Comparative study of fluid flow across orifice plate using Stokes and Navier-Stokes equations

Main Article Content


Miryam Lucía Guerra-Mazo
María Vilma García-Buitrago
Elizabeth Rodríguez-Acevedo


This paper presents the results of a comparison between Stokes and Navier-Stokes equations, in order to simulate the flow of liquid water at atmosferic conditions, through a concentric orifice plate. From experimental data taken from the fluids bank, the simulations of both equations were evaluated, using free software Freefem++CS, which is based on the finite elements method. The evaluated variables are velocity and pression in a time interval. When analyzing the results obtained with the simulations and comparing them with the experimental data, it was found that the Navier-Stokes equations represent better the system, than the Stokes equation.


Article Details


All articles included in the Revista Facultad de Ingeniería are published under the Creative Commons (BY) license.

Authors must complete, sign, and submit the Review and Publication Authorization Form of the manuscript provided by the Journal; this form should contain all the originality and copyright information of the manuscript.

The authors who publish in this Journal accept the following conditions:

a. The authors retain the copyright and transfer the right of the first publication to the journal, with the work registered under the Creative Commons attribution license, which allows third parties to use what is published as long as they mention the authorship of the work and the first publication in this Journal.

b. Authors can make other independent and additional contractual agreements for the non-exclusive distribution of the version of the article published in this journal (eg, include it in an institutional repository or publish it in a book) provided they clearly indicate that the work It was first published in this Journal.

c. Authors are allowed and recommended to publish their work on the Internet (for example on institutional or personal pages) before and during the process.
review and publication, as it can lead to productive exchanges and a greater and faster dissemination of published work.

d. The Journal authorizes the total or partial reproduction of the content of the publication, as long as the source is cited, that is, the name of the Journal, name of the author (s), year, volume, publication number and pages of the article.

e. The ideas and statements issued by the authors are their responsibility and in no case bind the Journal.


J. M. Cimbala and Y. A. Cengel, “Flujo en Tuberías”, Mecánica de Fluidos: Fundamentos y Aplicaciones. V.C. Olguin. Mexico: McGraw Hill, pp. 321-398, 2006.

R. L. Mott, “Medición del Flujo”, Mecánica de Fluidos. J. E. Brito. Mexico: Pearson Education, pp. 473-499, 2006.

B. Manshoor, F. C. Nicolleau and S. B. Beck, “The fractal flow conditioner for orifIce plate flow meters”, Flow Measurement and Instrumentation, vol. 22 (3), pp. 208-214, Jun. 2011. DOI:

J. Banks, J. S. Carson, B. L. Nelson and D. M. Nicol, Discrete-event system simulation. USA: Prentice Hall, 2009.

F. Hecht, O. Piro and A. Le Hyaric, “Freefem++,” 2014. [Online]. Disponible:

R. Lewandowski, “The mathematical analysis of the coupling of a turbulent kinetic energy equation to the Navier-Stokes equation with an eddy viscosity”, Nonlinear Analysis, Theory, Methods & Applications, vol. 28 (2), pp. 393-417, Jan. 1997. DOI:

M. M. Rhaman and K. M. Helal, “Numerical Simulations of unsteady Navier-Stokes Equations for incompressionable newtonian fluid using FreeFem++ based on Finite Element Method”, Annals of Pure and Applied Mathematics, vol. 6 (1), pp. 70-84, May. 2014.

C. L. Felter, J. H. Walther and C. Henriksen, “Moving least squares simulation of free surface flows”, Computers & Fluids, vol. 91, pp. 47-56, Mar. 2014. DOI:

Z. Li, K. Ito and M. C. Lai, “An augmented approach for Stokes equations with a discontinuous viscosity and singular forces”, Computers & Fluids, vol. 36 (3), pp. 622-635, Mar. 2007. DOI:

T. Geenen, M. ur Rehman, S. P. MacLachlan et al., “Scalable robust solvers for unstructured FE geodynamic modeling applications: Solving the Stokes equation for models with large localized viscosity contrasts”, Geochemistry, Geophysics, Geosystems. An Electronical Journal of the earth sciences, vol. 10 (9), pp. 1-12, Sep. 2009.

A. Mojtabi and M. O. Deville, “One-dimensional linear advection–diffusion equation: Analytical and finite element solutions”, Computers & Fluids, vol. 107, pp. 189-195, Jan. 2015. DOI:

J. Volker, K. Kaiser and J. Novo, “Finite Element Methods for the Incompressible Stokes Equations with Variable Viscosity”, Zeitschrift fûr Angewandte Mathematik und Mechanik, vol. 96 (2), pp. 205-216, 2016. DOI:

P. Gómez-Palacio, “Solución de la ecuación de Stokes”, Revista Universidad EAFIT, vol. 46, pp. 90-102, 2010.

E. Engineering, Análisis y Simulación de la dinámica de fluidos computacionales-CFD a fluidos internos [Online]. Disponible:

C. M. Institute, Navier-Stokes equation [Online]. Disponible:

J. L. Vázquez, Fundamentos matemáticos de la mecánica de fluidos. Madrid: Universidad Autónoma de Madrid, 2003.

P. K. Kundu, I. M. Cohen and D. R. Dowling, Fluids Mechanics. Elsevier, 2012.


Download data is not yet available.