# Jet Pump

Jet liquid-liquid pump

Pumps and Motors

## Description

The Jet Pump block represents a jet liquid-liquid pump consisting of a nozzle, throat, and diffuser, as shown in the following illustration.

The model is based on the following equations, described in [1]:

 ${q}_{1}=\frac{{A}_{n}}{\sqrt{1+{K}_{n}}}\sqrt{\frac{2}{\rho }\left({p}_{1}-{p}_{0}\right)}$ (1-8)
 ${q}_{2}=\frac{{A}_{n}\cdot c}{\sqrt{1+{K}_{en}}}\sqrt{\frac{2}{\rho }\left({p}_{2}-{p}_{0}\right)}$ (1-9)
 ${p}_{d}-{p}_{0}=Z{b}^{2}\left(\frac{2}{b}+\frac{2}{1-b}{M}^{2}-{\left(1+M\right)}^{2}\cdot \left(1+{K}_{th}+{K}_{di}+{a}^{2}\right)\right)$ (1-10)
`$b=\frac{{A}_{n}}{{A}_{th}}$`
`$c=\frac{1-b}{b}$`
`$Z=\rho \frac{{V}_{n}^{2}}{2}=\rho \frac{{q}_{1}^{2}}{2{A}_{n}^{2}}$`
`$M=\frac{{q}_{2}}{{q}_{1}}$`

where

 q1 Primary flow rate pumped through the nozzle q2 Secondary flow rate qd Output flow rate p1 Pressure at the nozzle inlet p2 Pressure at the secondary flow rate inlet p0 Pressure at the throat inlet pd Pressure at the pump outlet An Nozzle area Ath Throat area a Diffuser area ratio, Ath / Ad Ad Diffuser outlet area Kn Nozzle hydraulic loss coefficient Ken Throat entry hydraulic loss coefficient Kth Throat hydraulic loss coefficient Kdi Diffuser hydraulic loss coefficient ρ Fluid density

Equation 1-8 describes the nozzle, Equation 1-9 – throat entry, and Equation 1-10 – the combination of the throat and the diffuser. The equations correspond to a standard configuration of the pump, where all the longitudinal dimensions conform to established, empirically determined values. For more details, see [1].

The pump parameters are closely related to each other, and the methodology described in [1] is recommended to determine their initial values.

## Basic Assumptions and Limitations

• The model is based on the one-dimensional theory.

• The primary and secondary flows enter the mixing throat with uniform velocity distribution, and the mixed flow leaves the diffuser with uniform velocity distribution.

• The fluid in the primary and secondary flows is the same.

• The fluid is assumed to be incompressible and containing no gas.

## Dialog Box and Parameters

Nozzle area

Cross-sectional area of the nozzle. The parameter must be greater than zero. The default value is `1` cm^2.

Throat area

Cross-sectional area of the throat. The throat area is usually two to four times larger than the nozzle area. The default value is `4` cm^2.

Diffuser inlet/outlet area ratio

The ratio between the inlet and outlet diffuser areas. For a standard pump with a 5° – 7° included-angle diffuser, the ratio is close to 0.2. The parameter must be greater or equal to zero. The default value is `0.224`.

Nozzle loss coefficient

The hydraulic friction loss coefficient in the nozzle. The parameter must be greater than zero. The default value is `0.05`.

Throat entry loss coefficient

The hydraulic friction loss coefficient in the throat entry. The parameter must be greater than zero. The default value is `0.005`.

Throat loss coefficient

The hydraulic friction loss coefficient in the throat. The parameter must be greater than zero. The default value is `0.1`.

Diffuser loss coefficient

The hydraulic friction loss coefficient in the diffuser. The parameter must be greater than zero. The default value is `0.1`.

## Global Parameters

Parameters determined by the type of working fluid:

• Fluid density

Use the Hydraulic Fluid block or the Custom Hydraulic Fluid block to specify the fluid properties.

## Ports

The block has the following ports:

`A`

Hydraulic conserving port associated with the nozzle entry (primary flow entry).

`S`

Hydraulic conserving port associated with the pump suction (secondary flow entry).

`P`

Hydraulic conserving port associated with the pump outlet.

`N`

Internal nonvisible hydraulic conserving port associated with the throat entry section of the pump. You can view the variables associated with the port by logging simulation data. For more information, see Data Logging.

## Examples

The Well with Jet Pump example represents a well jet pump installation, consisting of a surface-mounted centrifugal pump and a jet pump installed in the well below water level.

## References

[1] I.J. Karassic, J.P. Messina, P. Cooper, C.C. Heald, Pump Handbook, Fourth edition, McGraw-Hill, NY, 2008