Dynamic of variation of the hydraulic parameters in the transient operating regime of the liquid propellant rocket engine (LPRE) depends on many factors. In this paper some of these factors such as pump inertia, power balance of pumps with turbine, temperature rise of working fluid in pump passages and variation of pump efficiency with the turbopump rotational speed are simulated. For the first time, filling of the inlet main pipeline and filling of the internal hydraulic channels of pump along with main pump equations are also simulated. To achieve this purpose, governing differential equations of each factor are derived, coupled with each other, and then solved by means of Finite Volume method in Simulink-MATLAB software. Results of this mathematical model are compared with experimental data of a real turbopump and shown that, without considering the internal hydraulic channels of the pump, “ the delay time of the turbopump” is not matched with real results, but by taking the mentioned hydraulic effects into consideration, acceptable agreement would be achieved. Also shown, by changing the resistance and inductance values of internal channels of pump, the settling time of turbopump could be changed, and used as a good factor to optimize the LPRE start process.