Ghyben Herzberg Relationship for Depth of Freshwater below Sea Level Calculator

Ghyben Herzberg Relationship:

\[ h_s = \frac{\rho_f \cdot h_f}{\rho_s - \rho_f} \]

Density of Fresh Water (ρf):

kg/m³

Height of the water table above sea level (hf):

Density of Seawater (ρs):

kg/m³

Depth of Freshwater below Sea Level (hs):

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1. What is the Ghyben Herzberg Relationship?

The Ghyben Herzberg relationship describes the hydrostatic equilibrium between freshwater and seawater in coastal aquifers. It provides a method to estimate the depth of the freshwater-seawater interface below sea level based on density differences.

2. How Does the Calculator Work?

The calculator uses the Ghyben Herzberg equation:

\[ h_s = \frac{\rho_f \cdot h_f}{\rho_s - \rho_f} \]

Where:

\( h_s \) — Depth of freshwater below sea level (m)
\( \rho_f \) — Density of fresh water (kg/m³)
\( h_f \) — Height of the water table above sea level (m)
\( \rho_s \) — Density of seawater (kg/m³)

Explanation: The relationship is based on the principle that for every unit of freshwater above sea level, there are approximately 40 units of freshwater below sea level (assuming typical density values).

3. Importance of Depth Calculation

Details: Accurate estimation of the freshwater-seawater interface depth is crucial for coastal groundwater management, preventing saltwater intrusion, and sustainable freshwater extraction from coastal aquifers.

4. Using the Calculator

Tips: Enter density values in kg/m³ and height in meters. Typical values: freshwater density ≈ 1000 kg/m³, seawater density ≈ 1025 kg/m³. All values must be positive, and seawater density must be greater than freshwater density.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical ratio between freshwater above and below sea level?
A: Typically, for every meter of freshwater above sea level, there are approximately 40 meters of freshwater below sea level, based on standard density values.

Q2: What factors can affect the accuracy of this relationship?
A: The relationship assumes hydrostatic equilibrium and doesn't account for dynamic effects, mixing zones, or geological heterogeneity that may occur in real aquifers.

Q3: How does temperature affect the calculation?
A: Temperature affects water density. Warmer water is less dense, which can influence the interface depth calculation.

Q4: Can this relationship be used for all coastal aquifers?
A: While widely used, the relationship provides a simplified estimation and may need modification for complex geological settings or where dynamic processes dominate.

Q5: What are the limitations of the Ghyben Herzberg relationship?
A: It assumes static conditions, neglects mixing and dispersion effects, and may not accurately represent situations with significant groundwater flow or complex aquifer geometry.