On weighting function for wall shear stress during unsteady turbulent pipe flow

This work deals, in general case, with the problem of mathematical modelling of the hydraulic resistance during unsteady turbulent pipe flow. Using Reynolds equation including four-layer model of turbulent viscosity a weighting function model of friction has been calculated. The results of the weighting function calculations have been compared with calculations for model given by Vardy. This model can be applied for calculations of transient flow using method of characteristics. The form of weighting function has been chosen in such way, that it is possible to make of inverse Laplace transform. It makes possible to receive relatively simple mathematical structure for matrix transfer function, which relates the pressure and rate flow in inlet and outlet cross-sections of pipe. It is useful for calculations of characteristics frequency for systems with hydraulic lines.