ERTH 430 - Fluid Potential

What is the main driving force of groundwater flow?

A difference in hydraulic energy or hydraulic head between two points.

In what direction does groundwater flow?

From higher hydraulic head to lower hydraulic head.

What potential drives heat flow under Fourier's Law?

Temperature.

What potential drives diffusion under Fick's Law?

Concentration.

What potential drives electrical current under Ohm's Law?

Electrical voltage.

What potential is used for groundwater flow under Darcy's Law?

Fluid potential, usually expressed as hydraulic head.

Write Darcy's Law in terms of specific discharge.

q = -K(Δh/ΔL)

What does Q represent in Darcy's Law?

Volumetric flow rate or outflow rate, with dimensions L^3/T.

What does q represent in Darcy's Law?

Specific discharge, with dimensions L/T.

Is specific discharge q the same as actual groundwater velocity?

No. The lecture explicitly notes that q is not a velocity.

What does K represent in Darcy's Law?

Saturated hydraulic conductivity, with dimensions L/T.

What does A represent in Darcy's Law?

Cross-sectional area, with dimensions L^2.

What does Δh/ΔL represent?

The hydraulic gradient, with dimensions L/L and therefore dimensionless.

Why is there a negative sign in Darcy's Law?

Because flow occurs in the direction of decreasing hydraulic head.

What is work?

Force multiplied by distance: W = F × d.

What is force?

Mass multiplied by acceleration: F = ma.

What are the dimensions of work?

ML^2/T^2.

How is hydraulic potential defined?

Work done per unit mass of fluid.

What are the dimensions of hydraulic potential?

L^2/T^2.

What three mechanical potential terms are important in this lecture?

Gravitational potential, pressure potential, and kinetic potential.

What is the total work done on a fluid mass?

WT = Wg + Wv + Wp.

What is the gravitational work required to move a fluid from z0 to z?

Wg = M g (z - z0).

What is gravitational potential?

Energy per unit mass due to position or elevation.

Write gravitational potential relative to a reference elevation.

Φg = g(z - z0).

If the reference elevation z0 is zero, what is gravitational potential?

Φg = gz.

What is a datum?

An arbitrary reference elevation used to define elevation head.

What datum is commonly used in hydrogeology?

Sea level, often assigned z = 0 m.

Why can the datum be chosen arbitrarily?

Because groundwater flow depends on differences in potential or head, not their absolute values.

What is pressure potential?

Energy per unit mass associated with fluid pressure.

For constant density, what is pressure potential relative to reference pressure P0?

Φp = (P - P0)/ρ.

When gauge pressure is used, what is the reference pressure P0?

Atmospheric pressure is treated as zero, so P0 = 0.

With gauge pressure and constant density, what is pressure potential?

Φp = P/ρ.

What is atmospheric pressure approximately at Earth's surface?

About 101,300 Pa, 101.3 kPa, or 1 atm.

How are absolute pressure and gauge pressure related?

Pabs = Pg + Patm.

What is kinetic potential?

Energy per unit mass due to fluid velocity.

Write the kinetic potential equation.

Φv = v^2/2.

Write the total mechanical potential equation.

ΦT = gz + P/ρ + v^2/2.

What familiar equation does the total mechanical potential expression correspond to?

Bernoulli's equation.

What is hydraulic head?

Mechanical energy per unit weight of fluid.

How is hydraulic head related to hydraulic potential?

h = Φ/g.

What are the dimensions of hydraulic head?

Length, L, usually expressed in metres.

Write the full hydraulic head equation including velocity.

h = z + P/(ρg) + v^2/(2g).

Why is the kinetic head term normally neglected in groundwater systems?

Groundwater velocities are very small, so v^2/(2g) is usually negligible.

What is the standard groundwater hydraulic head equation?

h = z + P/(ρg).

How is pressure head ψ defined?

ψ = P/(ρg).

Write hydraulic head using elevation head and pressure head.

h = z + ψ.

What does elevation head z represent?

Potential energy per unit weight due to elevation above the datum.

What does pressure head ψ represent?

