Box 1 – Review of Hydraulic Head

Mechanical energy is the primary driving force of groundwater flow. In other words, groundwater flows from locations of higher to lower mechanical energy. In some places, flow is driven by thermal or chemical differences. However, in many cases these situations are not important when drawing a flow net in a shallow groundwater system. Energy is force times distance. However, for groundwater evaluation it is convenient to express energy in terms of hydraulic head, defined as the mechanical energy per unit weight of water. Hydraulic head (h) is composed of two components: potential energy from the water’s elevation in the gravitational field and energy from the fluid pressure distribution. To have the same dimension as elevation (that is, length), we replace pressure with pressure head, which is pressure divided by the product of water density and the acceleration of gravity. Pressure head is the height of a column of water required to cause a given pressure. For example, a one-meter high column of water will produce a pressure of about 9800 pascals, or 1.4 pounds per square inch. Therefore, a pressure head of 1 meter is equivalent to a pressure of 9800 pascals.

Hydraulic head in a groundwater system is the sum of elevation head and pressure head as shown in Equation Box 1-1.

(Box 1-1)

where:

The components of hydraulic head in an open body of water are illustrated in Figure Box 1-1. A horizontal plane is chosen as a datum for elevation measurements. Sea level is often used as a datum. In these figures, the horizontal bedrock surface is used as the datum. For a hollow pipe that is open on both ends, as indicated by the solid vertical parallel lines in Figure Box 1-1, hydraulic head is being measured at the bottom of the pipe. The elevation of the measuring point, z, is the elevation of the bottom of the pipe above the datum; the pressure head, ψ, is the height of the column of water in the pipe above the measurement point; and, the hydraulic head, h, at the measurement point is the sum of the elevation head and the pressure head. The sum of the elevation and pressure head equals the elevation of the water level in the pipe. Figure Box 1-1 shows z, ψ, and h for both deep and shallow pipes in a static body of water. A reservoir is under hydrostatic conditions meaning that the water is motionless. In such a situation, the head is the same at all locations in the reservoir. One could observe this by placing a tube in a bathtub and noticing that the elevation of the water in the tube is the same no matter where the tube is located.

Figure Box 1-1 – Schematic illustrating components of hydraulic head in an open body of water upgradient of a concrete dam. Hydraulic head is equal at all locations within a static body of water.

In a groundwater system below a dam with reservoirs at different elevations, the groundwater is in motion. It flows from the upper to the lower reservoir through the porous material below the dam. Figure Box 1-2 shows z, ψ, and h for hollow pipes (monitor wells) in a groundwater system. Again, the water level in each well indicates the hydraulic head at the location of the bottom of the pipe. Because groundwater flows from a region of higher head to a region of lower head, flow is from the left side of the figure to the right side. Head is “lost” as water flows through a porous medium because mechanical energy is converted to thermal energy, but the change in temperature is too small to measure. As water flows from the upper reservoir to the first piezometer on the left, 1 m of head is lost. An additional 4 m of head is lost by the time the water reaches the location of the piezometer on the right.

Figure Box 1-2 – Schematic illustrating components of hydraulic head in the groundwater system for flow under a concrete dam.

Return to where text links to Box 1