Although the Muskingum equation was proposed nearly 75 years ago, it is still a subject of active research. Despite of its simple form, the real properties of this equation have not been comprehensively explained. This paper proposes a new interpretation of the linear McCarthy’s relation. This relation can be interpreted only together with the storage equation, whereas the Muskingum equation can be derived directly from the system...

Two nonlinear versions of the Muskingum equation are considered. The difference between both equations relates to the exponent parameter. In the first version, commonly used in hydrology, this parameter is considered as free, while in the second version, it takes a value resulting from the kinematic wave theory. Consequently, the first version of the equation is dimensionally inconsistent, whereas the proposed second one is consistent. It...

The paper presents a novel approach to the Pulse Width Modulation (PWM) duty cycle computing for complex or irregular voltage vector arrangements in the two (2D) and three–dimensional (3D) Cartesian coordinate systems. The given vectors arrangement can be built using at least three vectors or collections with variable number of involved vectors (i.e. virtual vectors). Graphically, these vectors form a convex figure, in particular,...

3D visualization is a key element of research and analysis and as the source used by experts in various fields e.g.: experts from water and sewage systems. The aim of this study was to visualize in three-dimensional space model of water supply network with relief. The path of technological development of GESUT data (Geodezyjna Ewidencja Sieci Uzbrojenia Terenu – geodetic records of public utilities) for water supply and measurement...

The seminal Navier-Stokes equations have been stated yet before creation of principles of thermodynamics and the first and second laws. In the literature there is the common opinion that the Navier-Stokes equations cannot be taken as a thermodynamically correct model of “working fluid” which is able to describe transformation of “ heat” into “work” and vice versa. Therefore, in the paper, a new exposition of thermodynamically...