Hydrogeology — Worked Examples

A uniform saturated section has hydraulic conductivity $K = 2.5 \times 10^{-4}\ \mathrm{m/s}$, average saturated thickness $12\ \mathrm{m}$ and width $500\ \mathrm{m}$. Heads measured from one datum are $45.2\ \mathrm{m}$ and $43.7\ \mathrm{m}$ at sections $150\ \mathrm{m}$ apart. Assume steady one-dimensional laminar flow and use positive flow from the first section toward the second. Find the discharge.

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A saturated laboratory specimen is $0.30\ \mathrm{m}$ long and $0.010\ \mathrm{m^2}$ in area. A maintained head loss of $0.60\ \mathrm{m}$ produces a collected volume of $0.0012\ \mathrm{m^3}$ in $60\ \mathrm{s}$. Estimate conductivity, assuming steady laminar flow and no bypass leakage.

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A homogeneous confined layer has saturated thickness $b = 35\ \mathrm{m}$ and transmissivity $T = 8.4\times10^{-3}\ \mathrm{m^2/s}$. Determine its hydraulic conductivity. Assume the reported transmissivity applies to the full layer thickness.

Use the first example's $K = 2.5\times10^{-4}\ \mathrm{m/s}$, gradient $i = 0.0100$ and travel distance $L = 150\ \mathrm{m}$. Effective porosity is $n_e = 0.30$. Estimate the average advective travel time for a conservative tracer under uniform steady flow, excluding dispersion, sorption, diffusion and decay.

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Take positive $x$ to the right. A saturated homogeneous section has left total head $12\ \mathrm{m}$, right total head $15\ \mathrm{m}$, length $100\ \mathrm{m}$, conductivity $1.0\times10^{-4}\ \mathrm{m/s}$ and area $200\ \mathrm{m^2}$. Determine the signed discharge and explain the zero-gradient state.

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For a representative material, porosity is $n = 0.32$ and specific yield is $S_y = 0.22$. Find specific retention. Then estimate drainable volume when a laterally uniform unconfined water table declines $0.50\ \mathrm{m}$ over $2.0\ \mathrm{km^2}$. Assume uniform specific yield and sufficient gravity drainage; ignore compressive storage and boundary inflows.

A homogeneous isotropic rectangular flow domain is $12\ \mathrm{m}$ long and $3\ \mathrm{m}$ thick, with no-flow top and bottom boundaries. Head loss is $H = 6\ \mathrm{m}$ and $K = 2.0\times10^{-5}\ \mathrm{m/s}$. The square-cell net has three channels and twelve potential drops. Find discharge per unit width, then total discharge across a $20\ \mathrm{m}$ width normal to the figure.

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A fully penetrating well extracts $Q = 50\ \mathrm{m^3/day}$ from a homogeneous isotropic confined aquifer with constant $T = 100\ \mathrm{m^2/day}$. A fixed-head boundary is specified at $R = 500\ \mathrm{m}$. Under steady radial flow without well loss, find drawdown at $r = 10\ \mathrm{m}$. Assume the aquifer remains confined throughout.

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A fully penetrating well pumps at $200\ \mathrm{m^3/day}$ in a homogeneous isotropic confined aquifer. At radii $10\ \mathrm{m}$ and $40\ \mathrm{m}$, the steady drawdown difference is $s_1-s_2 = 0.220\ \mathrm{m}$. Determine transmissivity without assuming an outer boundary radius. Neglect well losses at the observation points and assume confinement persists.

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An excavation leaves a uniform $3.0\ \mathrm{m}$ clay plug above a confined aquifer. Total clay unit weight is $20\ \mathrm{kN/m^3}$. The aquifer pressure head measured at the plug underside is $8.0\ \mathrm{m}$; the plug top is drained. Use water unit weight $9.81\ \mathrm{kN/m^3}$. Compare plug weight with underside water pressure per unit plan area, excluding side shear, structural resistance and all other loads.

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Consider a deliberately simplified unconfined control volume with plan area $1.0\ \mathrm{km^2}$ and uniform specific yield $0.20$. Recharge is $1.0\ \mathrm{mm/day}$ over that area and pumping is $1{,}500\ \mathrm{m^3/day}$. Assume no other inflows, outflows or storage mechanisms and representative gravity drainage over the interval. Find the net storage-change rate and average water-table change rate.