The equation is described by a number density function f j ( r , x , v , T , t ) d r d x d v d T , which represents the probable number of spray particles (droplets) of chemical species j (of M total species), that one can find with radii between r and r + d r , located in the spatial range between x and x + d x , traveling with a velocity in between v and v + d v , having the temperature in between T and T + d T at time t . Then the spray equation for the evolution of this density function is given by