The concept of permeability, the ease with which fluids flow through a medium (rock or sediment or sand), is difficult to get across; however it is important for people to understand what permeability is if they are to understand how fluids move in the earth, including in local watersheds.
Here we provide teaching materials about permeability, how it relates to porosity, and how it is relevant to our local water systems, for children in grades 5 through 12, and to provide research opportunities at high school and undergraduate levels.
The materials are presented as two laboratory demonstrations or exercises. Ideas about where these demonstrations best fit relative to the Massachusetts Science and Technology/Engineering Curriculum Framework are provided to help teachers decide how best to incorporate these ideas into their existing curriculum.
Laboratory demonstration/exercise #1: what is permeability, and how does it differ from porosity? Is there a direct relationship between the two?
a thick sponge
a graduated cylinder
beaker of water
two identical clear plastic cups with vertical sides
two identical tubes of similar diameter to cups
fine-mesh screen (that gravel does not pass through)
electrical tape or duct tape
knife or fine saw to cut sponge
pan to catch water
- Cut piece of sponge to diameter of clear plastic cup and insert into cup, filling to a level that should then be marked on the plastic cup (see Fig. 1a).
- Place a mark on the second cup at the same level as that marked on the cup with the sponge in it. Fill the second cup with water to the level of the mark.
- To determine the volume of the cups up to the marked levels, pour the water from the second cup into the graduated cylinder, and record this volume, which is Vm, the volume that will be filled by sponge plus pore space or gravel plus pore space. Leave the water in the cylinder.
- Fill the second, now empty, cup with fine gravel up to the level of the line.
- Pour just enough of the water from the graduated cylinder into the cup with the gravel to fill all of the space between the grains, but do not let water fill any space above the mark. Now record the amount of water remaining in the graduated cylinder, which is the volume of the gravel. Subtract the volume of the gravel from Vm (the volume of the gravel plus pore space) to calculate the porosity of the gravel, Pg.
- Now refill the graduated cylinder to Vm. Pour just enough of the water from the graduated cylinder into the cup with the sponge to fill all of the pore space in the sponge, but do not let water fill any space above the mark. Now record the amount of water remaining in the graduated cylinder, which is the volume of the sponge. Subtract the volume of the sponge from Vm (the volume of the sponge plus pore space) to calculate the porosity of the sponge, Ps.
- Compare Pg and Ps. Which is larger?
- Now cut a piece of sponge and place it in one of the two tubes. Tape a piece of fine mesh at the base of the tube to prevent the sponge from falling out of the tube. Tape a piece of fine mesh at the base of the second tube (to prevent the fine gravel from falling out of the tube) and fill with gravel.
- Place the two tubes mesh side down into a tray ( to catch water coming through mesh), and pour enough water into each tube to saturate the sponge or gravel.
- Fill the graduated cylinder with 50 ml of water. Lift up the tube with the gravel and pour the 50 ml of water into the tube and time how long it takes for the water to pass through the sponge (Tg). Now do the same with the tube with the sponge in it (Ts).
Compare Tg and Ts. Did the water pass more easily through the gravel or the sponge? Which is more permeable?
Compare Pg and Ps. Is the porosity of the sponge greater than the porosity of the gravel?
Is there a simple relationship between porosity and permeability?
The demonstration provides examples of two materials with similar porosities, but very different permeabilities. Even though the porosity of the gravel is less than that of the sponge, water flows much more easily through the fine gravel compared to through the sponge.
Laboratory demonstration/exercise #2: Constructing and using a permeameter
A clear plastic tube of diameter 3 to 6 cm and length ~1 meter
An end cap for the tube
Piece of fine mesh that is greater than the area of the tube opening
Chicken wire with 13 mm (1/2 inch) holes – ~1 square foot
Very fine wire - ~1 foot length
Tygon tube, ~1 meter long
Drill and bit of same diameter as tube connector
Fine gravel or sand
2 one liter containers
2 buckets of water
A marking pen
Constructing the permeameter:
- Cut a 3 cm wide strip that is slightly shorter than the perimeter of the tube. Use it to create a 3 cm tall cyclinder that fits inside the tube (use wire to tie the top and bottom of the edges together)
- Cut a circle of chicken wire that is slightly smaller than the circular area of the tube and place it on top of the chicken wire 3 cm tall cylinder. Use wire to attach this “top” to the chicken wire tube.
- Cut a circle of fine mesh that is slightly smaller than the area of the tube and attach it using wire to the circular chicken wire “top” of the chicken wire tube. Set aside.
- Drill a hole 1 cm up from the base of the tube.
- Cut away a slit the width of the hole into the chicken wire tube from the base up – the slit should be of height 1 cm plus the width of the hole.
- Insert the chicken wire tube into the tube so that its base is level with the base of the tube, and so that the cut-out slit coincides with the hole drilled in the tube.
- Insert one end of the tube connector into the hole.
- Put the end cap onto the base of the tube (but you will need to cut away a slit so that it fits around the tube connector).
- Use silicone sealant around the outside of the tube connector to prevent water leakage. Wrap electric tape around the end cap and the nozzle.
- Attach tygon tubing to tube connector.
Using the permeameter:
- Mark the level of the top of the screen plus fine mesh on the outside of the tube. This is “Lb”.
- Pour fine gravel or sand into the tube to a level about 20 to 30 cm above “Lb”. This level is “Lt”, and Lt-Lb is the thickness of the permeable medium (in this case sand or gravel).
