Question

A 45 cm diameter well penetrates an unconfined aquifer of 30 m thick. Under the steady pumping rate for a long time, the drawdown at two observation wells 10 m and 20 m from the pumping well are 5 m and 3.5 m respectively. What will be the discharge (cubic metre per sec), if the permeability of the aquifer is given as 20 m/day.

• A. 0.05
• B. 0.067
• C. 0.08
• D. 1.12

Answer 1

The correct option is C 0.08

$\text{Given that: Unconfined aquifer}$

$\text{Diameter of well}\left(d_w\right)=45\text{cm}$

$\text{Aquifer thickness}\left(H\right)=30\text{m}$

$\text{At}{r}_1=10\text{m};h_1=30-5=25\text{m}$
$\text{At}{r}_2=20\text{m};h_2=30-3.5=26.5\text{m}$

$\text{and Permeability of the aquifer (K)}=20m/day.$


Discharge for unconfined aquifer (Q);
$=\frac{\pi k(h_2^2-h_1^2)}{ln\left(\frac{r_2}{r_1}\right)}$

$Q=\frac{\pi \times 20\times \left[\right(26.5{)}^2-\left(25{)}^2\right]}{ln\left(\frac{20}{10}\right)}$
$Q=7002.496{\text{m}}^3\text{/day}$
$\therefore Q=0.081{\text{m}}^3\text{/sec.}$

$\text{Hence, the discharge from the given aquifer is}0.08{\text{m}}^3\text{/sec.}$

Note:
Discharge for confined aquifer (Q) ;
$=\frac{2\pi kB(h_2-h_1)}{ln\left(\frac{r_2}{r_1}\right)}$
where, B = Aquifer thickness
K = Permeability of the aquifer
r = Radial distance
h = Piezometric head.