Bernoulli correction to viscous losses. Radial flow between two parallel discs

TL;DR

This paper introduces a first-order correction method for viscous pressure losses in radial flow between parallel discs, combining analytical, numerical, and experimental approaches for validation.

Contribution

It presents a novel first-order correction technique for viscous losses using the velocity profile from the zero-density limit, validated through simulations and experiments.

Findings

Analytical solution matches numerical simulations.

Experimental results agree with the theoretical correction.

First-order approximation effectively predicts pressure drops.

Abstract

For a massless fluid (density = 0), the steady flow along a duct is governed exclusively by viscous losses. In this paper, we show that the velocity profile obtained in this limit can be used to calculate the pressure drop up to the first order in density. This method has been applied to the particular case of a duct, defined by two plane-parallel discs. For this case, the first-order approximation results in a simple analytical solution which has been favorably checked against numerical simulations. Finally, an experiment has been carried out with water flowing between the discs. The experimental results show good agreement with the approximate solution.