Two rivers 1000 m apart penetrate a confined aquifer 20 m thick. The hydraulic c

Question

Two rivers 1000 m apart penetrate a confined aquifer 20 m thick. The hydraulic conductivity of the aquifer is 20 m/day. The stages of the two rivers are 500 m and 495 m above sea level, respectively. What is the specific discharge for groundwater in the aquifer? If the reaches of the rivers are 600 m long and there are no pumped wells between them, what is the volume of groundwater outflow/inflow per year from the rivers? If a well were installed at a point exactly between the rivers, what would be the hydraulic head at this well prior to pumping?

Explanation / Answer

We know the Darcy law;

Specific Discharge, q = Q/A = -K(h/L)

where, K = hydraulic conductivity (20 m/day) and

(h/L) = hydraulic gradient; h = 500 - 495 = 5m and L = 1000m

Therefore, Specific Discharge, q = -K(h/L) = -20 * 5 / 1000 = - 0.1 m/day

since there is a pressure gradient, flow will occur from high pressure towards low pressure (opposite the direction of increasing gradient — hence the negative sign in Darcy's law). The growndwater flows from river at 500m to river at 495m.

As we know the specific discharge, the volume of water inflow from river at 500m to river at 495m per year will be,

Q = q * A where A = 20 m * 600 m = 12000 m2

Q = 0.1 m/day * 12000 m2 = 1200 m3/day = 1200 * 365 = 438000 m3/year

If a well is installed at a point exactly between the rivers, the L will now be = 1000/2 = 500m

Again using the Darcy Law

q = -K(h/L)

h = - q*L / K = 0.1 m/day * 500 m / 20 m/day = -2.5 m

Since, h=2.5m, the hydraulic head at well is 2.5m less than river at 500m = 500-2.5 = 497.5m.

Therefore, the hydraulic head at the well prior to pumping is 497.5m.

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