl, which was derived using the principles of continuum mechanics. A more detailed description of the derivation and equations can be found in textbooks such as White's Fluid Mechanics. The formula is obtained by assuming that the flow through the venturimeter is turbulent, and then using the Navier-Stokes equations to relate the pressure difference across the venturimeter to the velocity of the flow. The discharge coefficient is then determined by relating the pressure difference to the velocity of the flow at the throat. The Reynolds number and ratio of diameters of the throat and inlet are used to account for the effects of viscosity on the flow. The form of the equation is then determined by fitting numerical or experimental data to the theoretical equations.