# Approximate formula for the volume of water at a given temperature

Sorry for asking this kind of question. Do you recongnize this formula? $$V(T) = 0.0000679T^3+0.0085043T^2- 0.0624T+999.87$$ when $V$ is volume of water in $\mathrm{ml}$, $T$ is temperature in celsius. This is an approximation for volume of 1kg of water with temperatures between 0~30 celsius.

This formula is simple exercise from calculus, finding out extrema. However, I've seen this approximation so many times, even in many different books. So I googled it, and found those approximations were quite accurate with some conditions. (Elements of Physical Hydrology 46p table 3.1)

Is this an appropriate approximation? How can I get this approximation? Any references will be a great help. Thank you for reading

• Isn't it just like a Taylor expansion (about $T=0$) for the expression $\rho'=\rho/(1+\beta(T'-T))$? engineeringtoolbox.com/… – typesanitizer Jul 18 '16 at 15:16
• It is a fit from experimental data, ant it is probably good at atmospheric pressure. – valerio Jul 18 '16 at 16:25