The descriptions found in the literature, of cases of even relatively strong non-linearity of the water supply systems, as well as their mathematical treatment, are rare and incomplete. They refer mainly to the non-linearity with respect to smooth flow control components (for instance, to the operation of pressure reducing valves (PRV), flow reducing valves (FRV) and pumps with motors equipped with smooth rotational speed control - variable frequency drives (VFD)). The article proposes a formally correct method of a comprehensive solution of the above non-linearity cases based on successive simulations with some dynamic analysis of the sensitivity of the system to the operation of the smooth control components mentioned. An appropriate algorithm controlling the effectiveness of the calculations secures correct description of the behaviour of the system for an arbitrary, in practice, method of control of flows, even if all the proposed smooth control methods are used simultaneously. The effects of the use of the solutions presented in mathematical modelling are illustrated by selected results of simulation carried out for an existing water supply system.
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