Flow to Wells 2 Steady flow to a

Flow to Wells – 2 Steady flow to a well in an unconfined aquifer Groundwater Hydraulics Daene C. Mc. Kinney 1

Summary • Notation • Steady flow to a well in an unconfined aquifer with recharge 2

Flow to a Well in an Unconfined Aquifer 3

Groundwater Notation • Unconfined aquifer General equation, rectangular coordinates Steady flow, homogeneous, isotropic aquifer 4

Groundwater Notation • Unconfined aquifer General equation, radial coordinates Steady flow, homogeneous, isotropic aquifer 5

Steady Flow to a Well in an unconfined Aquifer Q Ground surface Pre-pumping Water level Pumping well Water Table Observation wells h 0 h 2 Unconfined aquifer Bedrock r 1 hw h 1 Q r 2 2 rw Governing equation in radial coordinates Assumptions: Steady state flow, radial symmetry (isotropic medium), 6

Steady Flow to a Well in an Unconfined Aquifer Q Ground surface Pre-pumping Water level Pumping well Water Table Observation wells Darcy’s law h 0 h 2 Unconfined aquifer Bedrock r 1 hw h 1 Q r 2 2 rw 7

Steady Flow to a Well in an Unconfined Aquifer Q Ground surface Pre-pumping Water level Boundary condition: Pumping well Water Table Observation wells h 0 h 2 Unconfined aquifer Bedrock r 1 hw h 1 Q r 2 2 rw 8

Example – Steady Flow to a Well in an Unconfined Aquifer • Given: Q = 300 m 3/hr Two observation wells, 1. h 1 = 40 m @ r 1 = 50 m 2. h 2 = 43 m @ r 2 = 100 m • Find: K Q Ground surface Prepumping Water level Pumping well Water Table Observation wells h 0 h 2 Unconfined aquifer Bedrock r 1 hw h 1 Q r 2 2 rw 9

Steady flow to a Well in an Unconfined Aquifer with Recharge radius of influence 10

Steady flow to a Well in an Unconfined Aquifer with Recharge Boundary condition 1: No flow across radius of influence 11

Steady flow to a Well in an Unconfined Aquifer with Recharge Boundary condition 2: Recharge within radius of influence is captured by the well radius of influence 12

Steady flow to a Well in an Unconfined Aquifer with Recharge Boundary condition 3: Recharge within radius of influence is captured by the well radius of influence 13

Example - Steady flow to a Well in an Unconfined Aquifer with Recharge 25 cm diameter well to maintain lowered water table K = 1 x 10 -5 m/s (0. 864 m/d) Bottom of aquifer is horizontal at 20 m bgs Water table is 1 m bgs Unconfined aquifer is recharged at W = 0. 06 m/d Water table must be lowered 3 m over site Drawdown at corners must be at least 3 m 50 m r r=35. 35 m Solve by iteration: r 0 = 70 m 14

Summary • Notation • Steady flow to a well in an unconfined aquifer with recharge 15