この ダーシーの法則計算機 is a tool used to determine the flow rate of a fluid through a porous medium based on ダルシーの法則. This principle is fundamental in hydrogeology, petroleum engineering, and soil science, helping engineers and scientists estimate fluid movement in reservoirs, aquifers, and filtration systems.
Darcy’s Law describes how a fluid flows through a porous medium under a pressure difference, considering permeability, viscosity, and the geometry of the medium. By using this calculator, professionals can assess groundwater movement, predict oil recovery, and optimize filtration systems.
Formula for Darcy’s Law Calculator
The flow rate of a fluid through a porous medium is calculated using the equation:
Flow Rate (Q) = (Permeability × Cross-sectional Area × Pressure Difference) / (Viscosity × Length of Flow Path)
どこ：
- Q (m³/s) = Volumetric flow rate
- Permeability (m²) = Measure of how easily a fluid can pass through a porous medium
- 断面積 (m²) = The area through which fluid flows
- 圧力差（Pa） = 圧力降下 across the medium
- 粘度（Pa·s） = Dynamic viscosity of the fluid
- Length of Flow Path (m) = Distance the fluid travels through the medium
This formula helps determine the スピード and volume of fluid moving through different geological and industrial systems.
Darcy’s Law Estimation Table
The table below provides estimated flow rates based on different permeability, viscosity, and pressure difference values.
| Permeability (m²) | 断面積 (m²) | 圧力差（Pa） | 粘度（Pa·s） | Flow Path Length (m) | 流量 (m3/s) |
|---|---|---|---|---|---|
| 1 × 10⁻¹² | 1 | 10,000 | 0.001 | 10 | 1.0 × 10⁻⁶ |
| 5 × 10⁻¹² | 2 | 20,000 | 0.001 | 15 | 1.33 × 10⁻⁵ |
| 1 × 10⁻¹³ | 0.5 | 5,000 | 0.0005 | 8 | 6.25×10⁻⁷ |
| 3 × 10⁻¹³ | 1.5 | 15,000 | 0.002 | 12 | 5.63×10⁻⁷ |
| 2 × 10⁻¹² | 3 | 25,000 | 0.003 | 20 | 2.5 × 10⁻⁶ |
This table provides quick reference values for estimating flow rates in various systems.
Example of Darcy’s Law Calculator
A hydrogeologist is studying groundwater flow through an aquifer with the following properties:
- 透過性 = 5 × 10⁻¹² m²
- 断面積 =2m²
- 圧力差 = 20,000Pa
- = 0.001 Pa·s
- Length of Flow Path = 15メートル
Step 1: Apply Values to the Formula Q = (Permeability × Cross-sectional Area × Pressure Difference) / (Viscosity × Length of Flow Path)
Q = (5 × 10⁻¹² × 2 × 20,000) / (0.001 × 15)
Q = (2 × 10⁻⁷) / 0.015 = 1.33 × 10⁻⁵ m³/s
This means the fluid flows at a rate of 1.33 × 10⁻⁵ cubic メートル/秒 through the porous medium.
最も一般的な FAQ
Darcy’s Law is essential in hydrogeology, petroleum engineering, and soil science to estimate the movement of fluids through porous materials. It helps predict groundwater flow, optimize oil extraction, and design filtration systems.
Higher permeability allows fluids to move more easily through a material, increasing the flow rate. Lower permeability results in restricted fluid movement.
Yes, but modifications are needed to account for gas compressibility. Darcy’s Law primarily applies to liquids, while gas flow requires additional considerations.