Groundwater and Well Hydraulics
Darcy’s law and the fundamental equations governing groundwater movement can now be applied to particular situations. Solutions of groundwater flow to wells rank highest in importance. From pumping tests of wells, storage coefficients and transmissivities of aquifers can be determined.
Steady Unidirectional Flow
Steady flow implies that no change occurs with time. Flow conditions differ for confined and unconfined aquifers and hence need to be considered separately, beginning with flow in one direction.
Confined Aquifer
Let the groundwater flow with a velocity v in the x-direction of a confined aquifer of uniform thickness. Then for one-dimensional steady flow-
∂2h/ ∂x2 = 0
Which has for its solution
h= C1x + C2
where h is the head above a given datum and C1 and C2 are constants of integration. Assuming h=0 when x=0 and from Darcy’s Law-
∂h/ ∂x= (-w/K)
Then we have-
h= -vx/K
This states that the head decreases linearly with flow in the x-direction-
Unconfined Aquifer
For the similar flow situation in an unconfined aquifer, the direct analytic solution of the Laplace equation is not possible. The difficulty arises from the fact that the water table in the two-dimensional case represents a flow line. The shape of the water table determines the flow distribution, but at the same time, the flow distribution governs the water table shape. To obtain a solution, Dupuit assumed the velocity of the flow to be proportional to the tangent of the hydraulic gradient instead of the sine as defined in Darcy’s law and the flow to be horizontal and uniform everywhere in a vertical section.
These assumptions made, although permitting a solution to be obtained, limit the application of the results. for unidirectional flow the discharge per unit width q at any vertical section can be given as
q= -Kh2/2 + C
and if h= h0 where x=0 then the Dupuit equation
q= (K/2x) (h02-h2)
results which indicates that the water table is parabolic in form.
Base Flow to a stream
Estimates of the base flow to streams or average groundwater recharge can be computed by applying the above analysis of one-directional flow in an unconfined aquifer. For example, picture the idealized boundaries with a continuous recharge rate W occurring uniformly over the aquifer. With the Dupuit assumptions, the flow per unit thickness is
q= -Kh(dh/dx)
and by continuity
q= Wx
Combining these equations and integrating leads to the result
h2 =ha2 + W(a2-x2)/K
where h, ha, a and x are defined in fig and K is the hydraulic conductivity. From symmetry and continuity
Qb= 2aW
Where Qb is the base flow entering each stream per unit length of the stream channel. If h is known at any point Qb or W can be computed, provided K is known.
More from the Hydrology and Groundwater
The occurrence of Ground Water
Shrinkage In Concrete: Types and Methods to Reduce
Chemical Shrinkage
Autogenous Shrinkage
Plastic Shrinkage
Drying Shrinkage
Carbonation Shrinkage
Continue Reading Shrinkage In Concrete: Types and Methods to Reduce
Soil: Definition and Names of Various Types of Soil
The term ‘soil’ in soil engineering is defined as an unconsolidated material, composed of solid particles, produced by the disintegration of rocks. The void space between the particles may contain air, water or both. The soil particles may contain organic matter.
Continue Reading Soil: Definition and Names of Various Types of Soil
Bricks: Uses, Size, Weight, Frog, Types, and Much More
What are Bricks? Bricks are one of the oldest building materials and it’s extensively used at present as a loading material in construction methods because of its durability, strength, reliability, low cost, easy availability, etc. Bricks are manufactured by molding burnt clay or a mixture of sand and lime or of Portland cement concrete, in…
Continue Reading Bricks: Uses, Size, Weight, Frog, Types, and Much More
Water Proofing Materials, Damp-Proofing Course, and much more
Water Proofing Materials Dampness in a building is the main cause of the deterioration of the building as well as for the ill-health of the occupants. The damp brickwork in the buildings is prone to fresh attack. Also, the soluble salts in bricks are liable to attack the cement mortar when the brickwork remains wet…
Continue Reading Water Proofing Materials, Damp-Proofing Course, and much more
Sound Insulation And Sound Insulating Materials
Sound Insulation A well-designed building should incorporate sound insulation to restrain the noise level. High noise conditions result in uncomfortable living conditions, mental strains, fatigue, and may even lead to a nervous breakdown or temporary deafness. Adequate insulation can be achieved by using sound-absorbing or sound repellent materials. Sound Insulating Materials Sound Insulating Materials fall…
Continue Reading Sound Insulation And Sound Insulating Materials
Heat Insulating Materials: Convection, Radiation, and Conduction
Heat Insulating Materials The purpose of thermal insulation is to restrict the heat transfer from warmer to cooler areas. Transfer of heat takes place by three processes- the convection, the radiation and, the conduction. Convection In convection, heat is transferred from one place to another by the movement and mixing of liquids or gases. Radiation…
Continue Reading Heat Insulating Materials: Convection, Radiation, and Conduction