Lecture 14

# Lecture 14 - Prepared by T Wagener P Reed T P Penn State...

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Water Resources Engineering repared by T Wagener & P Reed - Lecture 14 1 Prepared by T. Wagener & P. Reed Penn State University

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Topics • I. Saturated Flow Equations – A. Reynolds Transport Based Derivation – B. In-Class Exercise Alternative Forms of Governing Equations – C. Alternative Forms of Governing Equations • II. Flow Nets I Steady tate 1 flow • III. Steady-state 1-D flow – A. Confined Aquifer . Unconfined Aquifer B. Unconfined Aquifer 2
ast Time… Last Time… onstant: Constant: - Hydraulic gradient - Hydraulic conductivity K - Aquifer thickness b herefore the specific Therefore, the specific discharge can be calculated for any in the aquifer using: 3

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ransmissivity Transmissivity We can calculate the discharge per unit length of aquifer by multiplying by the thickness of the aquifer, b: Where T = Kb [L 2 T -1 ] is called the transmissivity of the quifer aquifer. Why would transmissivity be a useful 4 parameter to describe an aquifer?
Saturated Flow Equations We are going to use the control volume shown above to develop our governing equation for saturated flow. Note the sides have lengths dx, dy, dz along the coordinate directions. The total volume is constant and equal to dxdydz . We compute the total volume f water as dxdydz oil of water as θ (soil moisture*aquif vol) q in the diagram presents the Darcy flux. represents the Darcy flux. NOTE q IS DEFINED FOR ALL DIRECTIONS EVEN THOUGH THE FIGURE SIMPLY ILLUSTRATES VERTICAL FLUXES 5

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Preliminary Terminology & Clarifications Specific storage , S s : volume of water that a unit volume of aquifer releases from storage under a unit decline in hydraulic head, [units re 1/length]; note our prior discussion of defined torativity hich are 1/length]; note our prior discussion of defined storativity S, which is related to specific storage as follows () s S S b where S is a vertically averaged property = The text uses W to designate a “source/sink ” term that add or removes water over time within the control volume. It is worth discussing how the term is defined to avoid confusion.
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Lecture 14 - Prepared by T Wagener P Reed T P Penn State...

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