Groundwater Flow Rate Calculator

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Groundwater Flow Rate Calculator (Darcy's Law)

Please enter valid numeric values. Conductivity, Area, and Length must be positive.

Calculation Results

Hydraulic Gradient (i): –

Volumetric Flow Rate (Q): – m³/day

Interpretation:

function calculateGroundwaterFlow() { // Get input values var kVal = parseFloat(document.getElementById('gw_k').value); var areaVal = parseFloat(document.getElementById('gw_area').value); var h1Val = parseFloat(document.getElementById('gw_h1').value); var h2Val = parseFloat(document.getElementById('gw_h2').value); var lengthVal = parseFloat(document.getElementById('gw_length').value); var errorDiv = document.getElementById('gw_error'); var resultDiv = document.getElementById('gw-result'); // Validate inputs // K, Area must be non-negative. Length must be strictly positive to avoid divide by zero. if (isNaN(kVal) || isNaN(areaVal) || isNaN(h1Val) || isNaN(h2Val) || isNaN(lengthVal) || kVal < 0 || areaVal < 0 || lengthVal 0) { interpretation = "Water is flowing from Point 1 towards Point 2."; } else if (flowRate < 0) { interpretation = "Water is flowing in reverse, from Point 2 towards Point 1."; } else { interpretation = "There is no net flow (hydraulic heads are equal)."; } document.getElementById('gw_result_interpretation').textContent = interpretation; }

Understanding Groundwater Flow and Darcy's Law

Groundwater movement in aquifers is governed by fundamental physical principles. The primary equation used to estimate the volumetric flow rate of water through porous media like soil, sand, and rock is known as Darcy's Law. This calculator applies Darcy's Law to help hydrogeologists, engineers, and environmental scientists estimate how much water is moving through a specific subsurface cross-section.

The Formula Used in This Calculator

Darcy's Law states that the rate of fluid flow through a porous medium is directly proportional to the hydraulic conductivity of the medium, the cross-sectional area perpendicular to the flow, and the hydraulic gradient. The formula is expressed as:

Q = K × A × i

Where the hydraulic gradient (i) is the change in head divided by the flow path length:

i = (h₁ – h₂) / L

Key Parameters Explained

  • Hydraulic Conductivity (K): Often called permeability, this measures the aquifer's ability to transmit water. A high K value (e.g., clean gravel or sand) means water flows easily. A low K value (e.g., clay or solid granite) means water flows very slowly. Units here are meters per day (m/day).
  • Cross-Sectional Area (A): This is the vertical area of the aquifer through which the water is moving, perpendicular to the direction of flow. Units are square meters (m²).
  • Hydraulic Head (h₁ and h₂): Hydraulic head represents the mechanical energy per unit weight of the fluid. Water always flows from areas of higher head to areas of lower head. By measuring the head at two different points, we can determine the driving force of the flow. Units are meters (m).
  • Flow Path Length (L): The physical distance between the two points where hydraulic head was measured. Units are meters (m).

Example Calculation

Imagine a sandy aquifer. We want to know the flow rate between two monitoring wells situated 200 meters apart.

  • The aquifer material is medium sand with a Hydraulic Conductivity (K) of 15 m/day.
  • The aquifer is 50 meters wide and 10 meters deep, giving a Cross-Sectional Area (A) of 500 m².
  • The water level in Well 1 is at an elevation of 100m (h₁).
  • The water level in Well 2 is at an elevation of 98m (h₂).
  • The distance between the wells is 200m (L).

First, calculate the gradient: i = (100 – 98) / 200 = 2 / 200 = 0.01.

Next, calculate the flow rate: Q = 15 * 500 * 0.01 = 75 m³/day.

This means 75 cubic meters of water are passing through that cross-section every day toward the well with the lower head.

Limitations

Darcy's Law assumes "laminar flow," which means water moves smoothly through pore spaces. It may not accurately predict flow in situations with extremely high velocities (turbulent flow, sometimes near pumping wells) or in fractured rock systems where flow occurs through large cracks rather than porous matrix.

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