**Lecture 19**

*Ground-water Flow to
Wells*

**Fetter 7.1-7.3-1**

Wells used to extract ground water (or inject)

**Cone of depression -** area around a
discharging well where the hydraulic head

in the aquifer is lowered by pumping.

Want to compute __drawdown__ and T and S.

** Unsteady flow -** flow in which head
changes with time.

Assumptions | ||

(1.) Bottom confining layer | ||

(2.) All geologic units are horizontal and of infinite extent. | ||

(3.) Potentiometric surface is horizontal prior to the start of pumping. | ||

(4.) Potentiometric surface is not changing with time prior to the start of pumping. | ||

(5.) All changes in potentiometric surface position are due to the effect of the pumping well. | ||

(6.) Aquifer is homogeneous and isotropic. | ||

(7.) All flow is radial toward the well. | ||

(8.) Ground-water flow is horizontal. | ||

(9.) Darcy’s Law is valid. | ||

(10.) Ground-water has constant density and viscosity. | ||

(11.) Pumping well and observation wells are fully penetrating. | ||

(12.) Well has an infinitesimal diameter and is 100% efficient. |

Unsteady Radial Flow

Assume that
the aquifer has a radial symmetry . |
|||

Radial flow toward well. | |||

Plan view | Cross Section |

Use polar coordinates to describe flow.

Therefore, can express flow with-

(1) q value of angle | |

(2) r Radial distance |

If Aquifer is isotropic in horizontal plane. Then ® Flow is radial.

Equation for confined (radial) -Hantush 1964

r = radial distance from pumping well. |

If recharge- leakage through a confining layer

e = rate of vertical leakage (L/T) |

Solutions to the equations are extremely useful

Includes- | |

Laplace transforms | |

Fourier transform | |

Bessel functions | |

Error function |

Use these equations to determine drawdown around a pumping well.

Aquifer test in a confined aquifer.

Aquifer test in an unconfined aquifer.