A jet ejector is a device without moving parts that can be used as a pump. As shown in Fig. P11.6, on the upstream side are concentric tubes of diameters D and λD, where λ < 1. A liquid at a high velocity v_jet in the inner tube entrains another liquid of the same density, giving it a velocity v_an(< v_jet) in the annular region. Where the streams come into contact, the pressure in both is assumed to be P_jet. The device discharges to the atmosphere at a pressure P₀ and velocity v_out. The outlet is assumed to be just far enough downstream for the mixing to be complete and the plug-flow approximation to be valid again. Supposing that the flow is turbulent and that v_jet, P_jet, the dimensions, and the fluid properties are known, it is desired to find v_an, v_out, and the viscous loss E_v.

(a) Assuming that the plug-flow approximation is applicable separately to the jet and annular openings, show how the three velocities must be related.

(b) Supposing that the distance between the two planes shown as dashed lines is small enough to make the shear force on the wall negligible, relate v_an to v_jet and P_jet and show that it is necessary that ΔP = P₀ − P_jet > 0.

(c) Derive an expression for E_v.

(d) Calculate v_an, v_out, and E_v for water with v_jet = 5 m/s, λ = 0.3, D = 0.10 m, and P_jet = 0.99P₀.

Transcribed Image Text:

AD Figure P11.6 Jet ejector. jet Vjet an Vout Air Po