1 groundwater hydrology and contaminant transport ceve 518 p.c. de blanc c.j. newell 1.porosity and...

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GROUNDWATER HYDROLOGY AND CONTAMINANT TRANSPORTCEVE 518

P.C. de BlancC.J. Newell

1. Porosity and Density Continued

2. Saturation and Water Content

3. Darcy’s Law

4. Hydraulic Head

Lecture 3

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3. Darcy’s Law

4. Hydraulic Head

Lecture 3

3





3. Darcy’s Law

4. Hydraulic Head

Lecture 3

4

Capillary Rise in a Tube

Domenico and Schwartz, 1992.

=pw

xA

Qpw −=

xA

Qpw −=

5Charbeneau, 2000.

Soil Moisture Held by Capillary Pressure

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Soil Water Characteristic Curve isa Function of pore size

Charbeneau, 2000.

0 nclaynsandr,layr,and

Capillary forces hold water tightly in small clay pores.Capillary forces hold water tightly in small clay pores.

Larger sand pores produce lower capillary pressures.

Larger sand pores produce lower capillary pressures.

7Fetter, 1999.

Relatively wide range of pore sizes from small to large results in widely

varying capillary pressures.

Relatively wide range of pore sizes from small to large results in widely

varying capillary pressures.

Narrow range of particle sizes results in relatively small range of capillary

pressures.

Narrow range of particle sizes results in relatively small range of capillary

pressures.

Soil Water Characteristic Curve is a Function ofSorting (Pore Size Distribution)

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Soil Water Characteristic Curves Also Represent WaterContent as a Function of Height Above Water Table

Fetter, 1999.

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Capillary pressure May Be More EasilyConceived of as the Independent Variable

Charbeneau, 2000.

capillary pressure(increasing height above water table)

0 -103

wat

er

con

ten

tnclay

nsand

clay

sand

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3. Darcy’s Law

4. Hydraulic Head

Lecture 3

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Who Was Darcy? Henry Philibert Gaspard Darcy was born June 10, 1803 in

Dijon, France.

Admitted to the French School of Bridges and Roads in Paris, part of the Corps of Bridges and Roads. After graduation, he was eventually assigned by the Corps to a position in Dijon.

In 1828, Darcy designed a 12.7 km system of aqueducts to supply the city of Dijon with surface water. The system included 28,000 m of pressurized surface lines and required no pumps or filters.

Made important contributions to flow and friction loss in pipes, created an improved pitot tube design, and was the first to postulate the existance of a boundary layer in fluid flow.

In 1856, carried out experiments while researching sand filters that lead to Darcy’s Law.

Died unexpectedly January 3, 1858 from pneumonia during a trip to Paris.

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Darcy’s Experimental Apparatus


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Darcy’s Experimental Data

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Darcy’s Experimental Data

Darcy's Data from One Experiment

y = 2.6743x + 1.2547

R2 = 0.9972

0

5

10

15

20

25

30

35

0 2 4 6 8 10 12

Head Loss (m)

Flow Rate (L/min)

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L 0.58 mdiam. 0.35 mn 0.38

A 0.096211 m2

CalcExperiment Duration Q dp Ratio K K

No. (min) L/min (m) V/dp (m/min) cm/s1 25 3.6 1.11 3.25 0.019552 3.26E-022 20 7.65 2.36 3.24 0.019541 3.26E-023 15 12 4 3 0.018085 3.01E-024 18 14.28 4.9 2.91 0.017568 2.93E-025 17 15.2 5.02 3.03 0.018253 3.04E-026 17 21.8 7.63 2.86 0.017224 2.87E-027 11 23.41 8.13 2.88 0.017359 2.89E-028 15 24.5 8.58 2.85 0.017214 2.87E-029 13 27.8 9.86 2.82 0.016997 2.83E-0210 10 29.4 10.89 2.7 0.016275 2.71E-02

Darcy’s Data in English (One Experiment)

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Velocity through Porous Medium

“Porosity” = 0.5

en

qv =

xA

Qv =

Porosity = 0.5

Pipe Porous Medium

Solid

Void Space

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Darcy’s Legacy

Place Darcy, Dijon, France.

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Can you Help the French Postal Service?

39¢ 39¢

YoungDarcy

OldDarcy

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3. Darcy’s Law

4. Hydraulic Head

Lecture 3

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Pressure and Elevation Heads - Laboratory

Freeze and Cherry, 1979.

= pressure headz = elevation headh = + z = total head

21Freeze and Cherry, 1979.

= pressure headz = elevation headh = total head

Pressure and Elevation Heads - Field

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Horizontal and Vertical Head Gradients


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Two Confined Aquifers with Different Heads

Charbeneau, 2000.

Groundwater will tend to flow from the top aquifer to the bottom aquifer.

(Assuming that horizontal distance between piezometers is small)

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Hydraulic Head is a Potential Field

Hubbert (1940): potential – a physical quantity, capable of measurement at every point in a flow system, whose properties are such that flow always occurs from regions in which the quantity has a higher values of those in which it has lower, regardless of the direction in space.

Potential fields and associated physical laws:

Head (Darcy’s Law)

Temperature (Fourier’s Law) Conduction of heat in solids

Concentration (Fick’s Law) Diffusion of chemicals dx

dCDJ

dx

dTkF

dx

dhKq

m−=

−=

−= FluidFlux

HeatFlux

MassFlux

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Potentiometric Surface – Dakota Sandstone
