A novel educational methodology, Implementation of Mathematical, Experimental, and Computer-based Education (IMECE), where its name was derived from the letters of the word "imece" (a Turkish tradition) by taking into account the integrative meaning of this cultural concept, was proposed to explore the synergistic effect of the conventional mathematical solution procedure, visual application, and MATLAB-based simulation on the perceptions and learning quality of the engineering students. Within the scope the present research carried out both at the state university (undergraduate and graduate levels) and at the foundation university (undergraduate level), water discharge problem (a special case of the Bernoulli's principle/Toricelli's law) was chosen as an example application. In the study, the experimental results of three different tank models (vertical cylindrical, conical, and spherical) and the solution algorithms written in MATLAB were presented in detail, and new empirical equations were also developed for each laboratory scale system depending on the experimental data. The effectiveness of the proposed IMECE method was evaluated statistically within the framework of both "Student Survey" and "Student Assessment" conducted with the participation of 84 students. Based on the mean scores obtained for all participating students, the results of the statistical tests indicated that the quantitative performance (or effectiveness) of the applied IMECE methodology was determined as 97.73%, 67.36%, and 82.55% for the perception/satisfaction section, the learning section, and the overall evaluation category, respectively.