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Simulation of basin hydraulics by ideal flow.
The hydraulics of a water quality detention basin can be approximated using an ideal
flow model. In the present work the flow in a basin is approximated by a velocitypotential, stream-function formulation with internal (artificial viscosity) material
properties to allow the simulation of internal resistances to flow.
Figure 1 depicts four geometries studied. In each of the four basins the geometric length
to width ratio is held at 3:1 as per typical design criteria (REF to Harris Co. manual).
Basins 1 and 2 are relatively common configurations, as is basin 4. Basin 3 is an
intentional case of obvious short circuiting.
Basin_001
Basin_002
Basin_003
Basin_004
Figure 1. Four basin configurations; All basins have same geometric length to width
ratio; all have same hydraulic retention time.
A computer program was constructed that solves the LaPlace equation on a rectangular
region.
The velocity potential is the solution to




(k x
)  (k y
)0
x
x
y
y
The stream function is the solution to
 1 
 1 
(
) (
)0
x k y x
y k x y
k x , and k y are “material properties” that are used to adjust the internal flow behavior. In
the velocity-potential space, the values are made relatively small to induce the effect of
internal walls at particular spatial locations, and correspondingly large at the same spatial
locations in the stream-function space.
Boundary conditions in the velocity-potential space are either zero-flux (no-flow) or
constant value. The boundary conditions in stream-function space are the compliment of
the velocity-potential boundary conditions.
Thus, a zero-flux condition in velocity-
potential space becomes a constant value in stream-function space, while a constant value
in velocity-potential space will be a zero-gradient in stream-function space.
Table 1 lists the types of boundary conditions in each space – the conditions must be
complimentary for a meaningful solution.
Table 1. Boundary conditions for Velocity-potential and stream-function.
Velocity-Potential Boundary
Stream-Function Boundary
  const. on 1


or
 0 on 1
x
y
 
or
 0 on 2
x y
  const. on 2
Basin 1
Figure ## is a flow-net overlain on the velocity potential surface map for basin 1. The
image is looking up-stream from the outlet. Flow is uniform across much of the basin
with streamline distortion apparent at only the inlet and outlet.
[Describe relative
location inlet outlet – opposite each other, centered on short dimension of basin]
The velocity-potential map is used in a particle-tracking model to approximate the
residence time distribution of a tracer uniformly released over the entire basin at some
instant in time. Because the principal mechanism of treatment in these basins is thought
to be settling, the residence time distribution obtained by this simulation conveys
valuable information about the probable performance of the basin.
[Washout distribution and analysis here]
Basin 2
Corner to corner.
[Washout distribution and analysis here]
Basin 3
[Washout Distribution and Analysis Here]
Basin 4
[Washout Distribution and Analysis Here]