Pressure potential pressure head and hydraulic head

There are two principal forms of energy: kinetic and potential. Because subsurface water flow is relatively slow (with the exception of that within natural soil pipes), its kinetic energy, which is proportional to velocity squared, is considered negligible. In contrast, the potential energy, which is due to position or internal condition, is of critical importance in determining the state and movement of water in the soil. Water, like other forms of matter, flows from areas of high potential to areas where it is lower.

The unit quantity of water on which potential is based can be volume, mass or weight. A potential per unit weight of h metres is equivalent to gh J kg-1 on a mass basis or pwgh Pa on a volume basis (note acceleration due to gravity, g, is 9.806 65 ms-1 and density of pure water, pw, is approximately 103 kg m-3). The pressure potential is the amount of useful work that must be done per unit quantity of pure water to transfer reversibly and isothermally an infinitesimal quantity of water from a pool at a standard atmospheric pressure that contains a solution identical in composition to the subsurface water and is at the elevation of the point under consideration. Thus, the pressure potential per unit volume,

^p (volume) = p = Pwgh where p is the pressure, pw is the density of the water, g is the acceleration of gravity and h is the pressure head. Thus the pressure potential per unit mass,

When the hydrostatic pressure of water within the subsurface is greater than the atmospheric pressure, the pressure potential is positive. Where it is less than atmospheric pressure, the subsurface water system has a negative pressure potential, which is also termed the matric potential, capillary potential, suction or tension.

A further potential term is involved in subsurface water movement, namely the gravitational potential. To raise water against gravity requires work to be expended, and this energy is stored within water body as gravitational potential energy. The gravitational potential of subsurface water at each point is normally determined at a point relative to an arbitrary reference level. It is customary to set this level below the subsurface system being studied so that values are always positive. As with pressure potential, the gravitational potential can be expressed in three ways, rg(volume) = Pwgz

where Z is the elevation head. The combination of the pressure head and gravitational head gives the hydraulic head (H),

As the other terms of osmotic head, pneumatic head and envelope head are considered negligible for many applications, the hydraulic head often approximates the total head (Ht), which is equivalent to the total potential per unit weight ($).

6.2.1 Piezometer design

Within soil, regolith or rock that is fully saturated, the pressure potential can be measured with a piezometer. A piezometer is a narrow tube installed within the ground, where only the lower section is in contact with subsurface water system via a screened section and gravel pack (Fig. 6.5).

and per unit weight,

Protective cover with locking cap

6" clearance for sampler

Slope concrete pad away from casing

Slope concrete away from casing to prevent infiltration, but do not create a mushroom which will be subject to frost heave

Minimum 2" nominal diameter casing with flush threaded connections wrapped with PTFE tape or with O-rings (varies with casing material)

Borehole

Centralizer (semi-circle) Bottom cap, plug or plate

6" clearance for sampler

Slope concrete pad away from casing

Minimum 2" nominal diameter casing with flush threaded connections wrapped with PTFE tape or with O-rings (varies with casing material)

Borehole

Grout interval varies

Centralizer (expandable)

3-5' bentonite seal

1-2' secondary filter pack where conditions warrant

Extend primary filter pack 3-5' above well screen, unless conditions warrant less Well screen length varies

Sediment sump

Fig. 6.5 A piezometer. (Reproduced with permission from Nielsen, D. M. (2006) Practical Handbook of Environmental Site Characterization and Ground-water Monitoring, 2nd edn. Taylor & Francis, London.)

Well identification labelled inside and outside the cap Protective casing Vented cap Washed pea gravel or coarse sand mixture 1/4" weep hole at 6" above ground level

Bentonite pellets for cold weather climates

3-5' protective casing depth depending on frost heave conditions

Grout interval varies

Centralizer (expandable)

3-5' bentonite seal

1-2' secondary filter pack where conditions warrant

Extend primary filter pack 3-5' above well screen, unless conditions warrant less Well screen length varies

Sediment sump

Fig. 6.5 A piezometer. (Reproduced with permission from Nielsen, D. M. (2006) Practical Handbook of Environmental Site Characterization and Ground-water Monitoring, 2nd edn. Taylor & Francis, London.)

The top of the piezometer can be capped to prevent ingress of rainfall, but must not be sealed as the upper water surface in the piezometer must be at atmospheric pressure. For piezometers to be installed within soil horizons (the solum) of say 0-3 m, the hole for the piezometer can be hand-augered. Where the piezometer is to be installed to greater depths, mechanical drilling is required. This drilling can be rotary or percussive drilling; alternatively jetting methods or drive-in piezometers can be used. Todd and Mays (2005) provide comprehensive details of drilling methods. To prevent a leakage of water between the piezometer tube and ground, bentonite clay seals are added above the screened section, and sometimes also at the surface (Fig. 6.5). The height of the free-water surface above the screened piezometer base is called the piezometric head, and is equivalent to the pressure head, h. This pressure head can be measured using a manual dip meter, or continuously using a pressure transducer connected to a data logger, as used for river stage measurement (Section 7.3.3). Where the profile contains impeding strata, the pressure head within each stratum may be measured by installing several piezometers in close proximity, each with a piezometer screen in contact with a different stratum. This configuration is described as a piezometer nest. Comprehensive details of piezometer design and installation are given within Nielsen (2006).

6.2.2 Observation well design

Measurement of the pressure head at depth within rock aquifers (i.e. groundwater bodies with high porosity and high saturated hydraulic conductivity) is more commonly measured within an observation well rather than a piezometer. In contrast to the situation with a piezometer, the water column within an observation well is normally in direct contact with the whole depth of the rock aquifer via an extended screen and gravel pack. These devices often use larger diameter cases, allowing float-operated water-level recorders to be used; these float systems can be monitored electronically using shaft encoders (Section 7.3.2). Pressure transducers (Section 7.3.3) are, however, more commonly used for level measurements within observation wells.

If there are no confining strata along this screened length, then these devices give values of pressure head similar to those of the piezometer. If confining strata are present, then perched water tables may develop, which leak into the observation well; under these circumstances piezometers should be used.

6.2.3 Tensiometer design

Where saturated conditions are absent, pressure potential can be measured with a device called a tensiometer (Richards, 1928). A tensiometer can be used to measure both positive and negative pressure potential (Pa; this can be converted to a pressure head for comparison with piezometer data). A tensiometer consists of a porous cup, generally of ceramic material connected to a sealed tube (Fig. 6.6). Once installed within the soil and filled with (de-aired) water, the water within the tube equilibrates with the pressure potential in the soil surrounding the porous cup. The pressure potential within the tensiometer can be measured manually using an attached mercury manometer or vacuum/pressure gauge, and such devices are still manufactured. More commonly, tensiometers are fitted with a pressure transducer and the pressure potential

Fig. 6.6 A tensiometer with integral transducer. (Reproduced with permission of UMS GmbH)

data logged. The range of negative pressure potential that can be measured is normally 0-80 kPa (equivalent to 800 millibars) due to the air-entry point of the porous cup. When pressure transducers are used, the maximum value of positive pressure potential recorded is limited by the type and range of transducer used.

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