Steady Flow to Wells: Confined & Unconfined Aquifers
Subtopic: Thiem formula discharge in confined aquifer
Question Statement:
A fully penetrating well pumps water from a confined aquifer of transmissivity $T = 800\text{ m}^2/\text{day}$. Two observation wells situated at radial distances of $r_1 = 15\text{ m}$ and $r_2 = 90\text{ m}$ record steady drawdowns of $s_1 = 3.0\text{ m}$ and $s_2 = 1.0\text{ m}$, respectively. The steady pumping discharge is ________ $\text{m}^3/\text{day}$ (round off to one decimal place).
Answer Key:
5610.7
Step-by-Step Solution & Explanation
From the Thiem equilibrium equation for steady radial flow to a well in a confined aquifer:
$Q = \frac{2 \pi T (s_1 - s_2)}{\ln(r_2 / r_1)}$
Given $T = 800\text{ m}^2/\text{day}$, $s_1 - s_2 = 2.0\text{ m}$, $r_2/r_1 = 6.0$ ($\ln(6.0) = 1.7918$):
$Q = \frac{2 \pi (800) (2.0)}{1.7918} = \frac{10053.10}{1.7918} = 5610.7\text{ m}^3/\text{day}$