The drainage coefficient indicates the drainage rate from a unit area of the soil. For instance, a drainage coefficient of 13 mm/day implies that 13 mm of water drains from each square meter of soil per day. The drainage coefficient is critical in the design of tile drainage systems because it aids in the determination of the number and size of tiles required to drain a given area, as well as the spacing between the tiles.
S p = K D (A/D) where S p is the spacing between laterals, K is the hydraulic conductivity, D is the depth of the laterals, and A is the area of influence of the drain.
According to the base case, K = 0.1 m/d and D = 1.2 m.
We will calculate A by equating the drainage coefficient with the infiltration rate.
According to Darcy's law, the infiltration rate (I) is calculated as follows: I = K h where h is the hydraulic head. The hydraulic head is the difference in height between the water table and the soil surface, which is 5m for the given scenario.
Since the hydraulic conductivity (K) is 0.1 m/d, the infiltration rate (I) may be calculated as follows: I = K h= 0.1 * 5= 0.5 m/d= 500 mm/d.
Therefore, the area of influence (A) of the drain may be calculated as follows: A = (1000/13) * 500= 38,461.54 m²Now that we know A, we can calculate the spacing between laterals using the above formula. Sp = K D (A/D)= 0.1 * 1.2 (38,461.54/1.2)= 10000 m²Spacing between laterals for a parallel array is 10000 m².