And

(8.4)

The total discharge per unit width of the aquifer can be written as

(8.5)   (8.6)

And

(8.7)

Discharge between two reservoirs

Considering Dupuit assumption of horizontal flow, the discharge between two reservoirs can be calculated easily. Consider the phreatic aquifer shown in Fig. 8.3. The hydraulic conductivity of the homogeneous aquifer is K. The discharge per unit width of the aquifer in x direction can be obtained by

Fig. 8.3 Phreatic aquifer

(8.8)   (8.9)

Integrating between x = 0  to any distance x

(8.10) (8.11) (8.12) (8.13)

Equation (8.13) can be used to calculate discharge through the aquifer. This equation is also known as the Dupuit-Forchheimer discharge formula.