The advantage of the approximation arises because when considering a flow of, say, warm and cold water of density  and  one needs only to consider a single density : the difference  is negligible. Dimensional analysis shows that, under these circumstances, the only sensible way that acceleration due to gravity  should enter into the equations of motion is in the reduced gravity  where
(Note that the denominator may be either density without affecting the result because the change would be of order
.) The most generally used dimensionless number would be the Richardson number and Rayleigh number.
The mathematics of the flow is therefore simpler because the density ratio , a dimensionless number, does not affect the flow; the Boussinesq approximation states that it may be assumed to be exactly one.