The water percolation experiment is an example of a flowrate being a balance between a driving force and a retarding force:
Flowrate = Driving potential/resistance
For water flow, this law governs how fast water will flow out of your faucet, whether the water soaks in or runs off when you water your lawn, and how fast you can pump water from a well, and how fast Zone 7 can recharge the aquifer used in our valley to store water for drought years. We call it Darcy’s law.
The same basic law governs the flow of electricity in and through your house (Ohm’s law), the flow of heat through your wall (Fourier’s law), and the terminal velocity of an object falling from the sky.
In this case, water wants to drain out of the bottom of the tube. The time that takes depends on the stuff that gets in its way—primarily the sand or gravel in the tube, and to a lesser extent, the restriction associated with the valve.
In this exhibit, we ask the visitor which tube they expect will drain faster, and why. Most people guess that it will drain faster through the larger gravel, but they don’t really understand why. We’ll get back to that.
In this experiment, the object is to open a valve and measure the time for the water to drain between two marks on the tube. Here are some data taken with this simple apparatus:
First, notice that replication of the experiments is important. There are a few details missing, like the volume of the tube, but you can also see that the time to drain through the coarse gravel is less, and the corresponding flowrate is greater.
About 90 years ago, engineers with names of Carman and Kozeny figured out that the flow resistance through a porous bed was related to the surface area of the material in the bed. The small grain diameter means more surface area to cause drag, and they figured out that the flow rate was proportional to the square of the diameter. So we can make this plot of the data, which follows a straight line:
Most people think the flow is faster through the larger gravel because it has more space, but that is not quite correct. The total space in the three beds, called porosity, is about the same. To show that is true, we came up with a second experiment. Two jugs of the same size are filled with large and small marbles, respectively, and weighed. They are then filled with water and weighed again. The mass of the water is the same. Even though each space between the small particles is smaller, there are more spaces and the total space is the same. In the picture shown, both large and small marble beds have a porosity of about 39%, with is the typical value for random packing. These same packing relationships hold down to the atomic level, where scientists density to measure the void space between atoms in various types of crystals.