GROUNDWATER HYDROLOGY II

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GROUNDWATER HYDROLOGY II

• WMA 302
• Dr. A.O. Idowu, Dr. J.A. Awomeso and Dr O.Z.
  Ojekunle
• Dept of Water Res. Magt. Agromet
• UNAAB. Abeokuta. Ogun State
• Nigeria
• oojekunle_at_yahoo.com

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• COURSE CODE WMA 302
• COURSE TITLE Groundwater Hydrology II
• COURSE UNITS 2 Units
• COURSE DURATION 2 hours per week

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COURSE DETAILS

• Course Cordinator Dr. O.A. Idowu B.Sc., M.Sc.,
  PhD
• Emailolufemidowu_at_gmail.com
• Office Location Room B202, COLERM
• Other Lecturers Dr. J.A. Awomeso B.Sc., M.Sc.,
  PhD and Dr. O.Z. Ojekunle B.Sc., M.Sc., PhD

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COURSE CONTENT

• Non-steady radial and rectilinear flows in
  aquifers. Well pumping tests. Theis and Jacob
  methods, multiple well systems.
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• Types of wells, Methods for well construction.
  Well drilling methods Cable tool, rotary and
  reserve rotary well design, development and
  maintenance. Evaluation of aquifer behavior and
  water quality.
•  
• Analysis and interpretation of water level maps,
  laboratory determination of permeability,
  porosity, compressibility and velocity of flow.
•  
• Ground water in Nigeria, groundwater data
  analyses.
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• Pre-requisite WMA 303

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COURSE REQUIREMENT

• This is a Compulsory course for students in the
  Department of Water Resources Management and
  Agrometeorology and are supposed to passed WMA
  303 before Registering this course. As a school
  regulation, a minimum of 75 attendance is
  required of the students to enable him/her write
  the final examination

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READING LIST

• Celia Kirby and W.R. White 1994. Integrated River
  Basin Development, John Wiley and Sons Ltd,
  Baffins Lane, Chichester, West Sussex PO19 1UD,
  England
• Developing World Water 1988, Grosvenor Press
  International, Hong Kong.
• Hofkes E.H. 1983. Small Community Water Supplies.
  Wiley, Chichester
• Kay M.G. 1986. Surface Irrigation- Systems and
  Practice. Cranfield Press Bedford
• Schulz C.R. and Okun D.A. 1984. Surface Water
  Treatment for Community in Developing Countries.
  Wiley-Interscience, New York

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STEADY STATE FLOW AND TRANSIENT FLOW

• Steady-state flow occurs when at any point in a
  flow field the magnitude and direction of the
  flow velocity are constant with time.
• Transient flow (Unsteady flow or non steady flow)
  occurs when at any point in a flow field the
  magnitude or direction of the flow velocity
  changes with time.

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STEADY STATE FLOW AND TRANSIENT FLOW (Cont)

• Fig. 1 below show a steady-state flow groundwater
  flow pattern (dashed equipotentials, solid
  flowline) through a permeable alluvial deposit
  beneath a concrete dam. Along the line AB, the
  hydraulic head hAB 1000m. It is equal to the
  elevation of the surface of the reserviour above
  AB. Similar hAB 900m (the elevation of the
  tailrace pond above CD). The hydraulic head drop
  h across the system is 100m. if the water level
  in the reserviour above AB and the water level in
  the tailrace pond above CD do not change with
  time. The hydraulic head at point E, for example,
  will be hE 950m and will remain constant. Under
  such circumstances the velocity V -Kdh/dl will
  also remain constant through line. In a
  steady-state flow system, the velocity may vary
  from point, but it will not vary with time at any
  given point.

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STEADY STATE FLOW AND TRANSIENT FLOW (Cont)

• Let us now consider the transient flow problem
  schematically shown in fig. 2. At time t0 the
  flow net beneath a dam will be identical to that
  of fig. 1 and the hE will be 950m. If the
  reserviour level is allowed to drop over the
  period t0 to t1 until the water level above and
  below the dam are identical at time t1, the
  ultimate condition under a dam will be static
  with no flow of water from the upstream to the
  down stream side. At point E the hydraulic head
  hE will under a time-dependent decline from hE
  950m at time t0 to its ultimate value of hE
  900m. There may well be time lag in such a system
  so that hE will not necessarily reach the value
  hE 900m until sometime at t t1.

