# Coefficient of Permeability

This lab has two tests to find the coefficient of permeability: the constant head permeability test and the falling head permeability test.

#### Constant Permeability Test

Why is this test done?

This test is used to determine the coefficient of permeablity of a soil.  This is important in examining the movement of contaminants through soil or when characterizing flow nets.

How is this test set up?

A soil that has been air-dried is mixed with water for good compaction when it is added to the permeability device.  A porous stone is placed at the bottom of the flow chamber.  Then, soil is compacted in layers in the device.   Another porous stone is placed on top of the soil with a spring placed between the stone and the cap of the device.  The spring provides extra compaction for the soil.  In order to remove all the air and voids from the soil in the chamber, a tube was hooked up from the outflow nozzle to the water tap.  The inflow nozzle had a tube placed on the end of it which lead to the sink.  Water was then flushed through the system backwards with the air nozzle also open.  After a few minutes, the air nozzle was closed.  Water was continuously flushed through the system in order to regulate the temperature as well as to compact the soil as much as possible.  After determining that all the voids have been removed from the soil, we are now ready to begin the test.

In this test, a cone is hooked up to a tube which leads to the inflow nozzle.  Another tube that is connected to the water tap allows water to run into the tube.  In order to start the test, a constant amount of water must be in the cone at all times.  Water exits the system through an outflow nozzle at the bottom of the flow chamber.  The nozzle is hooked up to a tube which is used to collect water in a graduated cylinder.

How is the experiment performed?

The constant head test is performed by first running water through the system at a constant rate.  In order to determine this, one can examine the level of water in the cone.  If it is always at the same level, flow through the system is constant.  Now, we collected 100 mL of water in a graduated cylinder from the outflow nozzle.  We measured the amount of time necessary in order to collect 100 mL and recorded this in our data sheet.  We recorded the temperature of the water while it was in the graduated cylinder.  It was also necesary to measure the vertical distance from the level of the water in the cone to the outflow nozzle.  This value, h in our data section, was also recorded and factored into our calculation of the coefficient of permeability of the soil.  The test was performed four times in total.  Only one calculation was performed for this test, so the average value of time necessary to collect 100 mL was used in this calculation as well as the average temperature.

Results of our constant head test

Diameter of Flow Chamber = 6.327 cm
Cross-Sectional Area of Flow Chamber = A = 30.55 cm2
Height of Flow Chamber = L = 430.76 cm
Total Head Difference = h = 49.5 cm

 Test No. Time  t, ( s ) Flow  Q, ( cm3 ) Temperature ( oC ) 1 90.23 100 26.5 2 110.48 100 25 3 117.20 100 25 4 122.70 100 25 Average 110.15 100 25.38

kT = QL (100 cm3)(430.76 cm) =  0.008465 cm/s
Aht     (30.55 cm2)(49.5 cm)(110.15 s)

a = ht0.009019 =  0.8971
h20 0.01005

k20 = akt =  (0.8971)(0.0008465 cm/s)  =  0.007594 cm/s

Definitions

The coefficient of permeability of a soil describes how easily a liquid will move through a soil.  It is also commonly referred to as the hydraulic conductivity of a soil.  This factor can be affected by the viscosity, or thickness(fluidity) of a liquid and its density.  The number can also be affected by the void size, or region of non-soil, void continuity, and soil particle shape and surface roughness.  It is an important factor when determining the rate at which a fluid will actually flow through a particular type of soil.

A flow net is a graphical method by which one can characterize the flow of a liquid through a soil.  When performing the calculations associated with a flow net, it is important to know the coefficient of permeability, or hydraulic gradient, of a soil.

In this lab, the total head difference is defined as the distance from the point of the cone where water first enters the system and is at steady flow to the point at which the water is exiting the system through a flow tube and being collected in a graduated cylinder.

The value kT is the coefficient of permeability for the average temperature of the test fluid.  All coefficients of permeability are normalized to 20 oC since the viscosity of a fluid depends on the temperature at which it is.  As stated previously, the viscosity of a fluid will affect its ability to flow through a soil.

A porous stone is used to allow water to flow freely through the flow chamber.  The porous nature of the stone does not affect the flow of the water through the soil sample or out of the chamber.  However, the stone prevents any soil from washing away with the water.  This would affect the validity of the results of the laboratory session.

A void is a volume of space that is taken up by air or water in soil.

A pipet is a glass cylinder with graduated markings on the outside of the glass.  The top end of the pipette is open while the bottom of the pipette is a nozzle which, in the case of our experiment, is connected to a tube which is connected to the permeability device.  The nozzle allows one to release a known volume of liquid from the pipet.

A graduated cylinder is a glass tube which is open on end and closed on the other end.  It is used to measure the volume of a liquid.

Why is this test done?

This test is used to determine the coefficient of permeablity of a soil.  This is important in examining the movement of contaminants through soil or when characterizing flow nets.

