ИСТИНА

The motion of a liquid in a three-dimensional vertical pipe is considered. Based on Euler’s equations, Darcy’s law is valid for some modes. Then the problem is reduced to a one-dimensional system for density, pressure, and longitudinal velocity (averaged in the cross-section). We consider boundary problem with known pressure values at the beginning and the end of the pipe, and temperature value at the beginning of the pipe. This problem simulates the effect of overheating of the liquid at the end of the pipe: when the heat release increases above a certain threshold, the density turns to zero, and the temperature goes to infinity, as well as the effect of locking the flow in the end of the pipe (the velocity is zero). These effects occur both in the ideal gas approximation and for the Van der Waals model. Similar effects in the case of an ideal gas was observed in the work [2], where the system was solved for pressure, velocity, density and entropy. Obtained analytical and numerical results fit the experimental data from [1]. The authors are grateful to V. G. Danilov and A. A. Kovalishin for valuable discussions. The work was carried out in the frame of the government program (state registration No. 123021700044-0). 1. Investigation of the temperature conditions of the pipe wall during heat removal by supercritical pressure water / G. V. Alekseev [et al.] // High Temperature. — 1976. — Vol. 14, no. 4. — P. 769–774. 2. Maslov V. P., Myasnikov V. P., Danilov V. G. Mathematical Modelling of the Chernobyl Reactor Accident. — Moscow : Nauka, 1988. — 144 p.