Calculate Drainage Coefficient

The drainage coefficient represents the depth of water to be removed by a drainage system in a given period. It can be calculated using the drainable porosity and the rate at which the water table drops.

Formula for Drainage Coefficient

The drainage coefficient ($D$) is calculated using the following formula:

$ D = n_e \times R $

Where:

• $D$ = Drainage coefficient (in meters per day, initially)
• $n_e$ = Drainable porosity (dimensionless)
• $R$ = Rate of drop of the water table (in meters per day)

Given Data

• Drainable porosity ($n_e$): $5\% = 0.05$
• Rate of drop of water table ($R$): $0.25 \text{ m day}^{-1}$

Calculation Steps

1. Calculate Drainage Coefficient in Meters: Substitute the given values into the formula.

   $ D = 0.05 \times 0.25 \text{ m day}^{-1} $

   $ D = 0.0125 \text{ m day}^{-1} $

2. Convert to Millimeters: Since the answer is required in $\text{mm day}^{-1}$, convert meters to millimeters ($1 \text{ m} = 1000 \text{ mm}$).

   $ D = 0.0125 \times 1000 \text{ mm day}^{-1} $

   $ D = 12.5 \text{ mm day}^{-1} $

Therefore, the drainage coefficient of the command area is $12.5 \text{ mm day}^{-1}$.