**Calculation of Seepage Discharge through the Foundation of an Earth Dam**

To determine the seepage discharge through the foundation of an earth dam, we need to use the flow net method. The flow net is a graphical representation of the flow of water through a porous medium, such as soil.

**Step 1: Find the Flow Channels and Equipotential Drops**

Given that the flow net has 10 equipotential drops and 3.5 flow channels, we can draw the flow net accordingly. The flow channels represent the flow of water through the soil, while the equipotential drops represent the potential difference between adjacent flow channels.

**Step 2: Determine the Length of the Dam**

The length of the dam is given as 300 m. This length will be used to scale the flow net and calculate the seepage discharge.

**Step 3: Calculate the Coefficient of Permeability**

The coefficient of permeability of the soil is given as 2.5 x 10 cm/sec. This value represents the rate at which water can flow through the soil.

**Step 4: Determine the Head Difference**

The head difference is the difference in water level between the upstream and downstream sides of the dam. In this case, the level of water above the base of the dam is 12 m on the upstream side and 4 m on the downstream side. The head difference is calculated as the difference between these two levels.

**Step 5: Calculate the Seepage Discharge**

To calculate the seepage discharge, we can use Darcy's Law, which states that the seepage velocity is equal to the product of the coefficient of permeability, the hydraulic gradient, and the area through which the water is flowing.

In this case, the hydraulic gradient is calculated as the head difference divided by the length of the dam. The area can be calculated as the product of the width of the flow channels and the length of the dam.

The seepage discharge can then be calculated as the product of the seepage velocity and the area through which the water is flowing.

**Explanation of the Steps**

The seepage discharge through the foundation of an earth dam is determined by using the flow net method, which involves drawing the flow channels and equipotential drops. The length of the dam is used to scale the flow net, while the coefficient of permeability represents the rate at which water can flow through the soil.

The head difference is calculated as the difference in water level between the upstream and downstream sides of the dam. This head difference is then used to determine the hydraulic gradient.

Using Darcy's Law, the seepage velocity is calculated as the product of the coefficient of permeability, the hydraulic gradient, and the area through which the water is flowing. The seepage discharge is then calculated as the product of the seepage velocity and the area.

By following these steps and using the given values, the seepage discharge through the foundation of the earth dam can be determined.