How can I predict the temperature increase of water flowing through a long pipe?

[EzeTom]

Hi Folks,

It seems there are some differing opinions in my office with respect to the following.

If one is to pump water through a long lenth of 1.75" pipe (16000'), how would you go about predicting the temp rise of the water as it flows along the pipe?

From what we have found, when pumping at roughly 7000PSI @ 2.5 BPM we have a significant increase, but it seems we are not able to accurately predict precise values. The fluid is straight H2O, and is de-gassed. I know this is a simple problem ,but with all the bickering I've had with my colleauges, I thought I would ask here!

Thanks everyone for the excellent site!

 

[russ_watters]

I had an issue with this with my colleagues at work: Except for energy lost to radiation or convection at the pump (or anything else uninsulated), all of the energy of the pump goes into heating the water. So calculate the energy in and use the flow rate to find the delta-T.

Or, maybe you shouldn't listen to me...I lost the argument (by default - I was the junior).

 

[Q_Goest]

I hate it when you type up a lengthy reply and go to post it but the website comes back asking you to sign in – and then you loose everything! <argh>

Ok, I’ll have to shorten this. I think you’re asking how to determine the change in temperature as water flows through a pipe, not through a pump. If you’re looking for through a pump, the pressure rise through a pump can be modeled as an isentropic process with some loss of efficiency. Check out this web page to determine how to calculate discharge enthalpy from a pump given some isentropic efficiency:
https://ecourses.ou.edu/cgi-bin/ebook.cgi?doc=&topic=th&chap_sec=06.5&page=theory

For pipe flow, there is no work done by or on the fluid (exceptions to follow).

For a pipe with no change in elevation, and no heat is exchanged with the environment (adiabatic) the flow through the pipe is modeled as an isenthalpic process for small changes in velocity. Note that velocity is a form of energy and can be incorporated into Bernoulli’s equation, but for now I’ll neglect this since it is generally small and insignificant for pipeline flow.

So if you have the state of the water (or any fluid) at some point, you can determine the enthalpy from a properties database. This is the same enthalpy as any point downstream. Now all you need is the pressure, and you have enough information to determine the state of the fluid at any point downstream (ie: you have pressure and enthalpy).

For example, let’s say you have 7000 psi water at 70 F. Look up the enthalpy for this state. Now use the Darcey Weisbach equation to determine the irreversible pressure loss for the pipe. Let’s say you loose 1000 psi so your water pressure drops to 6000 psi. You now have enthalpy and pressure, so you can look up the temperature from the fluid properties database and get temperature. For this example, the final temperature of the 6000 psi water is 72.75 F.

If there is a change in elevation, you can model this as an isentropic process. Use Bernoulli’s equation to determine the rise/fall in pressure and if there’s no heat exchanged with the environment (adiabatic) then the process is isetropic.

For example. Say you have water initially at 7000 psi and 70 F with a total pressure loss of 1000 psi per Darcey Weisbach, but the water also drops in elevation so there’s a 1000 psi pressure RISE, bringing the pressure back up to 7000 psi. For the pressure rise, assume this is isentropic, so look up the entropy of water at 6000 psi and 72.75 F. Now you have the entropy and pressure when the water pressure increases back to 7000 psi due to the drop in elevation. Go to your properties database and find the temperature for water with the entropy found at 6000 psi and 72.75 F and the new pressure of 7000 psi. You should now find a temperature of 73.00 F.

This method is also applicable to gasses.

Note that the isenthalpic change in temperature sometimes results in a higher temperature but sometimes results in a lower temperature. In the example above, the isenthalpic pressure change in the water resulted in a temperature rise, but there could be cases of water temperature dropping. Whether temperature rises or falls during an isenthalpic process is a matter of how the molecules ‘rearrange’ themselves. For an ideal gas, and for a completely incompressible fluid, there is no change in temperature. It is only for non-ideal cases that we find a change in temperature.