A pumped well and two observation wells have been installed through a fine-to-medium sand as shown in Figure 8.23. A pump has been discharging water from the pumped well for a sufficient time to achieve steady-state conditions. The water levels in observation wells A and B were then observed to be

Question

A pumped well and two observation wells have been installed through a fine-to-medium sand as shown in Figure 8.23. A pump has been discharging water from the pumped well for a sufficient time to achieve steady-state conditions. The water levels in observation wells A and B were then observed to be 20 and 35 ft below the ground surface, respectively. Compute the hydraulic conductivity of the aquifer.

Accepted Answer

This is an unconfined aquifer, so use Equation 8.33 [latex]k=\frac{Q\ln \left(r_{1}/r_{2} ight) }{\pi \left(h^{2}_{1} - h^{2}_{2} ight) }[/latex].

[latex]Q=\left(150 gal/min ight) \left\lgroup\frac{1 ft^{3}}{7.48 gal} ight group \left\lgroup\frac{1 min}{60 s} ight group =0.33 ft^{3}/s[/latex]

[latex]h_{1} = 90 - 20 = 70 ft [/latex]

[latex]h_{2} = 90 - 35 = 55 ft [/latex]

[latex]k=\frac{Q\ln \left(r_{1}/r_{2} ight) }{\pi \left(h^{2}_{1} - h^{2}_{2} ight) } =\frac{0.33 ft^{3}/s\ln \left(170 ft/20 ft ight) }{\pi \left[\left(70 ft ight) ^{2} - \left(55 ft ight) ^{2} ight] } =1 imes 10^{-4} ft/s[/latex]

This answer seems reasonable, per Table 7.1.

Soil Description	Hydraulic Conductivity, [latex]k[/latex]
Soil Description	(cm/s)	(ft/s)
Clean gravel	1 to 100	[latex]3 imes 10^{-2}[/latex] to [latex]3[/latex]
Sand-gravel mixtures	[latex]10^{-2}[/latex] to [latex]10[/latex]	[latex]3 imes 10^{-4}[/latex] to [latex]0.3[/latex]
Clean coarse sand	[latex]10^{-2}[/latex] to [latex]1 [/latex]	[latex]3 imes 10^{-4}[/latex] to [latex]3 imes 10^{-2}[/latex]
Fine sand	[latex]10^{-3}[/latex] to [latex]10^{-1}[/latex]	[latex]3 imes 10^{-5}[/latex] to [latex]3 imes 10^{-3}[/latex]
Silty sand	[latex]10^{-3}[/latex] to [latex]10^{-2}[/latex]	[latex]3 imes 10^{-5}[/latex] to [latex]3 imes 10^{-4}[/latex]
Clayey sand	[latex]10^{-4}[/latex] to [latex]10^{-2} [/latex]	[latex]3 imes 10^{-6}[/latex] to [latex]3 imes 10^{-4}[/latex]
Silt	[latex]10^{-8}[/latex] to [latex]10^{-3} [/latex]	[latex]3 imes 10^{-10}[/latex] to [latex]3 imes 10^{-5}[/latex]
Clay	[latex]10^{-10}[/latex] to [latex]10^{-6}[/latex]	[latex]3 imes 10^{-12}[/latex] to [latex]3 imes 10^{-8}[/latex]

Question 8.4: A pumped well and two observation wells have been installed ...

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