Measuring Heat Generated by Tumbling Barrels for Beach Studies

[mfor040]

G'Day
Excuse my lack of physics expertise, I am a simple geographer (PhD student) studying sand... I have tumbling barrels in which I tumble an abrasive, water and a small sample of rock/sand/shells/coral. The barrel rotates at around 30RPM. Not surprisingly when I open the barrel after many hours of tumbling the water inside is noticeably warmer. I am wondering if anyone has any ideas as to whether I can get a useful measure of how much work has been done on the material in the barrel to create this heat. The ulitmate for me is ground truthing what is going on in the tumbling barrel with what is going on under the action of waves on a beach. I hope this makes sense and someone has some kind of helpful idea...
cheers
Murray

 

[Danger]

I think that you would have to take precise measurements of the before and after temperatures of all material, including the interior surface of the drum, before you could apply a formula to it. The heat gain of the water itself would just be part of it. You might also want to check your motor output power vs. the resistance of the drum to turning, but I don't know if that's helpful or not. In any event, though, I find it hard to think that this situation would be coincidental with wave action. The dynamics should be completely different.

 

[FredGarvin]

I'd take a first stab at it going as simple as possible. Try calculating heat added with Q = m C_p \Delta T and then use that with the first law of thermo which is \Delta U = Q - W. See what those numbers produce and see if they are believeable or make sense to you.

 

[Danger]

Oh sure, Fred, be a smartass with all of your education.
So, what do all of those symbols mean? You know my level of schooling. I'd like to know what all of that stands for in normal terms. I'm sure that it will come in handy in my future, but only if I know what your units are.

 

[FredGarvin]

The basic Heat Equation: http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html

The First Law of Thermodynamics:
http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html

I think there would be a tough step in characterizing the change in internal energy. However, if one could do that, the rest is easy.

 

[Danger]

Thanks for the link, Fred. That's a cool site.

 

[FredGarvin]

Hyperphysics is a nice source that has a lot of information available. It's worthy of a bookmark.

 

[mfor040]

thanks for your help.

 

[lalbatros]

mfor040,

You can safely consider that more than 99% of the power delivered to the barrels is converted to heat. The energy transformed in breakage of the material is extremely small even in more powerful equipments like cement grinding mills (much less than 1% goes to breakage in these mills).

Therefore, of course, the most important is to have a good measurement of the power transmitted to the barrel. Most often this is based on the electrical power absorbed by the motor and the efficiency of the transmission system as documented by the supplier.

However, you should take a few additional things into account if you want to analyse the temperature data:

wall heat losses, since warm walls will loose heat to the surrounding
possible gas flow flowing through the barrel, removing some heat
the effect of water evaporation that might cool down the material
(however, evaporation might saturate without air flow through the barrel)
any know chemical transformation that could be exo or endo thermic​

Clearly, the mechanical action on the content of the barrel is mainly derived from the absorbed power, indeed. What should be further investigated is how well this represents the action on the solid material