Weighting function approximation in transient pipe flow

A very important problem in the transient liquid pipe flow analysis is accurate and effective modeling of hydraulic resistance. The so called integral convolution of the mean local acceleration of liquid and a weighting function need to be solved in a numerical way in order to simulate unsteady resistance. A necessary condition in effective numerical calculations is that the weighting function needs to be defined as a finite sum of exponential terms. The function keeps a constant shape in a laminar flow, in a turbulent flow, its shape changes and it is dependent on the instantaneous Reynolds number. In this article an easy method is presented to determine a proper weighting function in a very straightforward manner in a quick time. A comparison of the determined functions and function prototypes in a frequency domain will be presented as well.