Advectiondispersion equation application to rivers

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Advection-dispersion equation application to
rivers
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• (Ex, Ey, Ez ) have been previously called
• (Dx, Dy, Dz ) or (Kx, Ky, Kz)
• S concentration of pollutant (for substrate,
  food, biodegradable organics etc), previously
  called c
• Source and sink terms have been added since we
  will typically be interested non-conservative
  pollutants and/or consider regions in which there
  may be generation terms

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Advection-dispersion equationvertically well
mixed, one directional (x) flow
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Advection-dispersion equationsteady state, one
directional (x), plug flow
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Advection-dispersion equationsteady state, one
directional (x), plug flow, constant velocity,
first order decay

• Eqn 2.22 TM, Fig 2.12

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• S0 is typically the concentration after a
  discharge point and can be obtained from simple
  mass balances assuming well mixed behaviour
  immediately below the mixing point. (Eqns 2.16
  2.19 TM).
• In reality, complete mixing is achieved only
  after some distance downstream (Fig 2.8 TM),
  estimated by Eqns 2.14 and 2.15 (Sample Problem
  2.2)

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Advection-dispersion equation with distributed
source steady state,one directional (x), plug
flow, constant velocity, first order decay

• Eqn. 2.28 and Fig 2.13

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Distributed sourcesFigure 2.13 TM
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Multiple sources - superposition

• The effects of multiple sources (point or
  distributed) are additive
• Fig. 2.15
• CASE I 2 point sources
• CASE II point source plus distributed source

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