Example problem on steady state horizontal flow:

Steady water flow is taking place in a horizontal column. The time-invariant boundary conditions are given in Fig. 5.5.

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Fig. 5.5. Problem description on flow through a horizontal column

Find out the head distribution along the column length when the following functional relationships are assumed for hydraulic conductivity

(i) 

where k _s = 0.1 cm/day and α = 0.001/cm

(ii) 

where α = 8 cm/day, b = 0.02/day

Solution:

(i) The suction head distribution can be expressed as (from eq. 5.7)

where hydraulic conductivity is assumed to vary .

It can be observed that the discharge flux is required to estimate the suction head distribution. It can be estimated by integrating the flux in the entire column. Therefore,

after solving,

q = 0.302 cm/day

Therefore,

Considering the similar approach,