Between a burning object and the device on the ceiling lies a physical path, and it is described by two fitted relations. The plume correlation gives the temperature and velocity on the axis of a buoyant column as a function of the heat release rate and the height above the fire, with the classic result that excess temperature falls off as \( (z - z_0)^{-5/3} \). Where the plume strikes the ceiling it turns and runs outward as a thin, fast layer, the ceiling jet, and Alpert's correlations give its maximum temperature and velocity as functions of heat release rate, ceiling height and radial distance from the plume axis. Together they answer the question a designer actually asks: given a fire of a certain size, how hot and how fast is the gas arriving at a point on the ceiling a known distance away, and therefore when will a device there respond. The correlations assume an unconfined ceiling and a fire well away from walls; a corner fire or a beamed ceiling breaks them. After this Concept you can estimate the gas temperature at a ceiling point from a fire's size and position.
Alpert's correlation is an empirical model in fire protection engineering (compartment fire dynamics) that estimates the gas temperature and velocity within an unconfined ceiling jet produced by a fi…