Editing Boussinesq approximation (buoyancy) (section)

==Advantages==
The advantage of the approximation arises because when considering a flow of, say, warm and cold water of density {{math|''ρ''<sub>1</sub>}} and {{math|''ρ''<sub>2</sub>}} one needs only to consider a single density {{mvar|ρ}}: the difference {{math|Δ''ρ'' {{=}} ''ρ''<sub>1</sub> − ''ρ''<sub>2</sub>}} is negligible. [[Dimensional analysis]] shows{{clarify | reason= What does dimensional analysis have to do with smallness or largeness of dimensionless numbers? The explanation doesn't make sense as it stands now. |date=May 2020}} that, under these circumstances, the only sensible way that acceleration due to gravity {{mvar|g}} should enter into the equations of motion is in the reduced gravity {{mvar|g′}} where

:<math>g' = g\frac{\rho_1-\rho_2}{\rho}.</math>

(Note that the denominator may be either density without affecting the result because the change would be of order
{{tmath|g \left( \tfrac{\Delta\rho}{\rho} \right)^2}}.) 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 {{math|{{sfrac|''ρ''<sub>1</sub>|''ρ''<sub>2</sub>}}}}, a [[dimensionless number]], does not affect the flow; the Boussinesq approximation states that it may be assumed to be exactly one.