Tanks for the storage of oil products and toxic substances in warehouses are the main ones. They can be in the form of separate tanks or a group of tanks. The most widespread are vertical steel tanks with a stationary roof that a placed in open areas. The tanks heat up, and the intensity of evaporation of the oil product increases in case of fire. If there is a permanent roof, the pressure in the tank will increase. If the capacity of the breathing valves is less than the intensity of evaporation then there is a risk of explosion. Explosions in the tank often lead to the separation of the bottom, and the side cylindrical surface and the roof fly away instantly, spilling oil on neighboring tanks and the territory of the tank’s park. Then the combustion area increases intensively. The destruction of the integrity of the tank, due to the separation of the bottom, contributes to temperature and power stresses, the value of which increases with increasing temperature of their heating and increasing pressure, respectively. The values of temperature stresses are added to the power stresses caused by pressure, and when the critical value is reached, destruction occurs.
In the article by the method of mathematical modeling using the laws of thermodynamics and mechanics of liquids and gases, analytical dependences for research of parameters of leakage of toxic substances and gases at action of high pressure from capacities at their storage are received. Saint-Venant’s principle was used to model the gas flow rate process. The dependence of the duration of gas leakage from special purpose tanks at the change of the area of the emergency hole and the pressure drop is obtained. The obtained results allow determining the velocity and mass flow rate of the gas depending on the area of the hole, the time flow, and the difference of pressure. Therefore, the task of research the emergency situations of engineering cylindrical tanks under the influence of temperature and pressure, which leads to the spillage of toxic substances and gassiness is actual. The researches results are presented graphically.