GATE 2025 ES – Question 54
A confined aquifer is 30 m thick with K=5 m/day and porosity .3. Observation wells X, Y are at radii100,200 m from a fully penetrating pumping well. Steady drawdowns are 5,3 m. A nonreactive pollutant enters at Y. Find advective travel time to X, in days, to two decimals.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 305.00 to 320.00
Explanation
Thiem’s equation gives $Q=2\pi Kb(s_X-s_Y)/\ln(r_Y/r_X)=2\pi(5)(30)(2)/\ln2=2719.416$ m³/day. Radial pore velocity magnitude is $v(r)=Q/(2\pi rb n)$. Integrate $dt=dr/v$ inward: $$t=\frac{\pi bn(r_Y^2-r_X^2)}Q=\frac{\pi(30)(.3)(200^2-100^2)}{2719.416}=\mathbf{311.92}\ \mathrm{days}.$$ Porosity converts Darcy flux to pore-water velocity.