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

Estudio comparativo de flujo de fluido a través de una placa de orificio usando las ecuaciones de Stokes y de Navier-Stokes

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.



Download data is not yet available.

Article Details

References (SEE)

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.

Citado por: