Coastal Aquifer: Fresh-Saline Interface Depth Calculation
This problem involves calculating the depth of the fresh-saline water interface below the water table in an unconfined coastal aquifer using the Ghyben-Herzberg principle. This principle relates the position of the freshwater table to the interface.
Ghyben-Herzberg Principle Application
The principle is based on the concept that the pressure at the fresh-saline interface must be equal when considered from the freshwater side and the saline water side, relative to sea level.
Formulating the Equation
Let:
- $h$ = Height of the freshwater table above Mean Sea Level (MSL). Given as $h = 1$ m.
- $z$ = Depth of the fresh-saline water interface below MSL.
- ${\rho_f}$ = Density of fresh water. Given as ${\rho_f = 1.001}$ g/cc.
- ${\rho_s}$ = Density of saline water. Given as ${\rho_s = 1.025}$ g/cc.
- The depth of the interface from the water table ($D_{wt\_interface}$) is related to $h$ and $z$ by $D_{wt\_interface} = h + z$.
The pressure balance equation at the interface is derived from:
$ \rho_f \times g \times (h + z) = \rho_s \times g \times z $Where $g$ is the acceleration due to gravity. Simplifying this equation:
$ \rho_f \times h + \rho_f \times z = \rho_s \times z $ $ \rho_f \times h = (\rho_s - \rho_f) \times z $Solving for $z$ (depth below MSL):
$ z = \frac{\rho_f \times h}{\rho_s - \rho_f} $Calculation Steps
- Substitute the given values into the formula: $ z = \frac{1.001 \, \text{g/cc} \times 1 \, \text{m}}{1.025 \, \text{g/cc} - 1.001 \, \text{g/cc}} $
- Calculate the difference in densities: $ \rho_s - \rho_f = 1.025 - 1.001 = 0.024 \, \text{g/cc} $
- Calculate the depth $z$: $ z = \frac{1.001}{0.024} \, \text{m} $ $ z \approx 41.7083 \, \text{m} $ This is the depth of the interface below MSL.
- Calculate the depth from the water table ($D_{wt\_interface}$): $ D_{wt\_interface} = h + z $ $ D_{wt\_interface} = 1 \, \text{m} + 41.7083 \, \text{m} $ $ D_{wt\_interface} \approx 42.7083 \, \text{m} $
- Round the result to one decimal place as required: $ D_{wt\_interface} \approx 42.7 \, \text{m} $
Final Answer
The fresh-saline water interface should be approximately 42.7 m from the water table.
Important Questions from Hydrogeology (Groundwater Flow and Exploration)
- With regard to occurrence of groundwater in an area, which of the given statements is CORRECT?
- The groundwater flow equation $\frac{\partial^2h}{\partial x^2} + \frac{\partial^2h}{\partial y^2} + \frac{\partial^2h}{\partial z^2} = 0$, where h refers to the hydraulic head and x, y, z are coordinates, is valid when the flow condition is
- Which one of the following increases over time when the soil is fully saturated?
