Hydraulic Head (i) is typically defined as:

Hydraulic head is a crucial concept in hydrogeology and fluid mechanics, representing the potential energy available to drive groundwater flow. It is defined as the sum of the pressure head and the elevation head at a given point in a fluid system. The hydraulic gradient, which describes the rate of change of hydraulic head over a distance, is essential in understanding how water moves through the ground.

When considering hydraulic head as related to the hydraulic gradient in relation to the length of the sample, it highlights the relationship between changes in hydraulic head and flow direction over a specified distance. This definition encapsulates the core principle of how groundwater flows from areas of higher potential (higher hydraulic head) to lower potential, indicating that the hydraulic gradient is a critical component for calculating flow rates and analyzing groundwater conditions.

This understanding is fundamental for engineers and hydrologists when assessing groundwater movement and designing systems such as wells, drainage, or other hydraulic structures, as it helps predict how changes in one part of the system can impact flow and pressure throughout the surrounding area.