Calculation and optimization of such complex systems as ventilating networks, water supply systems, etc. taking into account roughness of a surface and possible processes of heat and mass transfer demands use simple hydrodynamic models, which are at the same time sufficiently exact for engineering calculations. The goal of this paper is to develop such model. Prandtl’s model of a two-layer flow in the smooth pipe with the linear law of velocity distribution for a near-wall laminar layer and the logarithmic law for a turbulent core is used as a basis, which spreads to a case of rough pipes. The velocity profile equation and also the equations for the coordinate Yb of the laminar and turbulent border and its velocity Ub are derived. This paper is based on the use of the analytical description of Nikuradse’s experimental curves λ(Re,δ) (λ is the resistance coefficient, δ is the relative roughness) which earlier was found by the author. The dependence λ(Re*,δ) (Re* is the dynamic Reynolds number) is included into all above-mentioned equations. Results of numerical calculations of Yb and Ub as functions of Re* for the values of δ which are the same as in Nikuradse’s experiments are given. The calculation of velocity profiles for some values of Re* and δ is also fulfilled. Comparisons with the experimental velocity profiles obtained by Nikuradse demonstrate a good agreement.

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The version of simulating fans in mine ventilation network analysis by using the combination of FEM with the laminar solution method is considered. Two ways of fan insertion are discussed: in the form of a separate active element and in the form of combined element (an active element inserted into a passive element). The latter approach allows changing a position of the fan in a design stage without renumbering of a grid. The method of chords is used to linearize in general nonlinear fan characteristic. It is shown that the dependence of air discharge on the upstream-downstream pressure difference is an ascending curve for the fan. This provides a convergence for the iterative procedure of solving the FEM nonlinear equations system. A method of calculation of convective heat transfer between the air flow and the rock wall based on Lyon’s solution for a pipe with the constant density of boundary heat flow is described. As the density of heat flow and the air properties are slowly varying functions along a mine working (a branch of a network), then discretizing each branch into small segments permits to consider these parameters as constant along segments. Calculation of nonhomogeneous temperature field and treatment of gravity allow modelling the natural draught effect. The results of solution of the test problems validating used algorithms are given. Calculation results of flow mass rate in a mine network within the year are also represented which make it possible to estimate the influence of natural draught on venting capability.

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