Calculate the spacing acquired for the water table to drop from the soil surface to a depth of 30cm in a 2 day period over the area of 200hectars from the following data. K=4cm/hr, the drain area to be placed 105cm below the soil surface. The impeameable layer is 195cm below the soil surface table the discharge. qo=15cm per day
To calculate the spacing acquired for the water table to drop from the soil surface to a depth of 30cm in a 2-day period over an area of 200 hectares, you'll need to use Darcy's Law and some additional information provided.
Darcy's Law is given by:
Q = (K * A * ΔH) / ΔL
Where:
Q is the discharge rate (cm^3/sec)
K is the hydraulic conductivity (cm/hr)
A is the cross-sectional area perpendicular to the flow (cm^2)
ΔH is the change in the hydraulic head (cm)
ΔL is the distance over which the change in hydraulic head occurs (cm)
First, let's convert the units to match:
Given:
K = 4 cm/hr
qo = 15 cm/day
1. Converting hydraulic conductivity (K):
Since we have the value of K in cm/hr and we need to use it in cm/day, we'll convert it:
K = 4 cm/hr * 24 hr/day = 96 cm/day
2. Calculating the discharge (Q):
The discharge (Q) is given by:
Q = qo * A
Here, we need to determine the area A. Since we have the area in hectares, we'll convert it to square centimeters:
A = 200 hectares * 10,000 m^2/hectare * 10,000 cm^2/m^2 = 2 x 10^13 cm^2
Q = 15 cm/day * 2 x 10^13 cm^2
Q = 3 x 10^14 cm^3/day
3. Calculating the distance (ΔL):
To determine the distance ΔL, we'll use the change in hydraulic head. Here, the water table needs to drop from the soil surface to a depth of 30 cm. Given that the drain area is placed 105 cm below the soil surface, the total change in hydraulic head is:
ΔH = 30 cm + 105 cm = 135 cm
4. Calculating the spacing acquired:
Using Darcy's Law, we can rearrange the formula to solve for ΔL:
ΔL = (K * A * ΔH) / Q
Substituting the values we calculated:
ΔL = (96 cm/day * 2 x 10^13 cm^2 * 135 cm) / (3 x 10^14 cm^3/day)
Evaluating this expression will give you the spacing acquired for the water table to drop from the soil surface to a depth of 30 cm in a 2-day period over the given area.