# Solution to Exercise 4

4) A regional unconfined sand aquifer was developed during 1990. As a result of the extraction of water the water table dropped about 40 m over a 1 square km area. If the porosity is 34% and the specific retention is 12%, how much water (m3) was withdrawn from the impacted area? How might this volume differ if the aquifer were a 100 m thick confined sand with water at a temperature of 8°C?

Calculate the volume by using Equation 48 of this book.

 Volume of Unconfined Water Drained = SyA∆h

where:

 Volume = volume drained from an unconfined aquifer over an area, A, for a water table elevation change of ∆h (L3) Sy = specific yield (dimensionless) A = area over which the water table changes (L2) ∆h = change in water table elevation (L)

Sy can be determined as neSr as shown by Equation 13 of this book.

 Volume of Unconfined Water Drained = (0.34 – 0.12) 1000m 1000m 40m Volume from Unconfined Aquifer = 8,800,000 m3 = 8.8 million m3

If the aquifer were a 100-meter thick confined sand

 Ss = ρg (α + neβ)

where:

 Ss = specific storage (1/L) α = compressibility of the aquifer solid structure (T2L/M) ne = effective porosity (dimensionless) β = compressibility of water (T2L/M)

Use a compressibility value for sand found in Table 4 and a density for 8°C water from Figure 28 in this book.

Equation 49 of this book is used to determine storativity:

Equation 50 of this book determines the volume.

 Volume of Confined Water Drained = SAΔh Volume of Confined Water Drained = 4×10-3 1000m 1000m 40m Volume of Confined Water Drained = 160,000m3