# 13.7.2: Lockhart Martinelli Model

- Page ID
- 881

The second method is by assumption that every phase flow separately One such popular model by Lockhart and Martinelli. Lockhart and Martinelli built model based on the assumption that the separated pressure loss are independent from each other. Lockhart Martinelli parameters are defined as the ratio of the pressure loss of two phases and pressure of a single phase. Thus, there are two parameters as shown below.

\[
\phi_{G} =

\left. {

\sqrt{ { \left. {\left. \dfrac{dP}{dx} \right|_{TP}}

\right/ }

\left.\dfrac{dP}{dx}\right|_{SG}

}

} \;\right|_f

\label{phase:eq:LM_G}

\]

\[
\Xi =

\left. {

\sqrt{ { \left. {\left. \dfrac{dP}{dx} \right|_{SL}} \right/ }

\left.\dfrac{dP}{dx}\right|_{SG}

}

} \;\right|_f

\label{phase:eq:xi}

\]
where \(\Xi\) is Martinelli parameter. It is assumed that the pressure loss for both phases are equal.

\[
\left.\dfrac{dP}{dx}\right|_{SG} =

\left.\dfrac{dP}{dx}\right|_{SL}

\label{phase:eq:SG=SL}

\]
The pressure loss for the liquid phase is

\[
\left.\dfrac{dP}{dx}\right|_{L} = \dfrac{2\,f_L\, {U_L}^2\, \rho_l}{D_L}

\label{phase:eq:GDP}

\]

For the gas phase, the pressure loss is

\[
\left.\dfrac{dP}{dx}\right|_{G} = \dfrac{2\,f_G\, {U_G}^2\, \rho_l}{D_G}

\label{phase:eq:LDP}

\]

Simplified model is when there is no interaction between the two phases. To insert the Diagram.

## Contributors and Attributions

Dr. Genick Bar-Meir. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or later or Potto license.