Motion of fluid or gas in a two-dimensional conduit with suction through deep orifices in the lateral wall

Abstract

1. A lateral outflow pattern from a flow through a number of deep orifices (slits) varies in the same way as in the case of a single orifice [2], depending on the ratio of the velocities of the main flow (V~) and of the jet (V0) at infinity (Fig. 1). For some value of the ratio V~/V 0 = (V~/V0)' a shock-free flow takes place with the critical point on the frontal edge of the orifice (a similar case occurs under the conditions of lateral outflow from an unbounded flow through a normal slit of infinite depth if V~/V 0 = 1/4"-3, moreover, in the region of V~/V 0 ~ 1/4-3 the flow is of a shock-like nature [2, 6]). For V~/V 0 > (V~/V0)' the critical point is shifted into the orifice; on the surface between the orifices an eddy zone arises which for sufficiently high values of V~/V 0 or of a sufficiently small extension of the area between the orifices may join the free space of the neighboring orifice in the direction of the flow; a flow thus arises which corresponds to the flow past a lattice of infinitely thin plates. The coefficient of the jet compression is determined for the last case by assuming that the plates are positioned perpendicular to the velocity vector V~r and are of infinite length (l -- ~o), and the region of flow of the fundamental flux is unbounded.