Download - Soil water flow and Darcy’s Law
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Soil water flow and Darcy’s Law
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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)
LprQ
821 4
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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
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• insert fig
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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…
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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
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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
LHKq
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• Hpi = 100 cm; Hpo = 60 cm; L = 50 cm; K = 10 cm h-1 • q = ?
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• H1= 10 cm; L = 50 cm; K = 10 cm h-1 • q = ?
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Reading assignment
• p. 137-146
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• insert Fig. 7.7
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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 RRHq
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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
q
AA
tAV
tAVv
water
soil
soilwater
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Factors affecting hydraulic conductivity
• soil texture
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Factors affecting hydraulic conductivity
• soil texture
• soil water content and matric potential
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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
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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
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Reading assignment
• Infiltration, p.259-265