## Liquidjet Pump Theory For Three Secondaryflow Types

The liquid-jet pump model is based on conservation equations for energy, momentum, and mass. Real-fluid losses are accounted for by friction-loss coefficients (K). The primary or motive fluid is a liquid of density p1. In the following derivation, the secondary/pumped fluid can be a second liquid of density p1 or p2, or a gas-in-liquid bubbly mixture, or a gas. These three jet pump flow regimes are referred to as liquid-jet liquid (LJL), liquid-jet gas liquid (LJGL), and liquid-jet gas (LJG). Equations (1), (3), (5), and (7) below apply to all three.

Assumptions:

a. The primary and secondary streams enter the mixing throat with uniform velocity distributions, and the mixed flows leave the throat and diffuser with a uniform velocity profile.

b. The gas phase—if present—undergoes isothermal compression in the throat and diffuser.

c. All two-phase flows at the throat entry and exit consist of homogeneous bubble mixtures of a gas in a continuous liquid.

d. Heat transfer from the gas to the liquid is negligible—the liquid temperature remains constant.

e. Change in solubility of the gas in the liquid from pressure Ps to Pd is negligible.

f. Vapor evolution from and condensation to the liquid are negligibly small.

nozzle equation With reference to Figure 1

Vf Vf VI

For the nozzle equation is

throat-entry equation The two-phase secondary flow is described by

Density of the secondary fluid as a function of static pressure and flow ratios M and f is dP ( V 2\

m mG m1 m1

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