Derivation of formula for hydraulic conductivity of soil
Sun, 02/15/2009 - 10:21
I am looking for the derivation of formula for hydraulic conductivity of soil. We have this pump station and two observation wells. I try to look for books and the internet. I found the formula, but not the derivation of it. The formula says...
k = q ln (R2/R1) / pi (h2^2 - h1^2)
Thank you.
S P O N S O R E D L I N K S
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Sun, 02/15/2009 - 17:52
#1
Re: Derivation of formula for hydraulic conductivity of soil
I don't understand why you need to know the derivation of this formula. If you are a field engineer then you are one of a kind.
I just happen to gave a lecture to the students of Gillesania Engineering Review Center this week about the topic Flow of Water through Soils. According to Darcy, the velocity of water flowing through soils is v = ki where k is the hydraulic conductivity and i is hydraulic gradient. Using this equation of velocity, we can derive the formula.
Notation:
v = velocity, Q = discharge, A = area of soil in which the water flows, t = time, h = head lost between two points, R = radial distance from pumping well and observation well.
Q = vA = kiA = k(h/R)A and A = 2πLh
If we take the incremental head lost h = dh then R = dR in i = h/R, the above equation will become
Q = k(dh/dR)(2πRh)
Q (dR/R) = 2πk (h dh)
Integrating both sides will give you the desired equation.
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Mon, 02/16/2009 - 16:52
#2
Re: Derivation of formula for hydraulic conductivity of soil
Thanks RTFVerterra, or shall I say sir RTFVerterra. I was able to arrive to the formula through the integrable equation you gave but I don't understand why A = 2πLh. As far as I can recall, that formula is the area of the side of the cylinder. It is not clear for me why you use that to the area of the soil.
RTFVerterra wrote:
I don't understand why you need to know the derivation of this formula. If you are a field engineer then you are one of a kind.
Part of the job, nothing personal.
Tue, 02/17/2009 - 16:17
#3
Re: Derivation of formula for hydraulic conductivity of soil
RTFVerterra wrote:
According to Darcy, the velocity of water flowing through soils is v = ki
Allow me to interrupt. Who is Darcy?
Wed, 02/18/2009 - 15:12
#4
Re: Derivation of formula for hydraulic conductivity of soil
Jason wrote:
... I don't understand why A = 2πLh. As far as I can recall, that formula is the area of the side of the cylinder. It is not clear for me why you use that to the area of the soil.
You are correct by saying that the formula is the area of lateral side of right circular cylinder. Water enters into the pumping well from a radial distance L, the depth of water (water table) at L is h. I hope its clear.
Lj wrote:
Allow me to interrupt. Who is Darcy?
Henry Philibert Gaspard Darcy (June 10, 1803 – January 3, 1858) was a French engineer who made several important contributions to hydraulics.
More about Henry Darcy and his work.
