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This text is integrally taken from a document I found on the internet by Crystal Stream.
HYDRAULIC LOADING RATES
The commonly accepted formula for calculating particle capture is the Hydraulic Loading
Rate (HLR). It is expressed as the ratio of flow, in cubic feet per second, divided the
surface area of a wet basin or vault in square feet. This is expressed as:
HLR = Q / L W
The units will be ft. / sec. This calculation is often questioned because it does not include
any information on the volume of the basin, the depth of the basin, or the detention time
for a given storm. Detention time is also expressed as Hydraulic Retention Time, or HRT.
If a basin has a given length (L), width (W), and depth (D) which equals its volume (Vo),
and a particle has a certain settling velocity Vp, we can define certain formulas to
describe events in the basin.
The detention time (HRT) equals the volume of the basin in cubic feet divided by the flow
rate into the basin, in cubic feet per second:
HRT = LWD / Q
The time for a particle to settle to the bottom of the basin (tp) equals the depth of the
basin (D) divided by the settling velocity of the particle Vp:
tp = D / Vp
If we want a basin to be just large enough to settle out a particle with the velocity of Vp,
then we would set the HRT (detention time) equal to the settling time tp for that particle.
Setting the equations equal gives:
LWD / Q = D / Vp
Dividing by D gives:
LW = 1 / Q * Vp
or
Vp = Q / LW
This shows that the Hydraulic Loading Rate (HLR) is simply equal to the particles settling
velocity, and that a greater surface (LW) will allow capture of particles with smaller
settling velocities, as the denominator increases with the surface size of the basin.
This is easiest to see with two basin of identical volume with a Q of 5 cfs.
Consider a basin that is 10 feet L, 5 feet W, and 10 feet D where LWD = 500 cubic feet. The
detention time (HRT) is obviously 100 seconds. To find a particle settling rate that will
work for this basin, we need to find a particle that will fall 10 feet in 100 seconds. That
rate is 0.1 feet per second. Because we know that the Hydraulic Loading Rate (HLR) is
expressed as being equal to the settling rate of a target particle, we can test that
assumption, by calculating the HLR as Q/LW, or as 5 / 50, which gives us the same
answer as the particle setline velocity calculated above, or 0.1 ft./sec.
Consider a second basin that is 10 feet L, 10 feet W, and 5 feet D, where LWD = 500.
The detention time (HRT) is obviously 100 seconds. To find a particle settling rate that
will work for this basin, we need to find a particle that will fall 5 feet in 100 seconds.
That rate is 0.05 feet per second. Because we know that the Hydraulic Loading Rate
(HLR) is expressed as being equal to the settling rate of a target particle, we can test that
assumption, by calculating the HLR as Q/LW, or as 5 / 100, which gives us the same
answer as the particle settling velocity calculated above above, or 0.05 ft./sec.
These two basins are exactly the same volume, and have exactly the same detention time.
They vary only in surface area, which is a function of their variable depth. The
calculations clearly show that, given an equal basin volume, and equal detention time, a
basin with greater surface area will capture smaller particles. This is a direct relationship
where increasing surface area will increase particle capture rates.
It also shows that two basins of equal volumes and equal detention times can give very
different capture rates. Therefore, it is not the detention time, or the volume of the basin
that dictates the capture rate, it is the surface area.
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