Non-Linear and Simultaneous Equations
Soumendra Nath Kuiry, Dhrubajyoti Sen · 2021
This chapter begins with a few examples of non-linear equations for problems encountered in hydraulic engineering. It introduces a variety of physical processes in hydraulics, and water resources engineering and are described equivalently in the mathematical form as a single or a set of equations. The chapter demonstrates the algorithms by converting these into Python codes. The codes demonstrate the numerical solution of non-linear equations in one variable and simultaneous solution of a system of linear and non-linear equations. The system of interconnected reactors with steady incoming and outgoing flows, carrying a conservative contaminant dissolved with the flow, is analysed, which represents a typical case of a solution of linear simultaneous equations. Simultaneous equations containing non-linear terms may also be solved by extending the Newton–Raphson method accordingly. The chapter presents the Python code for solving a general pipe network.