12:166, Zhang

Spring, 2002

Darcy’s Law and Hydraulic Head

· Darcy’s Law (established in 1856 by Henry Darcy)

Where Q is the volumetric flow rate (L³ / T, cm³/sec, gal/min)

K is the hydraulic conductivity (L / T, cm/sec, gal/day/ft²)

A is the cross-sectional area (L², cm², ft²)

i is the hydraulic gradient and

q is the specific discharge or Darcy’s velocity or Darcy’s flux (L / T, cm/sec);

Remark: (1) Darcy’s law is often written as

(2) Darcy’s law is an empirical law, valid for most granular materials;

(3) Darcy’s law is valid for flow in any direction;

(4) Darcy’s law is a macroscopic law;

(5) Darcy’s law is a linear law.

Lower limit:

Upper limit: Reynolds number: 1 – 10

Laminar flow vs. turbulent flow

· Specific Discharge (q) and Average Linear (or Seepage) Velocity (v)

where n_e is the effective porosity.

Remark: (1) v is an average velocity; (2) v is always larger than q.

· Fluid Potential (F) and Hydraulic Head (h)

Piezometer is a tube or pipe which is open at the top and bottom.

Fluid potential is the mechanical energy per unit mass of fluid

Where r is the water density

Hydraulic Head is the mechanical energy per unit weight of fluid

Where z is the Elevation head and y the Pressure head

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Reading: Section 3.11 (p.104 -108) and Section 4.1 – 4.6 (p. 113 –125)