How long does it take for 150,000 metric tons of water to pass through a cross s

Question

How long does it take for 150,000 metric tons of water to pass through a cross section of the aquifer?

Fig.(8.6) Problem 7 8. Consider the aquifer shown in Fig.(8.7); the aquifer is 830 m wide. The yield porosity of the medium is 47.3% and its hydraulic conductivity equals 143 m/d (a) How long does it take the groundwater to move from well A to well B? (b) How long does it take for 150,000 metric tons of water to pass through a cross section of the aquifer? 1.82 km ...27.0m 42.0 m Fig.(8.7) Problem 8

Explanation / Answer

From Darcy's law, we know that flow rate through the aquifer= Q= {K*A*(H1-H2)}/L

where K= hydraulic conductivity

A =cross-sectional area of the aquifer

H1 & H2= water table elevation in well A and B

L = distance between the two well

Now, Darcy's velocity= q= Q/A= {K*(H1-H2)}/L

q={143*(36-27)}/1820=0.708m/day

remember here K=143m/day

and L = 1.82km= 1820 km

now discharge, Q= q*A=0.708*(830*830)=487150.8m3/day

now, 150000 metric tonnes= 150000litres=150m3.

so, the required time flow the water through the aquifer=150/487150.8=0.00031day.

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