Using this option, the inflow during each time step (called a plug) is labeled and queued through the detention unit. Transfer of pollutants between plugs is not permitted. The outflow for any time step is comprised of the oldest plugs, and/or fractions thereof, present in the unit.


As in a completely mixed unit, detention time is the most important indicator of pollutant removal ability. Removal equations are specified and in this case should be written as a function of detention time.

Removed pollutant quantities accumulate in a plug flow unit until they are drawn off by residual flow. The accumulated pollutants do not affect the amount of available storage and are assumed not to decay. When residual flow occurs the entire unit contents (including the removed pollutant quantities) are mixed and drawn off until the unit is empty or wet weather continues. If wet weather (inflow) occurs before the unit is empty, the contents are placed into one plug for further routing.

For pollutants characterised by particle size or velocity distributions, particle settling computations take into account the range of conditions that may exist in an actual detention unit, from very quiescent to highly turbulent, and proceeds as follows:

1. For each particle size and specific gravity range, a settling velocity is computed, or a distribution is settling velocities can be supplied directly. Settling velocity is computed from particle size by the equation:

Vs = SQRT (4 / 3 * g * d / Cd * (Sp - 1))

 where

Vs = terminal velocity of particle, ft/sec

g = gravitational constant, 32 ft/sec^2

Cd = drag coefficient

Sp = specific gravity of particle

d = diameter of particle, ft

and

Cd = 24 / Nr, if Nr < 0.5, or

Cd = 24 / Nr + 3 / SQRT(Nr) + 0.34, if 0.5 <= Nr <= 10^4

Cd = 0.4, if Nr > 10^4

where

Nr = Reynold's number, dimensionless

and

Nr = Vs * d / v

where

v = kinematic viscosity, ft^2/sec

and

 v ~= 8.46E-4 / (T + 10)

where

T = water temperature, degrees Fahrenheit


2. A turbulence factor is computed using the following equation:

a = (Vs * y^(1/6)) / (Vt * n * (g^0.5))

where

a = turbulence factor, dimensionless

Vs = terminal velocity of particle, ft/sec

y = depth of water in unit, ft

Vt = flow-through velocity of detention unit, ft

n = Manning's roughness coefficient

g = gravitational acceleration, 32 ft^2/sec

and

Vt = l / Td

where

l = travel length of detention unit, ft

Td = detention time, sec


3. A particle removal efficiency for quiescent conditions is computed by the equation:

Eq = minimum of (1, Vs*Td/y)

where

Eq = quiescent particle removal efficiency, fraction

Vs = terminal velocity of particle, ft/sec

y = depth of water in unit, ft

Td = detention time, sec


4. A particle removal efficiency for turbulent conditions is computed by the equation:

Et = 1 - e^(-Vs*Td/y)

where

Et = turbulent particle removal efficiency, fraction

 Vs = terminal velocity of particle, ft/sec

y = depth of water in unit, ft

Td = detention time, sec


5. The overall removal efficiency is weighted from the quiescent and turbulent conditions by the turbulence factor as follows:

E = Eq + ln(a) / 4.605 * (Eq - Et)

 where

Eq = quiescent particle removal efficiency, fraction

 Et = turbulent particle removal efficiency, fraction

 a = turbulence factor, dimensionless

In a normal simulation, several plugs leave the detention unit in any given time step. The effluent is all or part of a number of plugs depending on the required outflow as determined by the level-Puls storage routing technique. Thus, the effluent particle size or settling velocity distribution is a composite of several plugs. This composite distribution is determined by taking a weighted average (by pollutant weight in each plug) over the effluent plugs. This distribution is then routed downstream for release or further treatment. The particles that were removed from each plug are also composited and are used to characterise the sludge volume.