# Why isn't water running faster hotter?

I was running the washing up water this morning, and started to think about why the cold tap isn't hot, and why the water doesn't get hotter the faster it is flowing (if anything, the cold tap gets colder the faster it flows).

From my understanding

$K.E = \frac{mv^2}{2}$

and temperature is directly proportional to kinetic energy.

I know that the $v$ in the above equation is really the mean speed of the particles and therefore some are moving backwards and some moving forwards, it is the speed that is used. But surely the particles of water in the tap are all moving faster, therefore they should all be hotter. Perhaps the particles in the stream are moving at a much higher mean speed than the water is flowing, so the temperature increase is negligible... Am I correct in thinking this? or otherwise, why doesn't the cold tap get hot the more you turn it on?

• Temperature is defined your way for a system that is at rest. – ACuriousMind Jun 29 '14 at 17:29
• How are you measuring temperature? With a thermometer or with your hands? Convective cooling tends to make our hands a very unreliable gauge of temperature differences. – tpg2114 Jun 29 '14 at 17:32
• @tpg2114 Hands of course! :D Who runs the washing up water with a thermometer? :p Does that mean if I used a thermometer, the temperature would increase as the flow of water increases? – J_mie6 Jun 29 '14 at 17:35
• Things like friction with the pipes and turbulent dissipation within the higher speed flow should increase the temperature of the fluid, although not by much. I'll let somebody come along and give equations and orders of magnitude to give you a better idea because there are other, competing effects that may actually reduce temperature by more than is added. But I will say hands are not the right tool for the job! – tpg2114 Jun 29 '14 at 17:39
• Effectively a duplicate of Why am I not burned by a strong wind?. Or maybe only strongly related, but the answers to the early questions are strongly relevant here. – dmckee Jun 29 '14 at 18:14

The water gets colder the longer you run it (in the UK at least) because the water mains pipes buried in the ground are colder than the ones in your house, so sadly this isn't evidence for any fundamental physical effect.

In principle any fluid flowing in a pipe gets hotter because energy is dissipated in viscous flow. You could in principle calculate the energy dissipated using the pressure drop per length of pipe, which is described by the Darcy-Weisbach equation, but this would be a somewhat involved calculation for real pipes/taps and in any case it isn't relevant to the core of your question.

When you relate velocity to temperature you're presumably thinking of the Maxwell-Boltzmann distribution for the temperature dependance of the velocity profile in gases. The trouble is this distribution is arrived at by considering redistribution of energy between gas molecules due to collisions between them. If you simply add a constant velocity to every gas molecule you aren't making any difference to the way the gas molecules collide with each other, because it's only their relative velocities that matter.

Although water is a liquid not a gas the same argument applies. It's the velocities of the water molecule relative to each other that determine the temperature. So just adding a constant velocity to every water molecule makes no difference.

• I was typing the answer, and then I saw that there was a new answer :( Good answer though. – Gummy bears Jun 29 '14 at 18:09
• To whoever downvoted, I respect your opinion but I would like to know why you downvoted. If there's an error in my answer please tell me so I can correct it. – John Rennie Jun 29 '14 at 18:12
• i live in india and temperature over here is somewhat high [when compared to UK] and we have very high temperature and there will be no cool or normal water available during day time [pipes are not exposed directly to sunlight] can you comment the answer in that context – agha rehan abbas Jun 29 '14 at 18:18
• Well yes... In India, water is not directly supplied 24 hours a day. Therefore, water storage tanks, usually on top of the roof, are built to store the water. As they are in direct sunlight, the water gets heated. @agharehanabbas – Gummy bears Jun 29 '14 at 18:21
• @JohnRennie I will do :) I am frustratingly close to the upvote reputation aswell... – J_mie6 Jun 29 '14 at 18:31

To greatly simplify John's answer: the temperature gained by friction and velocity is insignificant compared to the current temperature of the liquid.

I expect frictional heating would kick in at higher pressures, but once the water had enough kinetic energy to heat up noticeably on impact with your hands, it would also have enough energy to strip the flesh off your bones, cut through said bones, and punch a hole through the sink. Water jet cutters will easily go through inches of steel and a foot of stone - they aren't overly concerned about heating.