Abstract
Models of unsteady flows and stationary ones in pipes and the requirements of their joining are considered. In this view, the problem of the description of a friction at a non-stationary flow is considered. So-called “quasi-stationarity hypothesis” is discussed. The formula for a friction coefficient generalized on a non-stationary case is offered. It is concluded that additional losses at the non-stationary mode are caused by energy consumptions for reorganization of speed chart.
Highlights
The processes occurring in pipeline systems can be divided into stationary processes and nonstationary ones
The flow here is described by the Bernoulli equation taking into account pressure losses [2, 12]
The well-known water hammer problem [4, 9] belongs to category of non-stationary problems, for example
Summary
The processes occurring in pipeline systems can be divided into stationary processes and nonstationary ones. The requirement of model joining can serve as additional criterion for the adequacy of the approach used, for example, at justification of a so-called quasi-stationarity hypothesis [10] This hypothesis assumes that friction losses in case of unsteady flow can be calculated by the dependences for the steady flow. Zhukovsky [9], did not contain a term taking the friction losses into account They gave the equations for the flow of an ideal inviscid fluid while transit to stationary flow model. Bernoulli's equation takes into account the losses and is used widely for hydraulic calculations of pipelines [2, 13,14,15] As it is noted in [10], such an approach gives sufficiently adequate results for low-velocity flows with weak wave processes. Identifying these additional terms requires a more rigorous obtaining the basic equations
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