Hydraulic resistance of unsteady turbulent liquid flow in pipes

The paper deals with the problem of mathematical modelling of the effects of liquid viscosity during an unsteady turbulent pipe flow. To determine the frictional losses, the Reynolds equation is used complemented with the equations describing the distribution of the turbulent viscosity in a cross-section of the pipe. A hydraulic resistance is defined due to the transfer function, that relates the shear stress at pipe wall and the mean velocity. It makes possible to define the weighting function w(t, Re m ) (where t - dimensionless time, Re m - an instantaneous Reynold's number), that takes into account viscosity liquid effects by including of a frequency-dependent friction at the wall of a pipe. Due to a complicated form of weighting function a method of its approximation has been worked out.