The Steady Flow of Viscous Fluid at Low Reynolds Numbers passing obliquely through a Plane Grid made of Equal Parallel Circular Cylinders

Abstract

The flow of a viscous fluid at low Reynolds numbers passing obliquely through a plane grid made of equal, parallel, circular cylinders regularly spaced is discussed on the basis of Oseen's equations of motion. Explicit expressions for the force experienced by a cylinder in the grid, for the direction of the flow at infinity downstream, and for the pressure drop caused by the grid are obtained correct to the first order in the Reynolds number and in the diameter-distance ratio of the grid. Among these the following results may be worth mentioning. The flow is deflected by the grid more or less to the direction of the normal to the grid surface and is always slowed down at infinity downstream. At very small Reynolds numbers, the flow becomes almost perpendicular to the grid even at far upstream and, hence, the component of force tangential to the grid surface vanishes, while the normal component of force to the grid surface becomes equal, in its magnitude, to the drag when the grid is set at right angles to...