So I'm doing some water hammer analysis and was calculating bulk modulus of water as a function of temperature. I took the speed of sound and density of water as functions of temperature and calculated bulk modulus from there ($K=c^2\rho$). This yields the following graph:

Bulk Modulus of water vs temperature @ 200 bar

I was wondering what causes this behaviour. Is it the same reason why water is most dense at 4ºC? ie Is is to do with intermolecular bonds being stronger/weaker at a certain point. If it is related, why isn't the maximum at 4ºC for bulk modulus as well?


This is a comment not an answer, but I can't put pictures in a comment. If Adri agrees this could be edited into his question.

If we include the speed of sound and the density on the graph then the result is:

Water properties

All data is from the Engineering Toolbox.

The density falls monotonically, so it's the maximum in the velocity that is related to the maximum in the bulk modulus and vice versa.

  • $\begingroup$ Thanks for the input. If you were too zoom in on the density I'm pretty sure there's an inflection point at about 4 degC. I'll edit the question to add these curves as well. $\endgroup$
    – Adri Jamil
    Nov 27 '15 at 10:43
  • $\begingroup$ @AdriJamil: you keep saying inflection when you mean maximum. A point of inflection is where the second derivative is zero. Yes, there is a maximum in the density at 4C. $\endgroup$ Nov 27 '15 at 10:46

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