Calculation of Discharge in Unconfined Aquifer Using Theim’s Formula for Steady Flow:

Considering the steady state condition, the discharge at any distance r towards the well is given by applying Darcy’s formula in conjunction with simplifying assumptions made by Dupit

Q = K A I = 2πr K h dh/dr

Integrating the equation (1) between limits h = H2 at r = rw h = head at any distance r

Equation (a) can be used to determine the distribution of head radially outward from the well. If the values of head h1 and h2 at any two observation wells at a distance r1 and r2 respectively (r2 > r1) from the test well are measured, coefficient of permeability K can be measured by substituting values in equation (a) above.

Then taking limit when h = H1 at r = R, (the radius of influence) equation (a) will become

It may be mentioned that in equation (a) as well as (b) H2 is head at well and — therefore is equal to the depth of water in the well.

Sichardt’s formula may be used to calculate radius of influence R.

It is expressed below to recapatulate:

R = 3000 s√K

where R is radius of influence in metres

s is drawdown at well in metres