Energy per unit weight due to fluid pressure; conceptually, the height of water supported above the measurement point.

What is pressure head at the water table?

ψ = 0.

Why is pressure head zero at the water table?

Because water pressure equals atmospheric pressure there, which is zero on the gauge-pressure scale.

What is the sign of pressure head in the saturated zone according to the lecture?

Positive.

What is the sign of pressure head in the unsaturated zone according to the lecture?

Negative.

In a static water column, how do elevation head and pressure head vary with depth?

Elevation head decreases downward while pressure head increases downward.

In a hydrostatic water column, what happens to total hydraulic head with depth?

It remains constant.

If hydraulic head is constant everywhere, what is the hydraulic gradient?

Zero.

If hydraulic gradient is zero, is there groundwater flow driven by head differences?

No.

In a 4 m deep pool with the bottom as datum, what are z, ψ, and h at the water surface?

z = 4 m, ψ = 0 m, h = 4 m.

In a 4 m deep pool with the bottom as datum, what are z, ψ, and h at the bottom?

z = 0 m, ψ = 4 m, h = 4 m.

What is a piezometer?

A vertical pipe installed in the subsurface that is open only at or near the bottom to measure hydraulic head at a specific depth.

What is a monitoring well?

A vertical pipe with a longer screened interval, allowing water to enter over one or more depth intervals.

What is the main difference between a piezometer and a well?

A piezometer samples a relatively localized depth, whereas a well generally has a longer screened interval and provides a more distributed measurement.

Where is the measurement point of a piezometer?

At the open or screened interval near the bottom, not at the water level in the pipe.

How is a piezometer analogous to a thermometer?

The open end is like the thermometer bulb—the measurement point—while the water level is the measurement reading.

What does the rise of water in a piezometer represent?

The pressure head ψ at the piezometer's measurement point.

Can the water level in a piezometer be above the aquifer in which it is installed?

Yes, especially in a confined aquifer under pressure.

What does the water-level elevation in a piezometer represent?

The hydraulic head at the piezometer's measurement point.

How can hydraulic head be calculated from a field depth-to-water measurement?

Hydraulic head = measuring-point elevation - depth to water.

What are common methods for installing shallow piezometers shown in the lecture?

Hand auger, drive-point piezometer, and backpack drill.

What is generally used for deeper or more substantial well installations?

A professional drill rig.

What is a piezometer nest?

Several piezometers at the same location with their open ends at different depths.

Why are piezometer nests useful?

They allow hydraulic head to be compared vertically and can reveal upward or downward groundwater-flow gradients.

What are three arrangements for multi-level groundwater monitoring shown in the slides?

Cluster type, nested type, and multilevel system.

What is the potentiometric surface?

The level to which water rises in a piezometer.

In an unconfined aquifer, what does the potentiometric surface correspond to?

The water table.

In a confined aquifer, where can the potentiometric surface lie?

Above the top of the confined aquifer.

What is a flowing well?

A well where hydraulic head is high enough for water to rise above ground surface and flow without pumping.

How are grouped piezometers used to determine horizontal groundwater-flow direction?

Compare hydraulic heads at different horizontal locations; flow is from higher head to lower head.

How are piezometer nests used to determine vertical groundwater-flow direction?

Compare heads at different depths; water tends to move from the depth with higher head toward the depth with lower head.

If shallow head is greater than deep head, what is the general vertical flow tendency?

Downward.

If deep head is greater than shallow head, what is the general vertical flow tendency?

Upward.

In the class example, ground-surface elevation is 140 m and well depth is 20 m. What is the elevation head z at the piezometer opening?

z = 140 - 20 = 120 m.

In the class example, ground-surface elevation is 140 m and depth to water is 5 m. What is hydraulic head h?

h = 140 - 5 = 135 m.

In the class example, if z = 120 m and h = 135 m, what is pressure head ψ?

ψ = h - z = 15 m.

What is the key relationship connecting elevation head, pressure head, and total head?

h = z + ψ.

What sequence links energy differences to groundwater flow?

Energy difference → hydraulic potential difference → hydraulic head difference → hydraulic gradient → groundwater flow.