- Raise the end of the tubing to a level near the top of the tube to prevent out flow of water, and fill the tube with water to a level about 20 cm above the top of the gravel/sand. Mark this level as “htop”.
- To measure the hydraulic conductivity of the medium (sand or gravel), have one person pour water at a constant rate into the top of the tube (keeping the water level at “htop”) while a second person lowers the end of the tubing to a level “hout” below “htop” and lets the water flow into a bucket. The difference between htop and hout is the hydraulic head, ∆h.
- To measure the hydraulic conductivity, K, once the flow rate is fairly steady, time how long it takes for one liter of water to flow through the medium (see Fig. 2). To do this, have a third person start a stop watch while placing the open mouth of the one liter container beneath the opening of the tube. Stop the stopwatch when the level of water in the container reaches the one liter mark*.
- Repeat the measurement of flow rate for the same “hout” level several times.
- Then lower the tube even more, so that “htop” – “hout” is larger, and the flow rate faster, and again measure how long it takes for one liter of water to flow through the medium. Repeat several times. The flow rates will be in units of liters/second.
*Make sure the 1 liter mark on the container is accurate: Use the graduated cylinder and measure exactly 1000 ml of fluid and pour into container. Use a marker to mark the 1 liter level on the container.
Create a table with columns Lt, Lb, ∆l (which is Lt-Lb), htop, hout, ∆h (which is hout-htop), time (for one liter of fluid to fill container), Q (=flow rate in liters/second, or 1/time), and A (area of tube = πr2, where r is the radius of the tube). In a final column, tabulate the calculated hydraulic conductivity (K = -(Q/A)( ∆l/∆h)).
What is hydraulic head? (It is the difference between htop and hout, and is proportional to the pressure difference that drives the flow).
How is the head related to the flow rate? (they are proportional, with the hydraulic conductivity times area (A) divided by the layer thickness (∆l ) being the proportionality constant).
Does hydraulic conductivity change when the head changes? (No, it shouldn’t. It is a function of the medium).
How does permeability differ from hydraulic conductivity? (Permeability is the ease with which a fluid passes through a medium, and it will differ depending on the density and viscosity of the fluid. For water, the hydraulic conductivity K = (kρg)/µ)
Flow rate of fluid (volume/time or m3/s) = Q
Area across which fluid flows (m2) = A
k = permeability of medium
ρ = density of fluid (kg/m3)
µ = dynamic viscosity of fluid (Pa s)
g = gravitational constant (m2/s)
when considering water flowing through the ground,
K = hydraulic conductivity = (kρg)/µ
P = pressure = ρgh in a column of interconnected fluid
Darcy’s Law:Q/A = -(k/µ)(∆P/∆l) = -((kρg)/µ)(∆h/∆l) if the fluid is water, so Q/A = -K(∆h/∆l)
The hydraulic conductivity of a medium (e.g., sand) can be calculated by measuring the volume flow rate Q through a tube of area A with a thickness ∆l of some medium, subject to a hydraulic head, ∆h.
Using the permeameter we can
- measure Q, A, and ∆l, and ∆h to calculate K.
- vary ∆h and see how it changes Q.
- change the medium (from sand to gravel) and measure K for a different medium.
Ideas for experiments using the permeameter:
1. Use it to better understand the concept of a pressure or hydraulic “head” (see figure 2). The students will be able to demonstrate through their measurements that the flow rate through the layer of sand or gravel differs depending on the “head,” but that the hydraulic conductivity or permeability is the same. In other words, flow rate is proportional to the pressure difference, or hydraulic “head,” and the proportionality constant is termed the permeability, or, for situations where the fluid is water, the hydraulic conductivity.
These concepts are important for understanding what controls fluid flow within watersheds, near ponds, and near septic systems. For example, water level affects the head which affects flow rates.
2. Use the permeameter to investigate how permeability differs for different, materials, e.g., sand, gravel, soil.
Relationship of these materials to the Massachusetts Science and Technology/Engineering Curriculum Framework, and to science instruction in the Falmouth Public Schools:
Our proposed strategy for teachers using our web site is to have the concepts of porosity and permeability introduced in grade 5, using lab demonstration #1, when, according to the Massachusetts Science and Technology/Engineering Curriculum Framework, “different properties of soil, including color, texture (size of particles), the ability to retain water” are taught.
In grade 8, when classes at the Lawrence Middle School in Falmouth have a project where they monitor water chemistry, groundwater levels, and invertebrate diversity in two ponds on school property, the lab exercises can be used to understand why they are measuring the groundwater levels. The exercises will help them to better understand why groundwater flows, and how water levels affect this flow. They can use the permeameter to learn about the concept of the pressure difference, or hydraulic “head” that drives fluid flow.
For grade 9 earth science classes, both laboratory exercises address the Massachusetts Science and Technology/Engineering Curriculum Framework, which includes “3. Earth Processes and Cycles 3.4 Explain how water flows into and through a watershed. Explain the roles of aquifers, wells, porosity, permeability, water table, and runoff.” Students can use the permeameter to measure the permeability of different materials.
For grade 12 physics students, lab exercise #2 is designed to be a starting point for a student’s science fair project.
Freeze, R. and J.A. Cherry, Groundwater, Prentice Hall: New York, 1979.
Turcotte, D.L., and G. Schubert, Geodynamics: Applications of Continuum Physics to Geological Problems, John Wiley abd Sons: New York, 1982.