Estimate the velocity of the groundwater flowing from a point 1000 feet from a creek. The point is 30 feet above the surface of the creek and the permeability of the subsurface is approximately 10-5. Approximately how long would it take the groundwater to reach the creek?
Isn't this Darcy's law?
I would seem to me that the velocity would be a function of many factors, including the height above the surface, the distance from the creek and the "permeability" of the subsurface, as seen in the data that you show.
You do not state how these are related and connected, and it would be unreasonable to expect anybody here to be familiar with such a topic.
Are they stated in the problem?
Darcy's law for the volume flow rate is explained at:
http://biosystems.okstate.edu/Darcy/LaLoi/Basics.htm
For the velocity, you also need to know the porosity
bobpursley and drwls,
how presumptuous of me to assume that nobody would be familiar with this.
I forgot that you are engineering and physics experts.
This simple "number-cruncher" says sorry.
No problem. I'm a presumptuous math contributor. :-)
To estimate the velocity of groundwater flowing from a point to a creek, we can use Darcy's Law, which states that the velocity of groundwater (V) is equal to the hydraulic conductivity (K) multiplied by the hydraulic gradient (I).
First, let's calculate the hydraulic gradient:
Hydraulic gradient (I) = elevation difference / distance
The elevation difference is given as 30 feet, and the distance is given as 1000 feet.
I = 30 ft / 1000 ft = 0.03
Next, let's calculate the velocity using Darcy's Law:
V = K x I
The permeability of the subsurface is given as 10-5.
V = (10-5) x 0.03
= 3 x 10-7 ft/s
Now, to estimate how long it would take for the groundwater to reach the creek, we need to consider the distance between the point and the creek. However, information about the distance from the point to the creek is not provided in the question, so we cannot estimate the time it would take for the groundwater to reach the creek without this information.