Three observation wells have been installed in an unconfined aquifer, as shown in Figure 7.15. Steady-state hydrostatic conditions are present. The aquifer has a uniform thickness, and its bottom is 50 ft below the groundwater table. The hydraulic conductivity is 3×10^-4 ft/s. Determine the

Question

Three observation wells have been installed in an unconfined aquifer, as shown in Figure 7.15. Steady-state hydrostatic conditions are present. The aquifer has a uniform thickness, and its bottom is 50 ft below the groundwater table. The hydraulic conductivity is [latex]3×10^{-4} ft/s[/latex]. Determine the hydraulic gradient, the direction of flow, the transmissivity, and the flow rate per unit width of the aquifer.

Accepted Answer

Evaluate the data on a horizontal plane by defining an [latex]x,y[/latex] coordinate system as shown, then define [latex]i_{x}[/latex] and [latex]i_{y}[/latex] as the hydraulic gradients in the [latex]x[/latex] and [latex]y[/latex] directions, respectively. This allows us to write the following equations:

[latex]A → B 8000 i_{x} + 1800 i_{y} = 35 - 22=13[/latex]

[latex]A → C 5000i_{x} - 2100i_{y} = 35 - 24 = 11 [/latex]

Solving these two equations simultaneously gives [latex]i_{x}= 0.00183[/latex] and [latex]i_{y} = -0.00089[/latex]. The resultant of these two components is:

[latex]i=\sqrt{i^{2}_{x} + i^{2}_{y}} =\sqrt{0.00183^{2} + \left(- 0.00089 ight) ^{2}} =0.0020[/latex]

[latex] heta = an ^{-1}\left\lgroup\frac{0.00089}{0.00183} ight group =26[/latex]°

Azimuth [latex]= 90 + 26 = 116[/latex]°

[latex]T=kh=\left(3 imes 10^{-4}ft/s ight) \left(50ft ight) =1.5 imes 10^{-2} ft^{2}/s[/latex]

[latex]q=Ti=\left(1.5 imes 10^{-2}ft^{2}/s ight) \left(0.0020ft/ft ight) =3 imes 10^{-5} \frac{ft^{3}/s}{ft} [/latex]

Alternative Solution

An alternative method of solving this problem would be to write the equation [latex]z=Ax +By+ C[/latex] at each of the observation wells. This would produce three equations and three unknowns, and thus could be solved. Such an equation could then be used to compute the groundwater elevation at any [latex]x,y[/latex] point. In addition, the coefficients [latex]A[/latex] and [latex]B[/latex] are equal to [latex]-i_{x}[/latex] and [latex]-i_{y}[/latex] respectively.

Question 7.5: Three observation wells have been installed in an unconfined...

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