Chapter 10

Darcy's Law and Hydraulic Conductivity

Water movement in soils is governed by physical laws. As described in Chapter 9, water movement follows a course of decreasing energy. In this exercise we will examine water movement through soil.

Infiltration is the movement of water into soil from the surface. Infiltration rate is the rate at which water will enter a soil under specified conditions. Infiltration rate is usually expressed as centimeters per hour. Water infiltration is largely governed by the surface properties of the soil. A soil high in organic matter, having good structure, and of medium to coarse texture will usually have a rapid infiltration rate. Many other factors, such as roughness of the ground surface, vegetative cover, and slope, will also affect infiltration. Water movement within soil also affects infiltration. Water already in the soil profile must move downward before more water can enter at the surface.

The ease with which water moves within a soil is termed permeability or hydraulic conductivity. Permeable soils conduct water readily through their mass. Other soils may conduct water slowly or have restricting layers or horizons which limit or prevent downward movement of water. Soils or soil layers which do not conduct water, at all, are termed impermeable. Permeability, like infiltration, is largely determined by texture, structure, and organic matter content. Other factors, such as the dominant ion on the exchange complex, presence of chemical cementing agents, and type of clay minerals present, also influence permeability.

Water movement through porous media (including soil) is governed by Darcy's Law. Below is the expression of Darcy's Law for saturated conditions.

Q = K ath Where: Q = water flow (or volume of output)

l (cm3)

K = hydraulic conductivity (cm/sec)

a = cross-sectional area of the soil


t = time (s)

h = water height (or 'head') (cm)

l = length of soil column (cm)

The driving force for water movement under saturated conditions is the height of water in the soil column. Darcy's Law can also be expressed for unsaturated conditions, but the driving force for water flow is then a potential gradient. The equation for saturated conditions shows that water flow decreases with the length of the soil column, but increases with the cross-sectional area of the soil, height of water (head pressure), and time. The proportionality constant (K) in the equation is called the hydraulic conductivity or soil permeability. Hydraulic conductivity is a measure of the soils' ability to conduct water. This factor is dependent on the parameters which affect water flow through soil, such as texture and structure. Water flow through a soil increases as the hydraulic conductivity increases.

The equation can be expressed in terms of hydraulic conductivity, K = Q1/(ath). With Darcy's Law expressed in this form and using the apparatus shown in Figure 10.1, the permeability of the soil can be determined. The cross-sectional area (a) and the length of the soil column (1), the height of the water column (h), and the time (t) can all be predetermined. The amount of water passing through the soil column (Q), in the predetermined time, is simply measured using a graduated cylinder and the hydraulic conductivity (K) calculated.

Figure 10.1. Permeameter used to determine hydraulic conductivity (K) of saturated soils in the laboratory.

Water Movement in Soil - A Film

The film demonstrates water movement in soils under a variety of conditions. How water flows, why it flows, and the differences between saturated and unsaturated water flow is illustrated. The affects of soil texture, structure, and porosity on water movement are also demonstrated. Carefully watch and take note of the following demonstrations as seen in the film.

1. Capillary action

2. Ceramic blocks

3. Glass plates

4. Flow, from furrow to soil

a. gravity vs capillary action

b. influence of sand layer

c. influence of clay layer

5. Flow, through sand vs soil aggregates

6. Flow in channels

a. exposed channel, saturated flow

b. buried channel, unsaturated flow

7. Flow, through moist vs dry sand

8. Sandy loam vs loam vs clay loam

a. rate of water entry

b. water retention

c. erosion control

9. Direction of water movement

a. movement of soluble salt

10. Water movement in potato hills

a. coarse vs fine aggregates

11. Soil management practices

a. buried straw layer

b. straw mixed throughout soil

c. buried root channels

d. vertical mulching

Laboratory Exercise

A. Darcy's Law and Hydraulic conductivity

1. Take measurement of cross-sectional area (a), height of water column (h), and length of soil column (l) on each of the soil permeameters.

2. Time (t) the collection of a measurable quantity of water (Q) from each permeameter. The time of collection will vary depending upon the hydraulic conductivity of each soil.

3. Calculate hydraulic conductivity (K) for each soil column.

4. Compare the results among the different soil textures and between the duplicates for each soil texture.

B. Water Movement in Soil - A Film

1. Carefully watch the film and make notes of the demonstrations as they are shown.

2. Review the list of demonstrations shown above.

3. Read the question list and incorporate the answers into the discussion section of the laboratory report.

Question List

1. How is infiltration dependent on permeability?

2. What are the factors which make hydraulic conductivity unique for each soil?

3. What is the driving force for water movement in a saturated soil? an unsaturated soil?

4. What forces account for the retention of soil water?

5. What forces account for the downward movement of soil water?

6. a) In the demonstration in which fine-textured soil overlaid a layer of sand, why didn't the water immediately flow into the sand when the wetting front reach the sand?

b) What were the wetness conditions in the overlying fine-textured soil when the water did enter the sand?

7. a) In the demonstration in which fine-textured soil overlaid a layer of clay, did the clay layer wet up as fast as did the sand layer after the wetting front reached it? Explain.

b) Explain the difference in the rate of water transmission through the sand and the clay layer.

8. In the demonstration with two sand channels, one surrounded by fine-textured soil and one exposed to the water furrow, describe, in each case, where saturated flow and unsaturated flow occurred.

9. Under what conditions will water flow into and through open, but buried, pores such as worm holes and old root channels?

10. What important limitation on the effectiveness of the practice of deep chiselling to increase water intake rate is suggested by the demonstration of saturated flow through sand and straw channels?

11. Under what conditions will water flow into drainage tiles placed in the soil?


Chapter 10

A. Darcy's Law and Hydraulic Conductivity

Soil (a) (h) (l) (t) (Q) (K)

--------- cm2 ------ cm ------ cm ------ s ------ cm3 -----

Sand 1

Sand 2

Loam 1

Loam 2

Clay 1

Clay 2

B. Water Movement in Soil - A Film