Electronic Journal of Differential Equations, Vol. 2024 (2024), No. 63, pp. 1-17.

Title: Curved-pipe flow with boundary conditions involving Bernoulli pressure

Authors: Tvrtko Doresic (Univ. of Zagreb, Croatia)
         Igor Pazanin (Univ. of Zagreb, Croatia)

Abstract: 
In this article, we study the steady-state flow of the incompressible 
viscous fluid through a thin distorted pipe with an arbitrary central 
curve. We prescribe the inflow and outflow boundary conditions involving 
the Bernoulli pressure with a given pressure drop. 
Using the multiscale expansion technique with respect to the pipe's 
thickness, we construct the higher-order asymptotic approximation of 
the flow given by the explicit formulae for the velocity and pressure. 
We also perform a detailed error analysis justifying the usage of the 
proposed solution and indicating its order of accuracy.

Submitted May 15, 2024. Published October 22, 2024.
Math Subject Classifications: 35C20, 35Q35, 76M45.
Key Words: Newtonian fluid; Bernoulli pressure boundary condition; curved pipe; asymptotic analysis