###### Abstract  
A mathematical model of pulsating flow is proposed in the paper. The model includes more accurate description of energy dissipation, so it allows, for example, better stability analysis of water power plant control and more effective operation. Flow in a pipeline system is usually treated as a one-dimensional flow. This is also applied for more difficult cases of the Newtonian and non-Newtonian liquids simulations in the rigid or flexible pipes. Computational simulations of pressure pulsations in pipelines often predict lower damping than what the experimental results show. This discrepancy can be caused by neglecting one of the important damping mechanisms. The second viscosity describes the energy losses due to the compressibility of the liquid. Its existence and use in the computations specifies the real pulsations damping descriptions and predictions. A frequency dependent model of pressure pulsations including second viscosity is introduced. The second viscosity is determined from the system eigenvalue. The experiments were performed with water for low frequencies (from 0.1 to 1 kHz). This area is not fully covered by the current available research results.  
second viscosity; bulk viscosity; damping; attenuation; pressure pulsation; frequency domain +
Footnote †: journal: Applied Physics Letters  
_Applied Physics Letters_  
Unfortunately, the model of unsteady friction is not as well described as the model of steady friction, and investigation in this area is still ongoing [5; 6; 7]. In contrast, the inclusion of second viscosity in the model instead of unsteady friction makes results more accurate and it has an advantage: second viscosity is associated with fluid matter, and it is possible to use it in the frequency domain.  
The energy dissipation due to second viscosity occurs when the fluid is being compressed or when the fluid is expanding. [PERSON] formulated a hypothesis that second viscosity equals negative two thirds of the shear viscosity \(\eta_{2}=-\frac{2}{3}\eta\); thus the fluid is supposed to be in thermodynamic equilibrium [8].  
It has already been proven that [PERSON] hypothesis is not valid for polyatomic gases and liquids [9]. The author showed the influence of second viscosity on the absorption and dispersion of sound in fluid and discussed the frequency dependence of the second viscosity.  
Examination of the theoretical model of liquid was performed in [10], where authors noted the role of second viscosity in the spreading of wave fronts, dilatation and compression of fluid or attenuation of sound waves. Numerical determination of the bulk viscosity of water was also conducted in [11; 12].  
When we look for experimental data of second viscosity, we find out that they are very rare. It is very difficult to find any experimental data within the last 150 years. Regarding water, possibly the oldest experiments were performed by [PERSON] [13]. [PERSON] published the dependence of second viscosity on pressure [14; 15]. In addition, [16] provided measured data for water, and [17; 18] measured the temperature dependence of the second viscosity.  
All published experiments were performed at high frequencies (on the order of MHz or GHz) in a narrow range.  
A method of the second viscosity determination from the damping of pressure pulsations is described within this paper. The suggested procedure allows determining of the second viscosity at low frequencies.