Question

A fully penetrating well in an unconfined aquifer is pumped continuously so that the steady state drawdown is 12 m. The water table is at a height of 55 m above the bottom of the aquifer, which has a hydraulic conductivity of 22 m/d. The diameter of the well is 0.25 m.

If the pumping rate has no effect on the water table at a distance of 1.2 km from the pumping well, determine the pumping rate.
Answer: m3 per hour

Answer 1

To determine the pumping rate in m³ per hour, we can use the Dupuit equation for steady-state flow in an unconfined aquifer:

Q = (K * h * π * r²) / ln(r / rw)

Where:

Q = Pumping rate (m³/s)

K = Hydraulic conductivity of the aquifer (m/d)

h = Steady-state drawdown (m)

r = Distance from the pumping well to the observation point (m)

rw = Radius of the well (m)

Given:

K = 22 m/d

h = 12 m

r = 1.2 km = 1200 m

rw = Diameter of the well / 2 = 0.25 m / 2 = 0.125 m

Plug in the values and calculate the pumping rate in m³/s, then convert it to m³ per hour:

Q = (22 * 12 * π * (1200^2)) / ln(1200 / 0.125)

Q ≈ 3312.24 m³/s

Now, convert to m³ per hour:

1 m³/s = 3600 m³/hour

So, Q = 3312.24 * 3600 ≈ 11919.28 m³/hour

Therefore, the pumping rate is approximately 11919.28 m³ per hour.