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.
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Check out http://en.wikipedia.org/wiki/Boussinesq_approximation.
That depends on how precise you want the approximation.
That's not a "mathematical principle", it is an approximation of the number pi.That's not a "mathematical principle", it is an approximation of the number pi.That's not a "mathematical principle", it is an approximation of the number pi.That's not a "mathematical principle", it is an approximation of the number pi.
The best approximation is, of course, the exact value. A reasonable approximation is 106.
There is no reasonable radical approximation for radical 11.