Time for Underground Pipe to Freeze???

[jrsc]

I'm working with a farmer putting in piping for transfer of digested effluent and milkhouse waste water and he would like to know how long it will take for any liquid in the pipe to freeze. I know I"m leaving out a lot of variables but how would you go about figuring this out? I'm sure it has to do with thermodynamics but I haven't kept up with that since school. Thanks for any help.

 

[MGX]

I'll bite.

What is the pipe type and size, bury depth, avg. temp of effluent and estimated sustained low air temperature?

 

[jrsc]

3" and 6" pvc pipe, 4' deep, 50 degree effluent, winter in wisconsin...I checked the plumbing code for sanitary sewer and found that there should be 1.5" thick insulation 5' to either side of the pipe to prevent it from freezing but I can't find anything on how long it will take it to freeze.

 

[RIP - VTEnviro]

I've worked in very cold climates before, specifically northern New England. If you're only going 4' deep, insulate the hell out of that thing.

We tended to bury stuff 6-7' to get around the freezing.

As for time to freeze, I guess you could always guesstimate using the specific heat of the wastewater and compare to the surrounding soils. Figure out the time for the temp to go from 50 to <32 or whatever the slop freezes at. Just a thought.

 

[snickerd3]

wow, only 4 ft deep. i ditto the insulation comment.

 

[jrsc]

The pipe is going to be insulated with 2" of insulation under 8" of concrete but the farmer wants to know how long it will take to freeze if no insulation is used.

 

[HITMANVQ35]

ok i'll try to help, I'm no expert in this area but I happen to come across this problem in the text book today

The thermal resistance of the pipe is R=(ln(2L/D)[1-ln(L/2z)/ln(2L/D)]/(2*pi*k*L)

where

L=pipe length

D=diameter outside

z=depth of pipe

k=soil thermal conductivity (typically range from 0.33-1.33 btu/hr-ft-F or 0.58 to 2.3 W/m-C)

and then heat transfer qdot = (tg-ts)/R

where ts=pipe surface temperature

tg = ground surface temperature

the source of these equations is McQuiston's Heating, Ventilation and Air Conditioning

Now from there i'm not entirely sure how to obtain time. Qdot will be in units of Btu/hr.

By quicky looking through my reference manual I came across equation for constant fluid temperature Qdot = -rho*V*Cp-(DT/Dt)

where rho = density of whatever fluid

V = volume of fluid

Cp= heat capacity

DT= change in temp

Dt=change in time.

I hope this helps. Let me know if otherwise.