estimate the volume of water that will infiltrate into a soil before surface saturation occurs using the Green-Ampt equation.The following data are known ;

1-saturated moisture content is 0.25
2-the initial moisture content is 0(zero)
3-the average rainfall rating is 2 in./hr
4-the average capillary suction head is 4 in.
5-K=1 in/h
What is the max. soil storage volume if the soil is homogeneous to a water table depth of 5 ft.?

To estimate the volume of water that will infiltrate into the soil before surface saturation occurs using the Green-Ampt equation, we need to follow these steps:

Step 1: Calculate the final moisture content (θf) of the soil.

The final moisture content (θf) can be calculated using the formula:

θf = θs + [(θi - θs) / (1 + (K / S))]

where:
θs = saturated moisture content
θi = initial moisture content
K = hydraulic conductivity
S = average capillary suction head

Given:
θs = 0.25 (saturated moisture content)
θi = 0 (initial moisture content)
K = 1 in/hr (hydraulic conductivity)
S = 4 in (average capillary suction head)

Substituting the given values into the formula, we can calculate θf as follows:

θf = 0.25 + [(0 - 0.25) / (1 + (1 / 4))]
θf = 0.25 - (0.25 / 1.25)
θf = 0.25 - 0.2
θf = 0.05

Step 2: Calculate the depth of rainfall (p) that will infiltrate until surface saturation occurs.

The depth of rainfall (p) that will infiltrate until surface saturation occurs can be calculated using the formula:

p = [(θf - θi) / (1 + (K / S))]

Given:
θf = 0.05 (final moisture content)
θi = 0 (initial moisture content)
K = 1 in/hr (hydraulic conductivity)
S = 4 in (average capillary suction head)

Substituting the given values into the formula, we can calculate p as follows:

p = [(0.05 - 0) / (1 + (1 / 4))]
p = 0.05 / 1.25
p = 0.04 in

Step 3: Calculate the maximum soil storage volume.

The maximum soil storage volume can be calculated by multiplying the depth of rainfall (p) by the cross-sectional area of the soil.

Given:
p = 0.04 in (depth of rainfall)
Water table depth = 5 ft = 60 in

The cross-sectional area of the soil is equal to the water table depth multiplied by the area of the soil.

Cross-sectional area = 60 in x Area of the soil

To calculate the area of the soil, we need additional information about the shape of the soil. Assuming it is a rectangular shape, we can estimate the width of the soil as follows:

Width of the soil = Volume of infiltrated water / (Area of the soil x Depth of rainfall)

Substituting the known values:

Width of the soil = 0.04 in / (60 in x (0.04 in))
Width of the soil ≈ 0.042 ft (assuming the unit conversion)

Now, we can calculate the maximum soil storage volume by multiplying the width, water table depth, and depth of rainfall:

Maximum soil storage volume = Width x Water table depth x Depth of rainfall
Maximum soil storage volume = 0.042 ft x 5 ft x 0.04 in
Maximum soil storage volume ≈ 0.0084 ft³

Therefore, the estimated maximum soil storage volume of water is approximately 0.0084 cubic feet.