Ground water flow

Criteria in ground water flow

Groundwater

Rainfall that infiltrates the soil and penetrates to the underlying strata.
Aquifers

Saturated formation of earth material which not only stores water but yields insufficient quantity. Therefore, an aquifer has high permeability which can transmits water more easy.
Permeability
It is a measure of the resistance to underground flow. For aquifers with large pores, they have better permeability.
Groundwater table/ Phreatic surface
Groundwater table can be defined as the surface of saturation. Groundwater table may slope steeply and it's stability depends on water supply above it. That means, it falls during dry spells and rises in rainy weather.
Confined aquifer

Confined aquifer is an aquifer that overlain by impermeable material, and so it should be under pressure.
Piezometric surface
It is the surface to which water would rise if it could.
Spring
Spring is an impermeable layer underlying aquifer. It outcrops on ground surface so groundwater appear on surface in seepage zone.
Artesian wells
They are the wells that drill into confined aquifers.

Factors influencing groundwater flow

Factors on liquid (normally water)
Density - density of water varies very slightly with temperature, so it can be ignored in groundwater flow.
Viscosity - is a measure of the shear strength of a liquid. For high viscosity, the liquid becomes hard to penetrate.
Factors on media through which liquid moves (Soil)
Porosity (n) - defined as n = total voids/total volume and ranges from a few percent to about 90 per cent.
Effective porosity (ne) - It is an important consideration of porosity. When water fills the voids of a soil, a thin layer would coat the particles. This water is not free to move and adheres to the particles, it captures part of the available space. Therefore, an effective porosity that may be less than the true porosity should be introduced.
Permeability - is a function of structure, porosity and geological history of the material. It can be described as the geometry of the pore system.
Compressibility - is a minor properties in groundwater flow, it would not greatly affect the groundwater flow.

Darcy's law

Darcy's law states the rate of flow per unit area of an aquifer is proportional to the gradient of the potential head measured in the direction of flow. There are some assumptions before applying Darcy's law:
1. The material is homogeneous and isotropic
2. There is no capillary zone
3. There is a steady state of flow
Darcy's law:


where k is the permeability coefficient.
For an aquifer of area A:

where      v is the velocity of water in m/day
                i is the hydraulic gradient
For small velocity,

As the actual velocity of water in the pores is greater than the specific velocity since the path of water flows through porous media is always longer than a straight line between two points. Therefore, the actual velocity should becomes:

Flow in a confined aquifer
Consider unidirectional flow, from Darcy's law:

Introduce flow in the aquifer per unit width, q:

Assume flow in steady state:


Flow in an aquifer with phreatic surface
Assume the aquifer is resting on an impermeable base. From Dupuit's assumptions, all flow lines in the aquifer are horizontal and vertical equipotential lines. Therefore:

Darcy's law becomes:



If the aquifer is recharged by rain, we need to introduce net infiltration rate, N to the equation.

The yield of wells

For confined flow

Since the flow is radial to well, the horizontal co-ordinate is measured as r. Qo is the steady-state discharge from the well. s is the drawdown.
From Darcy's law:

From continuity,



Introducing boundaries,

If s = 0 when r = R, then

Finally, we can plot s vs r graph to find kH and R.

You can get the value of Ro from the above figure.

For unconfined flow

Darcy's law:

Continuity:



If h = H when r = R, then

As drawdown, s = H - h,


Finally, we can plot s' vs r graph to find kH and R.

Example:

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