Length for Underground Pipe 1

[cmlewis]

I have been out of school for a while and do not work heat transfer or thermo problems on a regular basis. This is a question my boss approached me with for another co-worker.

Problem:
He will be pumping 100F water at 11gpm through polyethene pipe(s) that are 3-feet in the ground. Assuming soil temperature is 60F. How much 1/2-inch diameter pipe is needed to cool the water to 65F?

(This is what I have so far)
Water:
mass rate= 0.69 kg/s
Ti,initial= 310.8 K
Ti,final= 291.3 K
Cp(310.8K)= 4067.8J /kgK
K(water at 310.8K)= 0.6297 W/mK
Pr(310.8K)= 4.283
u(310.8K)= 6.631x10^-4 kg/m*s

Pipe:
D(inside)= .00158 m
D(outside)= .00173 m
K(pipe)= 0.465 W/mK

Soil:
T= 288.6K
K(soil)= 0.52 W/mK

Equations Tried:
I hope there is a way to simplify this problem, right now I am trying to solve for Internal Convection, Radial Conduction and 2D Heat Transfer.

Internal Convection: I have found the Re to be 8.39x10^4, then found the Nu to be 357.6 to then solve for h.
h=Nu*K/D = 1.43x10^4 W/M^2K

Radial Conduction: I solved for q.
q=Ti-T/([1/h2pir.iL)+(ln(r.o/r.i)/2pikL]
I found q= 1.03 W

2D Heat Transfer: I am not sure here. q=kS(deltaT)

Any help would be greatly appreciated.

 

[MaxTemp2]

I have a solution with a few approximations. The calculation can be found in the Excel sheet attached.
Main approximations:
- Dittus-Boelter calculation can be applied
- water properties do not vary with temperature
- heat transfer coefficient is constant (from previous approximation)

You can modify the parameter values as you wish. For example the inner diameter and outer diameter are very small. Did you want to write 0,00158m or 0,0158m? In the first case L=700m, in the other 70km!
Or you can modify the physical properties of water.

If you take into account temperature dependent water properties, the solution will become nonlinear. In this case I recommend that you take small volumes like in a FEM method.

I studied neutronphysics at university, but I hope, I did not made many mistakes in the calculation.

 

[cmlewis]

Thank you very much. You were correct the Di should be 0.0158. That is alot of pipe. Again THANK YOU!

 

[pmover]

Forget it cmlewis or re-analyze the problem again . . .

100°F water at 11-gpm through 0.5-inch pipe has a very velocity, thus a high head loss (flow is not listed in table in TP-410). the power required may very well be more than what is needed. the spreadsheet furnish shows velocity of 353 m/s, which i doubt is valid or practical.

feel free to investigate and/or clarify the problem again.

good luck!
-pmover

 

[stanlsimon]

Soil thermal conductivity can vary especially with soil moisture. I don't know if you did a soil thermal conductivity test but if the numbers are critical I would recommend doing so.

At a 3' depth there could be seasonal variation in soil temperature. You must not be in Minnesota because around here the frost depth can be 7'.

I hope you are talking about a 1-1/4" pipe or splitting the flow into multiple parallel pipes. Even steel or copper pipe will erode with that kind of velocity. Normally used flow for typical HVAC / plumbing is maximum 2 gpm for nominal 1/2" ID pipe.