Water loss in a storage pond
Water loss in a storage pond
(OP)
A dairy pumps water into a large lagoon. Typically, the pressure head averages 10'.
Currently, they lose a lot of water due to permeable soil at the base.
They want to empty the lagoon and emplace a clay liner. Soil samples have been sent, and a K value is requested from the lab.
My task is to calculate the before and after water loss as part of an economic feasibility assessment.
However, in reviewing Darcy's law, it looks like I need to take two hydraulic head measurements in the field. Am I correct?
I have this equation: Q= -KAi
i= (h1 - h2)/L
h1 and h2 are the two hydraulic head measurements, and L the distance between them.
Is there a way to calc this with just the K value?
Currently, they lose a lot of water due to permeable soil at the base.
They want to empty the lagoon and emplace a clay liner. Soil samples have been sent, and a K value is requested from the lab.
My task is to calculate the before and after water loss as part of an economic feasibility assessment.
However, in reviewing Darcy's law, it looks like I need to take two hydraulic head measurements in the field. Am I correct?
I have this equation: Q= -KAi
i= (h1 - h2)/L
h1 and h2 are the two hydraulic head measurements, and L the distance between them.
Is there a way to calc this with just the K value?





RE: Water loss in a storage pond
See http:
RE: Water loss in a storage pond
Thanks for the link. Yes, this is a steady state situation.
How do I account for the 10 feet of water? This will accelerate infiltration.
Is there another equation?
RE: Water loss in a storage pond
The gradient may be less than 1 if the groundwater table is shallow & "mounding" occurs. This is discussed in that document I referenced.
RE: Water loss in a storage pond
Today I learned there is a very high water table on this dairy. They install drain pipe at 8' below grade to drain water (which otherwise stymies crop growth).
So, there will not be a static state. water is constantly moved off-site by the drains.
So, how now to calculate i for my Darcy's equation, Q=-KAi ?
Alternate methods to calculate water loss will be appreciated.
Thanks.
RE: Water loss in a storage pond
RE: Water loss in a storage pond
We have exact evaporation rates calculated per local weather averages and extremes.
Yes, the pressure head in this case is depth.
Can you please elaborate on " a flow net for a unit width slice" ?
If you can give the reference for this procedure also, it is appreciated. Thanks.
RE: Water loss in a storage pond
The volume of water that would move vertically from the mudline to the drain would be calculated using Darcy's law as such:
Q=kiA
Using the drain pipe elevation as the datum, the gradient would be:
DeltaH/DeltaL where DeltaH is the difference in head between the mudline and the pipe. The head at the mudline is 18 ft (8 ft of elevation head and 10 ft of pressure head) and the head at the pipe would be zero (there is no pressure head and it's the datum). Delta L would be 8 ft. So the gradieint is 18/8, which is 2.25. The flow would then be:
Q=4x10E-3(2.25)45,560 = 392 cfm (about 3,000 gpm!)
Let's now say that you place a 6-in thick clay liner with a hydraulic conductivity of 4xE-6 ft/min. Under this scenario, you would then use Darcy's law for the liner thickness, which would have a completly different gradient - you'd have all of the head loss in the liner. Using the bottom of the liner as the datum, you'd have 10.5 ft of pressure head attenuated in 0.5 ft, which is a gradient of 21. For this case:
Q= 4xE-6(21)43,560 = 3.66 cfm (27 gpm)
Hope this helps.
f-d
¡papá gordo ain't no madre flaca!
RE: Water loss in a storage pond
v = k*i
where i = (H+d)/d
v = specific discharge
k = hydraulic conductivity (given by the lab)
H = total head (water depth)
d = liner thickness
RE: Water loss in a storage pond
Great posts. This is what I needed. Thanks very much.
-DD
RE: Water loss in a storage pond
RE: Water loss in a storage pond
You make a good point. The local inspector and my boss are likely thinking of the industry standard for effluent lagoons.
However, this lagoon is fresh water. I don't know if 6" thickness will be required.
However, there is not a specific "leak". The entire area drains well. The liner is intended to prevent water loss, and thereby reduce the cost of pumping water into it.
Thanks,
-DD
RE: Water loss in a storage pond
You can follow my example and use whatever thickness you want to.
f-d
¡papá gordo ain't no madre flaca!
RE: Water loss in a storage pond
This is a freshwater storage pond. The original designer did not account for the loss.
The pond will be drained and a clay bottom will be placed and compacted.
-DD
RE: Water loss in a storage pond
RE: Water loss in a storage pond
All dairies need water storage. This is usually done with tanks. This dairy has a fresh water pond.
RE: Water loss in a storage pond
Darcy's equation can be re-written for this situation as:
d=H*k/(v-k), where
d = pond liner thickness
H = water depth in pond
k = hydraulic conductivity (coefficient of permeability)
v = specific discharge
If k>v, then the answer is a negative thickness. What do you (or I) do with a negative answer? Is it valid? Should (v-k) be an absolute value?
-RR
RE: Water loss in a storage pond
Tim Grote - The Irrigation Engineers.
www.irrigationengineers.com
RE: Water loss in a storage pond
The ponds I deal with are runoff control ponds and are required to have a minimum of 12" of compacted soil liner. If your pond is a runoff control pond, check with you local environmental protection for required standards. If your pond is a fresh water pond as in the above situation, then there are probably no required construction standards. If your coefficient of permeability is low enough, then theoretically a liner thickness is not required and you would have very little seepage. That being said, the coefficient of permeability was determined by compacting the liner material to a specified compaction and moisture content. Your liner no matter the thickness should be constructed to the same compaction and moisture. The thicker the liner, the lower the seepage rate. If I were you, I would still recommend at least a 6" lift, and make sure you have proper compaction and moisture to match what the lab tests indicated.
RE: Water loss in a storage pond
Draining a pond and doing the liner can run into problems with mud causing significant construction problems. I'd look very carefully at this draining option before I jump in and do it. Asking you local contractors about this idea may help you decide.
RE: Water loss in a storage pond
v=ki, where
v=Darcy's velocity
k=hydraulic conductivity
i=hydraulic gradient
Hydraulic gradient is expressed as:
DeltaH/DeltaL, were
DeltaH is the change in head along the flow path
DeltaL is the length of the flow path.
For a liner system, we have to now make some assumptions. Let's say at the top of the liner, the full head is the height of the pond water. Let's call this "H." Let's also say the full value of DeltaH throughout the flow path equals this value "H" (i.e., there is no tailwater head).
We can now say:
v=k*H/L, where "L" is the thickness of the liner.
Reconfiguring terms you'd then get:
L=(k*H)/v
I have no way of knowing what your required value of "v," but from here you should be able to work something up. . .
f-d
¡papá gordo ain't no madre flaca!