text: This model for the rocket motor was developed by Probert, Williams and Tanasawa. It is reasonable to neglect , for distances not very close to the spray atomizer, where major portion of combustion occurs. Consider a one-dimensional liquid-propellent rocket motor situated at , where fuel is sprayed. Neglecting (density function is defined without the temperature so accordingly dimensions of  changes) and due to the fact that the mean flow is parallel to  axis, the steady spray equation reduces to
  where  is the velocity in  direction. Integrating with respect to the velocity results
  The contribution from the last term (spray acceleration term) becomes zero (using Divergence theorem) since  when  is very large, which is typically the case in rocket motors. The drop size rate  is well modeled using vaporization mechanisms as
  where  is independent of , but can depend on the surrounding gas. Defining the number of droplets per unit volume per unit radius and average quantities averaged over velocities,
  the equation becomes
  If further assumed that  is independent of , and with a transformed coordinate
  If the combustion chamber has varying cross-section area , a known function for  and with area  at the spraying location, then the solution is given by
  where  are the number distribution and mean velocity at  respectively.