How is this test set up?

A soil that has been air-dried is mixed with water for good compaction when it is added to the permeability device.  A porous stone is placed at the bottom of the flow chamber.  Then, soil is compacted in layers in the device.   Another porous stone is placed on top of the soil with a spring placed between the stone and the cap of the device.  The spring provides extra compaction for the soil.  In order to remove all the air and voids from the soil in the chamber, a tube was hooked up from the outflow nozzle to the water tap.  The inflow nozzle had a tube placed on the end of it which lead to the sink.  Water was then flushed through the system backwards with the air nozzle also open.  After a few minutes, the air nozzle was closed.  Water was continuously flushed through the system in order to regulate the temperature as well as to compact the soil as much as possible.  After determining that all the voids have been removed from the soil, we are now ready to begin the test.

In this test, a known volume of water is placed in a pipet.  The bottom end of the pipette is connected to a tube that connects at the other end to the inflow nozzle at the top of the flow chamber.  A tube is connected to the outflow nozzle at the bottom of the flow chamber.  This tube is used to collect a volume of water flowing out of the chamber in a graduated cylinder.  Theoretically, the volume of water flowing into the chamber from the pipette should be exactly equal to the volume of water flowing out of the chamber that is collected in the graduated cylinder.

How is the experiment performed?

The falling head test is performed by first placing a known volume of liquid in a pipet.  We needed to measure the height from the top of the amount of liquid in the pipette to the outflow nozzle.  We then opened the nozzle on the pipette and allowed a known volume of liquid to flow through the permeability device. At the same moment we record the amount of time that it took for that known volume to flow out of the pipet through the permeability device and finally to the out flow nozzle.   This volume of liquid recovered from the out flow nozzle was measured in a graduated cylinder, and should be equal to that of the volume that left the pipet.  This test was performed four times to reduce error.  All the data, including ther temperature of the out flow liquid, was collected into and recorded in a data table.

Results of our falling head test

Diameter of Flow Chamber = 6.327 cm
Cross-Sectional Area of Flow Chamber = A = 30.55 cm2
Height of Flow Chamber = L = 14.1 cm
Diameter of Standpipe = 1.44 cm
Cross-Sectional Area of Standpipe = a = 1.6286 cm2

 Test No. h1,  ( cm ) h2,  ( cm ) Time t,  ( s ) Qin,  ( cm3 ) Qout,  (cm3 ) Temperature, (oC ) 1 84.5 34.6 10.73 81.27 72.00 24.0 2 89.3 35.0 11.45 88.43 69.00 24.0 3 86.7 35.0 9.73 84.20 81.00 24.0 4 85.3 34.5 9.67 82.73 86.00 24.0 Average 86.45 34.78 10.40 NA NA 24.0

a = (0.00914)/(0.01005) = 0.9095

kT = aL ln (h1) = (1.6286 cm2)(14.1 cm) ln (86.45 cm) =  0.06581 cm/s
At     (h2)     (30.55 cm2)(10.40 s)       (34.78 cm)

k20 = akT = (0.9095)(0.06581 cm/s) = 0.0599 cm/s

Definitions

The coefficient of permeability of a soil describes how easily a liquid will move through a soil.  It is also commonly referred to as the hydraulic conductivity of a soil.  This factor can be affected by the viscosity, or thickness(fluidity) of a liquid and its density.  The number can also be affected by the void size, or region of non-soil, void continuity, and soil particle shape and surface roughness.  It is an important factor when determining the rate at which a fluid will actually flow through a particular type of soil.

A flow net is a graphical method by which one can characterize the flow of a liquid through a soil.  When performing the calculations associated with a flow net, it is important to know the coefficient of permeability, or hydraulic gradient, of a soil.

In this lab, the total head difference is defined as the distance from the point of the cone where water first enters the system and is at steady flow to the point at which the water is exiting the system through a flow tube and being collected in a graduated cylinder.

The value kT is the coefficient of permeability for the average temperature of the test fluid.  All coefficients of permeability are normalized to 20 oC since the viscosity of a fluid depends on the temperature at which it is.  As stated previously, the viscosity of a fluid will affect its ability to flow through a soil.

A porous stone is used to allow water to flow freely through the flow chamber.  The porous nature of the stone does not affect the flow of the water through the soil sample or out of the chamber.  However, the stone prevents any soil from washing away with the water.  This would affect the validity of the results of the laboratory session.

A void is a volume of space that is taken up by air or water in soil.

A pipet is a glass cylinder with graduated markings on the outside of the glass.  The top end of the pipette is open while the bottom of the pipette is a nozzle which, in the case of our experiment, is connected to a tube which is connected to the permeability device.  The nozzle allows one to release a known volume of liquid from the pipet.

A graduated cylinder is a glass tube which is open on end and closed on the other end.  It is used to measure the volume of a liquid.