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WQ 4.2 Governing Equations &4.2.1 - Coggle Diagram
WQ 4.2 Governing Equations &4.2.1
paragraph1
Ammon (1979)——
reviewed several theoretical approaches for urban runoff washoff
and concluded that
although the sediment transport based theory is attractive, it is often insufficient in practice
because of lack of data for parameter (e.g., shear stress) evaluation, sensitivity to time step and discretization
and because simpler methods usually work as well (still with some theoretical basis) and are usually able to duplicate observed washoff phenomena.
SWMM therefore incorporates three different choices of empirical models to represent pollutant washoff
exponential washoff
rating curve washoff
and event mean concentration (EMC) washoff
paragraph2&3
Sartor and Boyd (1972)——The most oft-cited results for pollutant washoff behavior
shown in Figure 4-1, constituents were flushed from streets using a sprinkler system
from the figure, an exponential relationship could be developed to describe washoff of the form
Eq4-1
W(t)=
m_B(0)*(1-e^(-kt))
clearly, k, is a function of both particle size and runoff rate
Ammon (1979) ——An analysis of the Sartor and Boyd (1972) data，
indicates，k increases with runoff rate, and decreases with particle size
paragraph4
The Sartor and Boyd data——
lend credibility to the washoff assumption included in the original SWMM release (and all versions to date) that
the rate of washoff, w, (e.g., mg/hr) is proportional to the remaining pollutant buildup at any time
w=-kmB
the amount of
buildup B remaining
on the surface, after a time t of washoff
m_B(t)=m_B(0)*e^(-kt))
k may be evaluated by assuming it is proportional to runoff rate
k=Kw*q
Kw:冲刷系数
q:子汇水区径流率
Mr. Allen J. Burdoin, a consultant to Metcalf and Eddy, first proposed this relation, during the original SWMM development.
paragraph5
Burdoin assumed, one-half inch of total runoff in one hour would wash off 90 percent of the initial surface load
leading to value of KW of 4.6 in-1,
the now familiar value(in SWMM modeling circles)
The actual time distribution of intensity does not affect the calculation of KW
there are no direct measurements to validate this assumption,
which is so often employed
to the authors’ knowledge,
paragraph6
Sonnen (1980) ——
Kw ranging (0.052, 6.6), from sediment transport theory
Kw increasing as
particle diameter decreases
rainfall intensity decreases
catchment area decreases
for Kw value,
4.6 is relatively large,
compared to most of his calculated values
Nakamura (1984a, 1984b)
verified exponential washoff formulation of Equations 4-2 and 4-3 experimentally
k depende on
slope
runoff rate
cumulative runoff volume
exponential washoff formulation of Equations 4-2 and 4-3 is not completely satisfactory
paragraph7
Huber and Dickinson(1988)——
the original exponential washoff formulation did not adequately fit some data
because of the behavior
Thus concentration c would decrease continually as the remaining buildup mB decrease over time
detail for why
substitute (4-4) into (4-2) and get
c=Kw × q × mB/(q*A)=Kw × mB/A
1 more item...
why
k be linearly dependent on runoff rate q, produced decreasing washoff concentrations
to avoid this behavior
k was modified as
k=Kw × q^(N_W)
NW: a washoff exponent
the resulting equation for exponential washoff
w=Kw × q^(N_W) × m_B
w: units of mass/hour