HYD-21

Darcy's law

Q = k i A. Discharge through a porous prism, i = Δh/L.

Reading speed

SeepageDarcy 1856

Governing equation

Q=k i A

where

k: Permeability (m/s)
i: Gradient (—)
A: Area (m²)
Q: Discharge (m³/s)

Lecture brief

Historical brief

Open-channel and pipe flow were written by Chezy, Manning, Darcy and Weisbach in the nineteenth century, then Bakhmeteff and Bélanger on the hydraulic jump. The sheets compute conveyance, head loss and gradually varied profiles. This sheet (HYD-21 — Darcy's law) is the form associated with Darcy 1856. Working symbols: $k$ , $i$ , $A$ $\rightarrow$ $Q$ . Linear laminar filtration. k is conductivity; i the hydraulic gradient. Valid at low Re.

Purpose

Purpose: compute

Q

from

k

i

A

in Hydraulics via

Q=k i A

Q = k i A. Discharge through a porous prism, i = Δh/L. Use it when a real hydraulics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

k = 1.000e-4\,\mathrm{m/s}

i = 0.050\,\mathrm{—}

A = 2.000\,\mathrm{m^{2}}

, the governing relation

Q=k i A

yields

Q = 1.000e-5\,\mathrm{m^{3}/s}

. A sand filter, a head drop, a seepage arrow. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Permeability k0.0001 m/sGradient i0.05 —Area A2 m²

Outputs

Discharge Q0.000010 m³/s

Reading speed

Watch on YouTube

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Narration of this film

A sand filter, a head drop, a seepage arrow.

Linear laminar filtration. k is conductivity; i the hydraulic gradient. Valid at low Re.

Reading speed

Watch on YouTube