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Aquifer: An aquifer is an saturated geological formation, underground layer of waterbearing permeable and porous or unconsolidated materials (gravel, sand, or silt) from which groundwater can be extracted using a water well.
Some Fundamental definitions
Type of aquifer
Groundwater profile or aquifer system1. Unconfined aquifer
Various type of Unconfined aquifer
2. Perched aquifer
Perched aquifer is small water body which is situated in unsaturated zone of soil above the main ground water table or main unconfined aquifer, separated by impervious strata.
Perched aquifer
3. Confined aquifer
Some important terminology used in well hydraulics
1. Cone of depression
2. Radius of influence
Note:
Different way of extracting water
1. Infiltration Galleries
These are horizontal tunnels constructed at shallow depth of the 35 m along the bank of river in water bearing strata.
Derivations:
Discharge through element
q_{x} = a_{x}*v_{x}
= (h*L)*k*i_{x} (by Darcy’s law V= k*i_{x})
= h*L*K* dh/dx
Total Discharge
Q= ∫q_{x}
= ∫h*L*k*dh/dx
Q*R = k*L* [H^{2} h_{0}^{2}]
Q = kL(Hh_{0})(H+h_{0})/(2R)
2. Infiltration Well
3. Artesian Spring
Artesian spring have potential sources of raw water, while nonartesian spring are not potential sources. Because in summer water table may get depleted.
4. Well
These are generally of two types
Derivation Part1
Let water level rises in well from s_{1} to s_{2} in T time
According to Darcy’s law
“For laminar flow through saturated soil mass, the discharge per unit time is proportional to the hydraulic gradient”.
Q = K.i.A  (1)
i = Hydraulic gradient = s/L  (2)
(Head s is lost in a length L of seepage path)
If ds is the water level rises in well in dt time than
Q dt = –A ds
Negative sign indicate the decrease in depression head with time during the recuperation of well.
From equation 1, 2 and 3
(K.s.A/L)dt = Ads
Integrating them
Where k/L a constant C and it is the specific yield of well. Dimension C is T^{1}.
So equation 4 become
Derivation Part2
The yield of the well is
Q = CAH
Assumption: entire flow in well is from the bottom of well (impervious steining of masonry)
Where Q = safe yield of the well
A = area of cross section of the well
H = safe working depression head
C = specific yield of the well
Specific yield: Specific yield soil is defined as discharge per unit area under a unit depression head (drawdown).
Steady flow into a well
Case1: Well in Confined Aquifer. (Theim’s theory)
Assumptions:
In this figure
r_{w} = radius of well, b = thickness of confined aquifer
s_{w} = Drawdown
h_{w} = Piezometric head at pumping well
H = original piezometric head or piezometric head before staring pumping
h_{r}, s_{r} = piezometric head and draw down of water table at distance r from centre of well
h_{1}, s_{1} = piezometric head and draw down of water table at distance r_{1} from centre of well
h_{2}, s_{2} = piezometric head and draw down of water table at distance r_{1} from centre of well
According to Darcy’s low
Velocity of flow at radial distance r
Here is hydraulic gradient (dh is head loss over dr radial distance)
Discharge from well Q = V_{r} x A {A = cylindrical surface area through which water enter into well}
A= 2πrb
Q = (k(dh/dr))(2πrb)
By integrating it
if H is the original piezometric head, h_{w} = piezometric head at well,
R = Radius of influence, = 3000S_{w}√K, K= Permeability of Soil,
r_{w} = radius of well
Above equation represent the discharge from pumping well for steady flow condition.
s_{1}= H  h_{1}; s_{2 }= H  h_{2}  (6)
And T= Kb  (7)
Note: T is Transmissibility and it defined as flow capacity or discharge of aquifer per unit width under unit hydraulic gradient. T has the dimension of [L^{2}/ T] .
From equation 5, 6 and 7
Note: Above equation is valid only for steady state flow condition and for well having complete penetration in aquifer
Case1: well in unconfined aquifer.
In this figure
r_{w} = radius of well
s_{w} = Drawdown
h_{w} = Piezometric head at pumping well
H = original piezometric head or piezometric head before staring pumping
h_{r}, s_{r} = piezometric head and draw down of water table at distance r from centre of well
h_{1}, s_{1} = piezometric head and draw down of water table at distance r_{1} from centre of well
h_{2}, s_{2} = piezometric head and draw down of water table at distance r_{1} from centre of well
According to Darcy’s low
Velocity of flow at radial distance r
V_{r} = K(dh/dr)
Here dh/dr is hydraulic gradient (dh is head loss over dr radial distance)
Discharge from well Q = V_{r} x A {A = cylindrical surface area through which water enter into well}
A = 2πrh
By integrating it
Above equation represent the discharge from pumping well for steady flow condition.
At r = R radius of influence
r_{2} = R, r_{1} = r_{w} than h_{1} = h_{w}, h_{2} = H
If s_{w} = (H h_{w}) is small compare to H than
From equation 10, 11
Transmissibility T= Kb  (13)
s_{1} = Hh_{1}; s_{2} = Hh_{2}
Put the value of s_{1} and s_{2} in equation (9)
Note: above all equation of Q is valid only for steady state flow condition and for well having complete penetration in aquifer
Head loss (drawdown) due to flow through soil pours, screen and in the well.
So
Well loss in confined aquiferSpecific capacity
So specific capacity (if well losses are ignored)
Example: (from engineering hydrology by k. subramanya)
Given
1. Radius of pumping well r_{w} = 15 cm
2. Aquifer depth = 40 m
3. Steady state discharge = 500 lpm = (1500*10^{3})/60 = 0.025m^{3}/s
4. Drawdown at two observation well
5. It is given that, the well is fully penetrated in aquifer.
Find
Solution:
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18 videos27 docs20 tests
