Мodel of spill shape and size when liquid is leaking and burning

A model was built to determine the maximum length and width of a spill of a flammable liquid burning and flowing down an inclined plane, under the condition of a constant speed of its outflow. The model is based on a parabolic differential equation that describes the thickness of the liquid layer on the soil surface. It is shown that the maximum spill length and width are achieved in a steady state, which occurs due to the establishment of a balance between the amount of liquid entering the spill due to leakage and the amount of liquid consumed due to burnout. As the angle of inclination increases, the shape of the spill becomes more and more elongated along the direction of the surface inclination. A decrease in the linear burnout rate or an increase in the volume flow rate has the same effect. On the contrary, decreasing the angle of inclination of the surface and increasing the linear speed of burning or decreasing the volumetric flow rate leads to the fact that the shape of the spill approaches a circle. It is shown that for surface inclination angles of no more than 20º, there is a similarity in the processes of liquid spreading. This means that an increase in the volume flow rate is equivalent to a linear transformation of the spatial and temporal coordinates with a simultaneous decrease in the angle of inclination and the linear burnout rate. An algorithm for calculating the maximum length and maximum width of a spill for an arbitrary combustible liquid at a given volume intensity of flow on an inclined surface is built, which is based on the similarity of the processes of liquid spreading on an inclined surface and uses diagrams of the dependence of the maximum length and width of the spill on the angle of inclination of the surface and the linear speed of burning for a reference volumetric flow rate of 10 l/s. The obtained results can be used to determine the height of the flame and the density of the heat flow from the fire to nearby technological objects.