Abstract
The accuracy and efficiency of water tank system problems can be determined by comparing the Symmetrized Implicit Midpoint Rule (IMR) with the IMR. Static and dynamic analyses are part of a mathematical model that uses energy conservation to generate a nonlinear Ordinary Differential Equation. Static analysis provides optimal working points, while dynamic analysis outputs an overview of the system behaviour. The procedure mentioned is tested on two water tank designs, namely, cylindrical and rectangular tanks with two different parameters. The Symmetrized IMR is used in this study. Results show that the two-step active Symmetrized IMR applied on the proposed mathematical model is precise and efficient and can be used for the design of appropriate controls. The cylindrical water tank model takes the fastest time in emptying the water tank. The approach of the various water tank models shows an increase in accuracy and efficiency in the range of parameters used for practical model applications. The results of the numerical method show that the two-step Symmetrized IMR provides more precise stability, accuracy and efficiency for the fixed step size measurements compared with other numerical methods.
Highlights
A modelling system is a representation of the actual form modelled to illustrate the construction of relationships and elements of feature dependence and how the system works
The mathematical model of the water tank system is described by the first nonlinear Ordinary Differential Equation (ODE) [3]
The results indicated that the 2PS had the highest efficiency in experimental emptying of the cylindrical and rectangular water tanks in the existing methods for the first and second parameters, followed by the 2AS, 1PS and 1AS methods in the Symmetrised Implicit Midpoint Rule (IMR)
Summary
A modelling system is a representation of the actual form modelled to illustrate the construction of relationships and elements of feature dependence and how the system works. Modelling is useful for the development of science, including creating systems that yet exist [1]. Models are a small representation of a nonlinear original system, with the expectation that the results of the experiments on this model are valid or comparable to those in the actual system. Predictions for models are needed because actual experiments are risky and costly [2]. The mathematical model of the water tank system is described by the first nonlinear Ordinary Differential Equation (ODE) [3]. The model simulation consists of static and dynamic analyses
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