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I am trying to figure out the energy of the sound generated when a droplet of water hits a glass full of water. So, I initially thought that it's potential energy would then completely be transfered into kinetic energy just before it hits the water beneath (assuming air resistance to be negligible over the height it falls, around $20$ cm). Now when the droplet hits the water, its kinetic energy $E_c$ would be transfered to a the splash energy, the sound energy (which I am trying to figure out) and then some heat.

At first, I tried to calculate the heat dissipated, so I thought about using convective transfer studies to calculate the convective heat, but, the droplet and the water in the glass have the same temperature, so that would yield no heat exchange and that suggests neglecting it completely.

AmI wrong in my reasoning? or could the heat loss be neglected in front of the sound energy and the splash energy?

Now, suppose that I had the answer for the latter, I am not done yet since I still need to calculate the splash energy which depends on the viscocity a priori given that the greater the viscocity, the harder it would be to make a splash (think of dropping objects in honey for example).

For the splash energy, does it require some advanced fluid mechanics to come by its expression? Would dimensional analysis give a result even if it's just an approximation?

I don't want a detailed answer, I just need hints that I can use to progress in the analysis of this problem.

Thanks in advance.

Edit 1: We have the following formula for the energy density dissipated by viscocity from a heat transfer course (convective heat tranfer) but I need someone to verify it: $e=\frac{\mu u_0}{x}$ where $\mu$ is the dynamic viscocity, $u_0$ the fluid speed and $x$ the distance relative to the point of entrance of the fluid.

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There is very little energy in sound. The energy flux at 0 dB (around the threshold of hearing) is $10^{-12}$ W/m$^2$. So at 60 dB (conversation level) it is 1 microwatt per square meter. A splash of water would create much less than a microjoule of energy.

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  • $\begingroup$ I have just edited my question. I am asking for a derivation of the splash energy or at least the dissipation by viscocity. As per the sound energy, I am aware that it is very little, but I still need as I can resolve the sound frequency from it. $\endgroup$ – Oussama Boussif Feb 25 '18 at 18:52

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