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DIFFERNCES BETWEEN STEADY STATE FLOW AND
TRANSIENT FLOW

• One important difference between steady and
  transient lies in the relation between their
  flowline and pathlines. Flowlines indicate the
  instantaneous direction of flow throughout a
  system (at all times in a steady system, or at a
  given instant in time in a transient system).
  They must be orthogonal to the eqiuipotential
  lines throughout the region of flow at all times.
  Pathlines may take the route that an individual
  particle of water follows through a region of
  flow during a steady or transient event. In a
  steady flow system, a particle of water enter the
  system at an inflow boundary will flow towards an
  outflow boundary along a pathline that coincides
  with with a flowline such as that shown in fig.
  1. In Transient system, on the otherhand,
  pathline and flowline do not coincide. Although a
  flow net can be constructed to describe the flow
  conditions at any given instant in line in a
  transient system, the flowline shown in such a
  snapshot represent only the configuration of the
  flowlines changes with time, the flowlines cannot
  describes, in themselves, the complete path of a
  particle of water as it transerves the system.
  The delineation of transient pathline has obvious
  importance in a study of groundwater
  contamination.

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Note

• The practical methodology that is presented later
  is often based on theoretical equations, but it
  is not usually necessary for practicing
  hydrogeologist to have the mathematical equations
  at his/her fingertips. The primary application of
  steady state techniques in groundwater hydrology
  is the analysis of regional groundwater flow. An
  understanding of transient flow is required for
  the analysis of well hydraulic, groundwater
  recharge, and many of the geochemical and
  geotechnical application.

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STEADY-STATE SATURATED FLOW

• Consider a unit volume of porous media such as
  that shown in fig. 3 such an element is usually
  called an elemental control volume. The law of
  conservation of mass for a steady-state flow
  through a saturated porous medium requires that
  the rate of fluid mass flow into any elemental
  control volume. The equation of continuity that
  translate the law into mathematical form can be
  written with reference to fig. 3 as

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STEADY-STATE SATURATED FLOW (Cont)

• A quick dimension analysis on the v terms will
  show then to have the dimension of a mass rate of
  flow across a unit cross-sectional area of the
  elemental control volume. If the fluid is
  incompressible, (x,y,z) constant and the s can
  be removed from eqn 1. even if the fluid is
  compressible and (x,y,z) is not equal constant,
  it can be shown that the terms of the form dvx/dx
  are much greater that terms of the form vxd/dx,
  both of which arise when the chain rule is used
  to expand eqn 1 in either case eqn 1 simplifies
  to

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STEADY-STATE SATURATED FLOW (Cont)

• Substitution of darcys law for Vx, Vy and Vz in
  eqn. 2 yield the equation of flow for
  steady-state flow through anisotropic saturated
  porous medium.
• For an anisotropic medium, KxKyKz, and if the
  medium is also homogeneous, then
  k(x,y,z)constant. Eqn. 3 then reduces to the
  equation of flow for steady-state flow through a
  homogeneous isotropic medium.

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STEADY-STATE SATURATED FLOW (Cont)

• Eqn. 4 is one of the most basic partial
  differential equation to mathematician. It is
  called laplaces equation. The solution of the
  equation is a function of h(x,y,z) that describes
  the value of hydraulic head h at any point in a
  three dimensional flow field. A solution of
  equation 4 allows us to produce a contoured
  equipotential map of h1 and with the addition of
  flowline, at a flow net.
• For steady-state saturated flow in a two
  dimension flow field, say in the xz plane, the
  central term of eqn. 4 would drop out and the
  solution would be a function of h(x,z).

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TRANSIENT SATURATED FLOW

• The law of conservation of mass for transient
  flow in a saturated porous medium requires that
  the net rate of fluid mass flow into any
  elemental control volume be equal to the time
  rate of change of fluid mass storage with the
  element with reference to fig 3, the equation of
  continuity takes the form

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TRANSIENT SATURATED FLOW (Cont)

• The first term on the right hand side of eqn. 6
  is the mass rate of water produced by the
  expansion of water under a change in its density
  . The second term is the mass rate of water
  produced by the compaction of the porous medium
  as reflected by the change in its porosity n. The
  first term is controlled by the compressibility
  of the fluid and the second term is controlled by
  the compressibility of the aquifer . It is
  necessary to simplify the second terms in the
  right of equation 6. We known that the change in
  and the the change in n are both produced by the
  change in hydraulic head h, and that the volume
  of water produced by the 2 mechanisms for a unit
  decline in head in Ss, where Ss is the specific
  storage given by Ss g ( n). The mass rate of
  water produce (time rate of change of fluid mass
  storage) is Ssdh/dt and the eqn. 6 becomes