I am seeking some help related to part of a project I am currently working on, where I require to (data-driven) model the pressure drop due to friction for natural gas flowing along a horizontal pipeline (not underground). I have data for the following variables:
P1: Pressure at the entry side.
P2 : Pressure at the exit side, P1>P2
Q: Volumetric Flow Rate at the entry side
T1: Temperature at the entry side.
T2: Temperature at the exit side.
Z: Compressibility of the natural gas
M: Molar Mass of the natural gas.
D: Density of the natural gas at the entry side.
I found out that a linear regression fit between [(P1)^0.5 - (P2)^0.5]^0.5 vs Q can be used to obtain an empirical model for the pressure drop because the scatter plot converges acceptable well to a 'straight' line. I am showing the scatter plot below based on the real data here.
Can someone kindly suggest me how can I improve the convergence towards a linear plot more by including more variables and hence improving the accuracy of the model? I would be grateful for any insightful help or a general suggestion.