Applying Darcy's law

[deleted-328367]

Hi, so I have a project and I need to apply darcy's law to my results. The information I have is: flow rate (mL/sec), inlet/outlet height and distance between the inlet and outlet. For the apparatus, I had 2 bottles set up, one half filled with sand and the other was for water collection. Then, I had a tube connecting the two bottles. I poured 500 mL of water into the bottle filled with material and recorded the amount of water that flowed out in a certain amount of time.

[norman40]

Hi jantjt120,

What is the application of Darcy’s Law that you have in mind? From your description it seems that you built an apparatus that allows water to flow from a known height through a bed of sand and into a collection vessel. And you’ve used this apparatus to measure the flow rate.

Darcy’s Law states that the flow rate of a fluid in a porous medium (like the sand in your set-up) is proportional to the pressure differential across the medium. In your apparatus the pressure differential is dictated by the height of the water above the sand. The flow rate is also governed by properties of the porous medium. These properties include how tightly the material is packed and the particle size of the material.

You might use your apparatus to find the “hydraulic conductivity” of the sand bed that you used. Refer to the section on one-dimensional flow at the following site:

https://bae.okstate.edu/faculty-sites/D ... Basics.htm

You might also try varying the height of your water reservoir to observe the effect of pressure on flow rate.

I hope this helps and good luck with your project. Please post again if you have more questions.

A. Norman

[deleted-328367]

I used the formula Q=KA [(h1-h2)/L] to find the hydraulic conductivity. Is this correct?

Where:
Q=flow rate (Measured in m3/s or cm3/min)
K=hydraulic conductivity (Commonly referred to as permeability. Measured in m/s or cm/min)
A=area through which the water is flowing
L=distance between h1 and h2
h1=inlet height
h2=outlet height
*(h1-h2)L is the hydraulic gradient
(the height difference between h1 and h2 equals the pressure)

[norman40]

Hi jantjt120,

I think you have the correct equation. And you are correct that “K” is often called the permeability of the porous medium through which the fluid flows.

Please note that “L” is not always the distance between h1 and h2. Rather, “L” is the length of the flow path through the porous medium. The inlet and outlet heights are independent of the porous medium path length. The difference between inlet and outlet heights is a distance that is proportional to the pressure difference across the porous medium.

I’ll respond here to your other post from yesterday on this topic to keep everything on the same thread.

I agree with you that Darcy’s Law can be used in engineering and hydrodynamics. Does your science fair include these categories? The high school science fairs that I judge have broader divisions including physical science, earth science, chemistry and biology. I think your project could fit into physical science or physics.

I hope this helps and good luck with your project. Please post again if you have more questions.

A. Norman

[deleted-328367]

Thank you and sorry, I'm new to sciencebuddies, so I don't really know how everything works.

For the challenges the options are: Discovery, energy, environment, health, information (communication, use of information, technology) , innovation and resources (better way to use resources). I was thinking our topic would go under environment, but I'm not exactly sure.

Also, regarding the different categories, I narrowed down the options to: Engineering (materials and bio-engineering), environmental sciences/management, mathematical sciences and physics and astronomy. I believe the best choice would be physics and astronomy or environmental sciences/management.

[norman40]

Hi jantjt120,

I agree with you that your project might be categorized as physics or as environmental science. If your project is about how water moves through sand or other soils environmental science may be the better category choice. But if your project is more about the mechanics involved with flowing water, physics might be more descriptive.

I hope this helps. Please post again if you have more questions.

A. Norman