# 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 If the porosity is 34% and the specific retention is 12%, how much water (m^{3}) was withdrawn from the impacted area?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 = S_{y}A∆h |

where:

Volume |
= | volume drained from an unconfined aquifer over an area, A, for a water table elevation change of ∆h (L^{3}) |

S_{y} |
= | specific yield (dimensionless) |

A |
= | area over which the water table changes (L^{2}) |

∆h |
= | change in water table elevation (L) |

*S*_{y} can be determined as *n*_{e} – *S*_{r} 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 m^{3} = 8.8 million m^{3} |

If the aquifer were a 100-meter thick confined sand

S_{s} = ρg (α + n_{e}β) |

where:

S_{s} |
= | specific storage (1/L) |

α |
= | compressibility of the aquifer solid structure (T^{2}L/M) |

n_{e} |
= | effective porosity (dimensionless) |

β |
= | compressibility of water (T^{2}L/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 = 160,000m^{3} |