GATE-2018 (24) :Wyllie – Time average equation

 

26) Specific discharge of 1 cm per day is observed in a porous medium where hydraulic head difference is 0.5 m and the flow length is 20 m. calculate the hydraulic conductivity(in m/day).

 (Thanks to Chandrasekhar, ANU)

Solution:

 The specific discharge can be defined as

$\frac{Q}{A}=K \frac{dh}{dl}$------------------(1)

 Where $\frac{Q}{A}$ is the specific discharge = 1 cm per day

                                                                   = 0.01 m per day

 dh is the hydraulic head difference = 0.5 m

dl is the flow length = 20 m

K is the hydraulic conductivity =?

Therefore by substituting all the given values in the equation (1)

$\frac{Q}{A}=K \frac{dh}{dl}$

 

$0.01=K \frac{0.5}{20}$

 

$K =\frac{0.01 \times 20}{0.5}$

 

$K = 0.4 meter per day$