Using Darcy's Law, how can velocity be determined?

The correct answer, which states that velocity can be determined using the relationship ( v = K \cdot i ), directly derives from Darcy's Law, which describes the flow of fluid through porous media. In this context:

• ( v ) represents the velocity of the fluid,

• ( K ) is the hydraulic conductivity, which is a measure of a material's ability to allow water to flow through it,

• ( i ) is the hydraulic gradient, calculated as the change in hydraulic head per unit distance in the direction of flow.

Darcy's Law emphasizes that the flow rate is proportional to the driving force, represented by the gradient, and the medium's ability to transmit that flow, represented by hydraulic conductivity. Combining these factors provides an effective means to determine the flow velocity of water or other liquids through soil or geological formations.

The other options do not accurately represent the relationship derived from Darcy's Law. For instance, the equation ( v = Q/A ) relates to flow rate, where ( Q ) is flow volume and ( A ) is the cross-sectional area, which describes velocity in a different context not specific to the flow characteristics of porous media. The equations involving ( Q/v ) and ( K/H \