A method is proposed for calculating the rarefaction occurring in the reverse-flow zone behind a jet ejected from an infinitely long slit at a right angle to a flow bounded by the walls of a channel.The calculated results are compared with experimental data.Jets which develop in a confined entraining flow are encountered in different types of equipment and are particularly widely used to organize mixing in different types of mixers. When the jet is discharged into a transverse flow, the pressure in the region behind the jet is lower than the pressure in the incoming flow.This has an effect on the characteristics of the jet and especially on its path.It therefore also affects the depth of penetration of the jet, which in turn has a significant effect on the degree of mixing.The problem of the rarefaction in the reverse-flow zone was solved in [I] for a plane jet in an infinite entraining flow.The main idea behind this solution was the use of the momentum equation in a projection normal to the entraining flow: since the pressure far above the jet is equal to the pressure in the undisturbed flow and there is no vertical projection of momentum (the jet practically rotates in the flow direction --see Fig. la), the increase in pressure in front of the jet on the wall from which it is discharged and the momentum of the jet should be compensated for by the rarefaction behind the jet.To determine the integral of pressure on the wall ahead of the jet and the ve]ocity and pressure on its front boundary, it is necessary to know the form of the "displacement body" formed by the jet.Based on the fact that the jet must again become attached to the wall to ensure closure of the circulation zone, it was assumed in [I] that this "displacement body" has the form of an ellipse.Thus, it is necessary to find three quantities: the pressure in the reverse-flow zone behind the jet, and two parameters determining the form of the ellipse --its semimajor and semiminor axes.As the second and third equations to determine these quantities we used the conditions of transverse equilibrium at the nozzle edge and at a distance from the jet source in the region of minimum curvature of the "displacement body" --at the point of intersection of the curve of the ellipse with its semiminor axis.Since the pressure gradient is proportional to the square of the mean velocity in the jet in this section (which is less than the velocity of the entraining flow) and is inversely proportional to the radius of curvature, then from the condition of transverse equilibrium we find that the pressures above the jet in the region of minimum curvature of the displacement body and under it should be close to each other. The results of calculation of rarefaction behind a plane jet and the jet path obtained by the above-described method agree quite satisfactorily with the experimental data.Below we present a solution to the problem of determining the rarefaction behind a plane jet in a confined entraining flow.The solution is based on the solution in [1] for a jet in an in...
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