Fluid flow in regions bounded by porous surfaces

Abstract

The aerodynamic effects of sucking away boundary layers or blowing air into them through a porous surface have been studied on the assumption that the rate of discharge through the pores is under the control of the experimenter. When all the fluid reaches the field of flow through the pores the pressure at any point in the field depends on the distribution over the porous surface of the flow through it, and the through-flow at any point of it depends on the pressure there. To describe flow of this kind mathematically is difficult and no case seems to have been discussed before. In § 1 a particular case, that of flow through a wedge, cylinder or cone made of a material the resistance of which is proportional to the square of the velocity through it, is treated by means of an integral equation. This equation is solved and the results reduced to a form which lends itself to experimental verification. In § 2 experiments are described in which the physical conditions assumed in the analysis were very nearly attained and the theoretical conclusions then verified. The most striking result was the agreement, to within 1%, between the calculated and the measured discharge of water from a tank through an internal porous tube whose base was an orifice in the bottom. The measured distribution of velocity in the plane of the orifice also agreed with the calculations. Experiments with porous cones also yielded results agreeing with theory when the correct experimental conditions could be satisfied.