• Fig. 15.5 Control volume

For the control volume shown in Fig. 15.5 above,

The inflow to the system is Q_r

The outflow from the system is

The net inflow to the system is        (15.12)

Applying principle of mass conservation on the control volume

Inflow - outflow = Time rate of change in volumetric storage

Time rate of change in volumetric storage             (15.13)

                                                                                     (15.14)

where S_o is the specific storage

Replacing V by 2πrdrh, we have

                                                           (15.15)

                                                          (15.16)

Where S_y is the specific yield which is equal to S_o / h .

Now putting equation (15.16) in equation (15.14), we have

                                                                   (15.17)

As per Darcy's law

                                                            (15.18)

Putting in equation (14.17)

                                                     (15.19)

Simplifying,                                                       (15.20)

                                                                       (15.21)

                                                           (15.22)

                                                                    (15.23)

This is the flow equation for radial flow into a well for unconfined homogeneous isotropic aquifer.

In case of steady state condition, the governing equation becomes,

                                                                               (15.24)

Or,                                                                              (15.25)