Green-Ampt Equation 🌿💦: and Kostiakov Equation 📐💧:

 Kostiakov Equation 📐💧:

The Kostiakov equation is an empirical formula used to model the rate of water infiltration into soil over time. The formula is:

$�(�)=��{�}^{(�-1)}$

where:

• $�(�)$ is the infiltration rate at time $�$ 🕒,
• $�$ and $�$ are empirical constants 📊,
• $�$ is the time since infiltration began ⏰.

This equation assumes the intake rate declines over time according to a power function. To address its limitation of assuming a zero final intake rate, a variant known as the Kostiakov-Lewis equation is used:

$�(�)=��{�}^{(�-1)}+{�}_0$

where ${�}_0$ is the steady-state infiltration rate 🔄.

Green-Ampt Equation 🌿💦: The Green-Ampt equation is a method for estimating infiltration into soils during rainfall events 🌧️, given by the formula:

$�(�)=��+�\mathrm{\Delta }�\ln (1+\frac{�(�)}{�\mathrm{\Delta }�})$

where:

• $�(�)$ is cumulative infiltration at time $�$ 🕒,
• $�$ is hydraulic conductivity of the soil 🌱,
• $�$ is time since infiltration began ⏰,
• $�$ is the wetting front soil suction head 🌀,
• $\mathrm{\Delta }�$ is the change in volumetric water content 🌊.

The assumptions of this equation include homogeneous soil, constant hydraulic conductivity, and ponding conditions on the soil surface 💧. By rearranging and integrating, one can solve for either cumulative infiltration $�(�)$ or the infiltration rate $�(�)$:

$�(�)=�[\frac{�\mathrm{\Delta }�}{�(�)}+1]$