Question

A well of diameter $20\text{cm}$ fully penetrates a confined aquifer. After a long period of pumping at a rate of $2720\text{L/min}$, the observations of drawdown taken at $10\text{m}$ and $100\text{m}$ distances from the centre of the well are found to be $3\text{m}$ and $0.5\text{m}$ respectively. The transmissivity of the aquifer is ________.

• A. $676{\text{m}}^2/\text{day}$
• B. $576{\text{m}}^2/\text{day}$
• C. $526{\text{m}}^2/\text{day}$
• D. $249{\text{m}}^2/\text{day}$

Answer 1

The correct option is B $576{\text{m}}^2/\text{day}$

Transmissivity,
$T=k.D$
where,
$k=$ coefficient of permeability
$D=$ Depth of Aquifer
$T=\frac{Qln\left(\frac{r_2}{r_1}\right)}{2\pi (h_2-h_1)}$

Given,

$Q=2720\text{L/min}$
$=2.72{\text{m}}^3/\text{min}$
$=272\times 24\times 60{\text{m}}^3/\text{day}$
$=3916.8{\text{m}}^3/\text{day}$

$\text{At}{r}_1=10\text{m},\text{drawdown}{d}_1=3\text{m}$
$\text{At}{r}_2=100\text{m},\text{drawdown}{d}_2=0.5\text{m}$

and
$(h_2-h_1)=(d_1-d_2)$
$=2.5\text{m}$

$T=\frac{Qln\left(\frac{r_2}{r_1}\right)}{2\pi (h_2-h_1)}$

$=\frac{3916.8ln\left(\frac{100}{10}\right)}{2\pi \times 2.5}$

$=574.44{\text{m}}^2/\text{day}$