soil water flow and darcy’s law. laminar flow in a tube poiseuille’s law, ~1840: where: q =...

Soil water flow and Darcy’s Law

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Soil water flow and Darcy’s Law

Laminar flow in a tube

• Poiseuille’s Law, ~1840:

where:

Q = volume of flow per unit time (m3 s-1)r = radius of the cylindrical tube (m)p = pressure drop across the tube (Pa)L = length of the tube (m) = viscosity (Pas)

prQ

1 4

Page 3: Soil water flow and Darcy’s Law. Laminar flow in a tube Poiseuille’s Law, ~1840: where: Q = volume of flow per unit time (m 3 s -1 ) r = radius of the

Macroscopic flow-velocity vector

• the overall average of the microscopic velocities over the total volume considered

• the volume considered must be large relative to the scale of heterogeneity

• the ratio of the path length through the soil pores to the net travel distance is the tortuosity

Page 4: Soil water flow and Darcy’s Law. Laminar flow in a tube Poiseuille’s Law, ~1840: where: Q = volume of flow per unit time (m 3 s -1 ) r = radius of the

• insert fig

Page 5: Soil water flow and Darcy’s Law. Laminar flow in a tube Poiseuille’s Law, ~1840: where: Q = volume of flow per unit time (m 3 s -1 ) r = radius of the

Water flux

• the volume of water flowing through a unit cross-sectional area per unit time (V/At)

• units of m s-1 , cm h-1, etc…

Page 6: Soil water flow and Darcy’s Law. Laminar flow in a tube Poiseuille’s Law, ~1840: where: Q = volume of flow per unit time (m 3 s -1 ) r = radius of the

Hydraulic gradient

• the drop in water potential per unit distance in the direction of flow (H/L)

• a driving force for water flow

• units depend on how water potential is specifieda) commonly water potential is in units of “head” (e.g. cm of

water) and the hydraulic gradient is unitless

Darcy’s Law

• Henry Darcy; Dijon, France; 1856• the flux is proportional to the hydraulic gradient

• q = flux• H/L = hydraulic gradient• K = hydraulic conductivity; a measure of the soil’s

ability to transmit liquid water

HKq

Page 8: Soil water flow and Darcy’s Law. Laminar flow in a tube Poiseuille’s Law, ~1840: where: Q = volume of flow per unit time (m 3 s -1 ) r = radius of the

• Hpi = 100 cm; Hpo = 60 cm; L = 50 cm; K = 10 cm h-1 • q = ?

Page 9: Soil water flow and Darcy’s Law. Laminar flow in a tube Poiseuille’s Law, ~1840: where: Q = volume of flow per unit time (m 3 s -1 ) r = radius of the

• H1= 10 cm; L = 50 cm; K = 10 cm h-1 • q = ?

Page 10: Soil water flow and Darcy’s Law. Laminar flow in a tube Poiseuille’s Law, ~1840: where: Q = volume of flow per unit time (m 3 s -1 ) r = radius of the

Reading assignment

• p. 137-146

Page 11: Soil water flow and Darcy’s Law. Laminar flow in a tube Poiseuille’s Law, ~1840: where: Q = volume of flow per unit time (m 3 s -1 ) r = radius of the

• insert Fig. 7.7

Page 12: Soil water flow and Darcy’s Law. Laminar flow in a tube Poiseuille’s Law, ~1840: where: Q = volume of flow per unit time (m 3 s -1 ) r = radius of the

Hydraulic resistance

• the resistance of a specified thickness of a particular soil to water flow (Rh)

• Rh = L/K

• For flow through two soil layers, Darcy’s Law is

21 hh RR

Page 13: Soil water flow and Darcy’s Law. Laminar flow in a tube Poiseuille’s Law, ~1840: where: Q = volume of flow per unit time (m 3 s -1 ) r = radius of the

Page 14: Soil water flow and Darcy’s Law. Laminar flow in a tube Poiseuille’s Law, ~1840: where: Q = volume of flow per unit time (m 3 s -1 ) r = radius of the

Pore water velocity• the average velocity of water flow through the soil

pores

• water flow takes place through the liquid phase in the pores, not through the whole soil

• pore water velocity > water flux

water

soil

soilwater

Factors affecting hydraulic conductivity

• soil texture

Page 16: Soil water flow and Darcy’s Law. Laminar flow in a tube Poiseuille’s Law, ~1840: where: Q = volume of flow per unit time (m 3 s -1 ) r = radius of the

Page 17: Soil water flow and Darcy’s Law. Laminar flow in a tube Poiseuille’s Law, ~1840: where: Q = volume of flow per unit time (m 3 s -1 ) r = radius of the

Factors affecting hydraulic conductivity

• soil texture

• soil water content and matric potential

Page 18: Soil water flow and Darcy’s Law. Laminar flow in a tube Poiseuille’s Law, ~1840: where: Q = volume of flow per unit time (m 3 s -1 ) r = radius of the

Page 19: Soil water flow and Darcy’s Law. Laminar flow in a tube Poiseuille’s Law, ~1840: where: Q = volume of flow per unit time (m 3 s -1 ) r = radius of the

Factors affecting hydraulic conductivity

• soil texture

• soil water content and matric potential

• soil structure

• electrical conductivity of the soil solution

• species of cations present

• entrapped air

Page 20: Soil water flow and Darcy’s Law. Laminar flow in a tube Poiseuille’s Law, ~1840: where: Q = volume of flow per unit time (m 3 s -1 ) r = radius of the

Page 21: Soil water flow and Darcy’s Law. Laminar flow in a tube Poiseuille’s Law, ~1840: where: Q = volume of flow per unit time (m 3 s -1 ) r = radius of the

Factors affecting hydraulic conductivity

• soil texture

• soil water content and matric potential

• soil structure

• electrical conductivity of the soil solution

• species of cations present

• entrapped air

• viscosity of the soil solution

• soil temperature

Page 22: Soil water flow and Darcy’s Law. Laminar flow in a tube Poiseuille’s Law, ~1840: where: Q = volume of flow per unit time (m 3 s -1 ) r = radius of the

Reading assignment

• Infiltration, p.259-265

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