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Numerical on Ground Water

A 30 cm diameter well penetrates 20 m below the static water table. After 24 hours of pumping at 5000 lit per minutes, the water level in a test well at 100 m away is lowered by 0.5 m and in a way at 30 m away, the drawdown is 1 m. What is the transmissibility of the aquifer?

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d = 3cm = 0.3m r = 0.15m

H =20m

$S_2$ = 0.5 at $r_2$ = 100m

$H_2$ = 20 – 0.5 = 19.5

$S_1$ = 1 m at $r_1$ = 30m

$h_1$ = 2 – 1 = 19m

$Q=5000\ lit/min=\frac{5000\times10^{-3}}{60}=0.0833\ m^3/sec$

$$Q=\frac{1.36k(H^2-h^2)}{\log\left(\frac{r_2}{r_1}\right)}$$ $$0.0833=\frac{1.36k(19.5^2-19^2)}{\log\left(\frac{100}{30}\right)}$$

K = 1.663 x 10$^{-3}$ m/s

Transmissibility of aquifer

T = KH = 1.663 x 10$^{-3}$ x 20

T = 0.0332 m$^2$/s

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