GATE 2024 AG – Question 58
A 15 cm diameter tubewell has initial groundwater depth 40 m above screen bottom, K=20 m/day, influence radius980 m and maximum drawdown12 m. A second identical well is installed500 m away and both pump equal flows. Find first-well discharge loss in percent, to two decimals.
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Correct answer: 6.60 to 6.70
Explanation
Use superposition of the steady unconfined discharge potential for the keyed interference approximation. Let $a=\ln(R/r_w)=\ln(980/.075)$ and $b=\ln(R/d)=\ln(980/500)$. For the same limiting well drawdown, the isolated discharge is proportional to 1/a, whereas each equal interacting discharge is proportional to 1/(a+b). Relative loss is $1-a/(a+b)=b/(a+b)=.06629496$,or **6.63%**. K and the common head-potential difference cancel.