Flow rate and pressure are variables of great interest in the process control industry, especially in pumping systems. With the help of modeling and simulation, it is possible to understand the operation of these systems prior to their construction, in addition to allowing their behavior to be analyzed in various operational scenarios and testing different control strategies. In this work, the hydraulic, mechanical, electrical and electronic models of the different components of the system are studied. Two study cases for automatic flow control are assembled, using Simscape library from MATLAB/Simulink R2019b. This study cases are: i) with a control valve and ii) with a variable speed drive. The simulations determined that both cases keep the flow constant in the face of pressure disturbances, with a good dynamic response. Case 2 consumes less power than case 1, between 24 and 64% less, especially at low flow rates. It also reduce unwanted mechanical and electrical problems due to sudden starts and stops. Case 2 produced harmonic pollution on both the grid and motor sides, which implies a potential risk for the motor and the electrical grid. Case 2 was experimentally validated, obtaining errors of less than 10%.