A uniformly accelerated laminar flow in a pipe, initially at rest, is analyzed. One-dimensional unsteady flow equations for start-up flow were derived from the Navier–Stokes and continuity equations. The dynamical boundary layer in a pipe is described theoretically with the Laplace transformation method for small values of time. A mathematical model describing the development of the velocity profile for accelerating flow starting from rest up to the point of transition to turbulence is given. The theoretical results are compared with experimental findings gained in a large-scale pipeline. Particle image velocimetry (PIV) technique is used to deduce the development of accelerating pipe flow starting from rest. The measured values of the axial velocity component are found to be in a good agreement with the analytical values.

Hydraulic power capacity of the water distribution network (WDN) is analyzed, and energetically maximum flows in pipes and networks are determined. The concept of hydraulic power for the analysis of WDN characteristics is presented. Hydraulic power capacity characterizes the WDN capacity to meet pressure and flow demands. A capacity reliability indicator called the surplus power factor is introduced for individual transmission pipes and for distribution networks. The surplus power factor s that characterizes the reliability of the hydraulic system can be used along with other measures developed to quantify the hydraulic reliability of water networks. The coefficient of the hydraulic efficiency η n of the network is defined. A water distribution system in service is analyzed to demonstrate the s and η n values in the water network in service under different demand conditions.In order to calculate the s factor for WDNs, a network resistance coefficient C was determined. The coefficient C characterizes overall head losses in water pipelines and is a basis for the s factor calculation. This paper presents a theoretical approach to determine the coefficient C through matrix equations. J. Vaabel

This paper describes the development of the surplus power factor s that characterizes the reliability of the hydraulic system and the values of which vary between 0 to 1. In order to calculate the s factor for water distribution networks (WDNs), a network resistance coefficient C has to be determined. This paper compares different approaches in order to calculate the coefficient C and determine the s factor for WDNs.

The so-called dissipative model [i, 2] has recently found wide use when describing unsteady flow of a compressible fluid in circular pipes.The solution of particular problems of unsteady flow of a compressible fluid in pipes on the basis of the dissipative model presents certain mathematical difficulties, since the classical method of separation of variables is not applicable here, and on using the operational method there are difficulties in inverting the transforms of the solution. Therefore, the solutions of particular problems on the basis of this model were obtained mainly by means of the method of approximate inversion of the Laplace transform for small times [2,5].The Kantorovich variational method together with the numerical finite-difference method is used in this article for solving the problem of unsteady fluid flow in a pipe. As in [4,5], by means of the variational method integration of the system of differential equations for a function of three variables is reduced to integration of an infinite system of differential equations for a function of two variables. The solution of this system is expressed by one integrodifferential equation. The finite-difference method is used for solving the latter equation.The temporal change of the velocity components at different points of the cross section of the flow and change in the average velocity and pressure are found by the described method for the initial stage of fluid flow upon a rapid drop of pressure at one end of the pipe. (5) (6)where S, ~, T are dimensionless coordinates and us, u~, q are dimensionless parameters determined by means of the relations