Check out http://en.wikipedia.org/wiki/Boussinesq_approximation.
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The change in density of a fluid can be neglected if the temperature change in it is small. This assumption is however not applicable when buoyant forces are in consideration as gravity changes the specific weight of a fluid considerably.
Logarithmic equation
what is the equation
The equation is "What = ?"
If this value a satisfy the equation, then a is a solution for that equation. ( or we can say that for the value a the equation is true)