Darcys law

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Lecture 5 6

• Darcys law its applications

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Darcys observation Law

• One form of Darcy law

By comparison with N-S.E solution for simple
cases it was concluded that
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Estimating the hydraulic conductivity
Kozney-Carman Equation
Fair and Hatch Equation
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Example (Bear 1972)

• 1 darcy 9.8697 x 10-9 cm2
• a porous media has a permeability of 1 darcy.
• a) What is the hydraulic conductivity of this
  medium for water (? 0.013 cm2/s)
• b) What is the hydraulic conductivity of this
  medium for oil (? 1.8 cm2/s)

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Simple Applications

• Flow in confined, homogeneous constant thickness
• What if we allow K to be a given function
• What if we allow b to be variable
• Range of DL validity (NRqd/v less than 10)

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Determination of Flow Direction (horizontal flow)
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Problem 2.2.4 TEXT
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Constant head permeameter
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Falling head permeameter
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Example
A long narrow reservoir (area 1.5 km2)is
hydraulically connected to a stream though a 7 m
thick sand body. To keep the water level
constant, (25 m above the stream level), a flow
of 4.2 m3/min is added to the reservoir. a)
calculate K for the sand. b) If the inflow is
stopped, neglect evaporation and calculate how
much time is required to drop the water level by
3 m c) If a layer of silt (K0.003 m/d) 0.5 m
thick is formed on the face of the aquifer
calculate the reduction of seepage.
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Equivalent K for Layered Media
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Anisotropy
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Example on anisotropy

• x and y are principal axis and Kx 25 m/d, Ky
  5 m/d estimate the flow direction if the head
  gradient I has a magnitude of 0.01 and makes an
  angle of 50 with the x-axis, estimate the
  magnitude and direction of the Darcy velocity.

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Refraction of q
Flow across boundary is equal Pressure at
interface is the same in both PMs
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Example

• Downward seepage occurs from a shallow pond
  to a water table. A conservative traces is
  introduced at point A. Calculate the location of
  tracer appearance at the water table and the time
  it takes. Neglect dispersion, diffusion and
  assume subsurface fully saturated.

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K for fractured PMsection 2.2.4 text
Example 2.2.2 Fracture thickness 0.01
cm Fracture spacing 220 cm Q (total) Q (pm)
Q (fracture)