# 13.7.2: Lockhart Martinelli Model

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.

$\phi_{G} = \left. { \sqrt{ { \left. {\left. \dfrac{dP}{dx} \right|_{TP}} \right/ } \left.\dfrac{dP}{dx}\right|_{SG} } } \;\right|_f \label{phase:eq:LM_G}$

Where the $$TP$$ denotes the two phases and $$SG$$ denotes the pressure loss for the single gas phase. Equivalent definition for the liquid side is

$\Xi = \left. { \sqrt{ { \left. {\left. \dfrac{dP}{dx} \right|_{SL}} \right/ } \left.\dfrac{dP}{dx}\right|_{SG} } } \;\right|_f \label{phase:eq:xi}$ 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.