Water in the hole

November 14, 2007 6:34 PM

Say you're going to dig a hole...a deep hole...a hole that goes below the water table. I know it's going to fill with water, but the question is, at what rate?

I regret in advance making my first AskMe on such an excessively boring topic, but I've been trying for days to answer this question, to no avail. Somehow, my engineering books don't seem to say anything about it, and google too, is leaving me empty handed.

I know the dimensions of the hole, and the height of the water table. I also have a permeability coefficient for the soil in the water table, if it helps.

Is it just the permeability coeff * surface area of the hole or something? Any answers, ideas, or resources would be much appreciated.

posted by gueneverey to technology (5 comments total)

I think the only really correct answer is: it depends, and if you really want to know, sink a test bore.
posted by flabdablet at 6:46 PM on November 14, 2007

You know the permeability, so you can figure out the rate of seepage with Darcy's law. Multiply that by the area of the sides (and bottom) of the hole and you have your flow rate.

Depending on the depth of the hole relative to the elevation of the water table, you might have to work the sides and bottom separately to account for the different hydraulic gradients.

See chapter 4 in Fundamentals of Geotechnical Engineering by Das.
posted by Uncle Jimmy at 6:52 PM on November 14, 2007

It depends not just on the permeability coeff but also the degree of saturation etc.

More info here:
http://physics.uwstout.edu/geo/perm_dewat.htm

IOW it's really impossible to say without detailed hydrology information. You could have the same permeability, the same hole, and radically different fill rates.

For example, I live on the top of a hill and holes drilled here (like wells) fill insanely fast. We have unlimited water. It's because we are right next to a massive watershed wetland with porous rock beneath, so drilling a hole is like punching a hole in a bag of water.

About 10km away, where my brother in law has a well, they have the same rock/permeability but the fill rate is much lower presumably because there's no big local body of water providing the pressure.
posted by unSane at 6:55 PM on November 14, 2007

hmm, I was kind of afraid that might be the answer. Without doing an in depth study, is there any way I can get some rough estimate? Or even a rate for an example area? (I don't see how I can apply Darcy's law, since I don't know the hydraulic gradient)

Also, the area in question is close to a river, which I forgot to mention before. And this is not deep like a well, but deep like 9 feet.
posted by gueneverey at 7:11 PM on November 14, 2007

Household wells are usually rated as producing a certain number of gallons per minute. This varies even between wells that are fairly close (distances measured in hundreds of feet) to each other. You can probably get a median rate from asking people in the area with wells, if it's not important that this be the exact number for your hole in the ground.

Wells usually go as deep as they need to for water. Your hole will be deep like a 9 foot well.
posted by yohko at 11:56 PM on November 14, 2007