Question

For steady flow to a fully penetrating well in a confined aquifer, the drawdowns at radial distances of $r_1$ and $r_2$ from the well have been measured as $s_1$ and $s_2$ respectively, for a pumping rate of $Q$. The transmissivity of the aquifer is equal to

• A. $\frac{Q}{2\pi }\left[\frac{ln\frac{r_2}{r_1}}{s_1-s_2}\right]$
• B. $\frac{Q}{2\pi }\left[\frac{ln(r_2-r_1)}{s_1-s_2}\right]$
• C. $\frac{Q}{2\pi }ln\left[\frac{\frac{r_2}{r_1}}{\frac{s_2}{s_1}}\right]$
• D. $2\pi Q\frac{r_2-r_1}{ln\left(\frac{s_2}{s_1}\right)}$

Answer 1

The correct option is A $\frac{Q}{2\pi }\left[\frac{ln\frac{r_2}{r_1}}{s_1-s_2}\right]$

Transmissivity,
$T=kD$
$k=\text{coefficient of permeability}$
$D=\text{depth of aquifer}$

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

$\therefore T=kD=\frac{Qln\left(\frac{r_2}{r_1}\right)}{2\pi (s_1-s_2)}$

$h_2-h_1=\text{Difference in piezometric heads}$
$=s_1-s_2=\text{Difference in drawdowns}$