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Chapter: DARCYíS LAW

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Yield of an open well

The term yield of the well is used to indicate the rater of with drawl of water without causing failure of well. It is the rate at which a well can supply the water.

YIELD OF AN OPEN WELL

 

The term yield of the well is used to indicate the rater of with drawl of water without causing failure of well. It is the rate at which a well can supply the water.

 

The factors which influences the yield of an open well are:

 

1.     Well dimensions

2.     Location of nearby wells

3.       Porosity of aquifers

4.     Quantity of water available in aquifers

5.     Slope of water table

 

 

6.     Coefficient of permeability of soil.

7.     Rate of pumping water.

 

CO-EFFICIENT OF PERMEABILITY (k)

 

It is defined as the velocity of flow which will occur through the total cross sectional area of soil (or Aquifer) under a unit hydraulic gradient.

 

CO-EFFICIENT OF TRANSMISSIBILITY

It is defined as the rate of flow of water in m3/day through a vertical strip of the aquifer of unit width and extending the full sanitation height under unit hydraulic gradient at a temperature of 600F.

T = BK

Where

 

B = Aquifer thickness

 

DARCY'S LAW

 

The percolation of water through soil was fist studied by darcy(1856) who demonstrated experimentally that for laminar. Flow conditions in a saturated soil, the rate of flow or the discharge per unit time is proportional to the hydraulic gradient.

 

i.e  Q = Ki.A

V = Q/A = Ki

WHERE,

Q = Discharge

 

K= Darcy?s Co-efficient of permeability i = hydraulic gradient

 

A = Total C/S area of soil V = Flow velocity.

 

EXPRESSION  FOR  YIELD  OF  AN  OPEN  WELL  OR  DISCHARGE  FROM  AN UNCONFINED AQUIFER

 

Let,

 

H= depth of water before pumping h= depth of water after pumping

i = slope of hydraulic gradient - dy/ dx

r = radius of well

 

R = Radius of circle of influence K= coefficient of permeability S = draw dawn at the well.

 

Consider any point ĄP? on the draw down curve (cone of depression) whose co-ordinates are(x,y). THEN from DARCY?S law

 

Q = KM.Ax ix


Where

Ax = Area of C/S at the saturated part of Aquifer at ĄP?

Ax = (2Pi x)y  = 2  xy

Ix  = hydraulic gradient

 

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