Question

A fully penetrating confined aquifer is pumped at a constant rate of $Q{m}^3/sec$. The drawdowns at an observation well at a distance r from pumping well are in the ratio of 3 : 4 after one and two hours of pumping respectively. The storage coefficient is s, the transmissibility of the aquifer (in $m^2/sec$) is :

• A. $32r^{2}S/9$
• B. $r^{2}S/9$
• C. $2r^{2}S/2025$
• D. None of above

Answer 1

The correct option is C $2r^{2}S/2025$

Given,
$S_1:S_2=3:4at{t}_1=1hrand{t}_2=2hr,\text{respectively}$

Let,
$S_1=3S,S_2=4S,$

We know
$S_2-S_1=\frac{Q}{4\pi T}ln\frac{t_2}{t_1}$

$4S-3S=\frac{Q}{4\pi T}ln\left(\frac{2}{1}\right)$

$\frac{Q}{4\pi T}=\frac{S}{ln2}$

Again we know
$S_1=\frac{Q}{4\pi T}ln\left[\frac{2.25Tt}{r^{2}S}\right]$

$3S=\frac{S}{ln2}ln\left[\frac{2.25T\times 3600}{r^{2}S}\right]$

$8r^{2}S=2.25T\times 3600$

$T=\frac{8r^{2}S}{2.25\times 3600}$

$T=\frac{2r^{2}S}{2025}$