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## Q. 6.4

An aquifer of $20\:m$ average thickness is overlain by an impermeable layer of $30\:m$ thickness. A test well of $0.5\:m$ diameter and two observation wells at a distance of $10\:m$ and $60\:m$ from the test well are drilled through the aquifer. After pumping at a rate of $0.1\:m^3/s$ for a long time, the following drawdowns (amount that head is lowered from the initial position) are stabilized in these wells: first observation well, $4\:m$; second observation well, $3\:m$. Determine the hydraulic conductivity of the aquifer and the drawdown in the test well.

## Verified Solution

1. Arrangement is shown in Figure 6.5.

$H=(Z–3)$ and $h=(Z–4)$ as shown in Fig. 6.5

hence, $(H–h)=(Z–3)–(Z–4)=1\:m$

2. From eq. (6.3),

$H\:\:\:\:h\:\:\:\:\frac{Q}{2πbK}\:\ln\frac{R}{r}\:\:\:\:[L]$                   (6.3)

$1\:\:\:\:\frac{0.1}{2π\:\:20\:\:K}\:\ln\frac{60}{10}$

$K\:\:\:\:\frac{0.1\:m^3/s}{2π\:\:20\:m\:\:1\:m}\:\ln\frac{60\:m}{10\:m}$

$1.43×10\:\:^3\:m/s$

3. Apply eq. (6.3) between the test well and the first observation well.

$H=(Z–4)$, $h=(Z–s)$

hence, $(H–h)=(Z–4)–(Z–s)=(s–4)$

4. From eq. (6.3),

$(s\:\:\:\:4)\:\:\:\:\frac{0.1}{2π(20)(1.43×10\:\:^3)}\:\ln\frac{10}{0.25}$

$2.05$

or $s\:\:\:\:6.05\:m$