Darcy’s Law Calculator

by

Darcy’s Law Calculator:

Enter the values of permeability of the porous medium, k(m2), cross-sectional area, A(m2), pressure difference, ΔP(Pa), dynamic viscosity, μ(Pa-s) and length, L(m) to determine the value of Volumetric Flow Rate, q(m3/s).

Enter Porous Mdium: m/s2
Enter Area: m/s2
Enter Pressure Difference: Pa
Enter Dynamic Viscosity: Pa-s
Enter Length: m
   
Result – Volumetric Flow Rate: m3/s

Darcy’s Law Formula:

Darcy’s Law is a fundamental equation in fluid mechanics and hydrogeology that describes the flow of a fluid through a porous medium. It was formulated by Henry Darcy in 1856 and is widely used in engineering, groundwater hydrology, petroleum engineering, and soil science.

The law states that the volumetric flow rate of a fluid through a porous material is directly proportional to the pressure difference and inversely proportional to the viscosity. It assumes that the flow is laminar, meaning there is no turbulence, and that the medium is homogeneous and isotropic.

Darcy’s Law is useful for predicting the movement of groundwater, the permeability of soil, and the extraction of oil and gas from reservoirs. The hydraulic conductivity or permeability of the medium plays a crucial role in determining the rate of fluid movement.

The equation considers factors such as the cross-sectional area of the medium, fluid viscosity, and pressure gradient. A higher permeability or pressure gradient leads to a higher flow rate, while increased viscosity reduces the flow rate.

The negative sign in the equation indicates that the flow occurs in the direction of decreasing pressure. Darcy’s Law can be applied to both saturated and unsaturated flow conditions in porous media.

It is valid for slow, steady flows where inertial forces are negligible compared to viscous forces. Real-world deviations from Darcy’s Law occur at high flow velocities, in heterogeneous materials, or when chemical reactions alter the medium.

Volumetric Flow Rate, q(m3/s) in cubic metres per second is equal to the permeability of the porous medium, k(m2) in square metres, multiplied by the cross-sectional area, A(m2) in square metres, multiplied by the pressure difference, ΔP(Pa) in Pascals, divided by the dynamic viscosity, μ(Pa-s) in Pascal-seconds and the length, L(m) of the porous medium in metres.

Volumetric Flow Rate, q(m3/s) = k(m2) * A(m2) * ΔP(Pa) / μ(Pa-s) * L(m)

q(m3/s) = volumetric flow rate in cubic metres per second, m3/s.

k(m2) = porous medium in square metres, m2.

A(m2) = area in square metres, m2.

ΔP(Pa) = pressure difference in Pascals, Pa.

μ(Pa-s) = dynamic viscosity in Pascals-second, Pa-s.

L(m)  = length in metres, m.

Darcy’s Law Calculation:

  1. A porous medium has a permeability of 1.2 * 10−12 m2, a cross-sectional area of 0.05 m2, a pressure difference of 5000 Pa, a fluid viscosity of 0.001 Pa-s, and a length of 2 m. Calculate the volumetric flow rate.

Given: k(m2) = 1.2 * 10−12m2,  A(m2) = 0.05 m2, ΔP(Pa) = 5000Pa, μ(Pa-s) = 0.001 Pa-s, L(m)  = 2m.

Volumetric Flow Rate, q(m3/s) = k(m2) * A(m2) * ΔP(Pa) / μ(Pa-s) * L(m)

q(m3/s) = 1.2 * 10−12 * 0.05 * 5000 / 0.001 * 2

q(m3/s) = 3 * 10-8 / 0.002

q(m3/s) = 1.5 * 10-5m3/s.

  1. Given: k(m2) = 2.5 * 10−12m2, A(m2) = 0.08 m2, ΔP(Pa) = 7000Pa, μ(Pa-s) = 0.002 Pa-s, q(m3/s) = 2.0 * 10-5m3/s.

Volumetric Flow Rate, q(m3/s) = k(m2) * A(m2) * ΔP(Pa) / μ(Pa-s) * L(m)

L(m)  = k(m2) * A(m2) * ΔP(Pa) / μ(Pa-s) * q(m3/s)

L(m)  = 2.5 * 10−12 * 0.08 * 7000 / 0.002 * 2.0 * 10-5

L(m)  = 1.4 * 10-7 / 4.0 * 10-8

L(m)  = 3.5m.

Leave a Comment