A class of HagenPoiseuille flows
Abstract
The NavierStokes equations for steady laminar pipe flow are solved for cases in which the pipe cross section is symmetrical with respect to the coordinate axes, generalizing the solutions of Hagen and Poiseuille. The conformal mapping of the cross section onto the unit circle is obtained as the solution of a Fredholm integral equation of the second kind; the velocity is determined as the sum of a known particular ansatz and the solution of the Dirichlet problem of the Laplace equation; and an expression for the mass flow is derived. Numerical results for an ellipse with a = 1 and b = 0.5 are found to be in good agreement with the exact solution of Oroveanu (1967).
 Publication:

Revue Roumaine des Sciences Techniques Serie de Mecanique Appliquee
 Pub Date:
 April 1986
 Bibcode:
 1986RvRST..31..115Z
 Keywords:

 Laminar Flow;
 NavierStokes Equation;
 Pipe Flow;
 Steady Flow;
 Conformal Mapping;
 Dirichlet Problem;
 Flow Velocity;
 Fredholm Equations;
 Fluid Mechanics and Heat Transfer