## Chapter 6

## 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.

## Step-by-Step

## 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