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An aquifer has three different formations. Formation A has a thickness of 22 ft and a hydraulic conductivity of 17.0 ft/d. Formation B has a thickness of 3.5 ft and hydraulic conductivity of 99 ft/d. Formation C has a thickness of 26 ft and hydraulic conductivity of 22 ft/d. Assume that each formation is isotropic and homogeneous. Compute both the overall horizontal and vertical conductivities.

Respuesta :

Answer:

[tex]k_h=25.09\ ft/d[/tex]

[tex]k_v=20.5ft/d[/tex]

Explanation:

Given that

h₁= 22 ft ,k₁= 17 ft/d

h₂= 3.5 ft, k₂=99 ft/d

h₃=26 ft ,k₃=22 ft/d

Horizontal conductivity

[tex]k_h=\dfrac{k_1h_1+k_2h_2+k_3h_3}{h_1+h_2+h_3}[/tex]

Now by putting the values

[tex]k_h=\dfrac{17\times 22+3.5\times 99+26\times 22}{22+3.5+26}\ ft/d[/tex]

[tex]k_h=25.09\ ft/d[/tex]

Vertical conductivity

[tex]k_v=\dfrac{h_1+h_2+h_3}{\dfrac{h_1}{k_1}+\dfrac{h_2}{k_2}+\dfrac{h_3}{k_3}}[/tex]

[tex]k_v=\dfrac{22+3.5+26}{\dfrac{22}{17}+\dfrac{3.5}{99}+\dfrac{26}{22}}\ ft/d[/tex]

[tex]k_v=20.5ft/d[/tex]

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