A Mass-Change Model for the Estimation of Debris-Flow Runout, a Second Discussion: Conditions for the Application of the Rocket Equation

A geology colleague, Dr. Alan Benimoff, brought to my attention the article on debris flow in this journal written by Cannon and Savage (1988) and the subsequent discussion by Hungr (1990) and reply by Cannon and Savage. The purpose of this note is to clarify and extend the discussion and also to point out a problem with Cannon and Savage's viscous force. A reader of the Journal who is unfamiliar with the problem of systems that gain or lose mass would perhaps have been confused by the discussion and reply. Both Hungr and Cannon and Savage (hereafter abbreviated as CS) are using the same rocket equation except, unfortunately, they use the symbol u to mean two different things. Hungr uses it to denote relative velocity with respect to the main mass (the rocket), whereas CS use it to denote absolute velocity with respect to the ground. If we denote Hungr's a by UH and CS's u by Ucs then UH = Ucs v. Making this replacement in Hungr's eq. (1) we find