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Line 146: + − <math>V = \frac{gRd^2}{18v + (0.75CgRd^3)^\frac{1}{2}}</math>+ − + − {{plainlist|1=Where − * ''V'' = settling velocity of particles (m/s) − * ''g'' = gravitational acceleration constant (9.81 m/s<sup>2</sup>) − * ''d'' = diameter of the solid (spherical) (µm) − * ''v'' = kinematic viscosity of water (1 mm<sup>2</sup>/s)}} − * ''R'' = Specific gravity for solid in question (i.e. 1.58kg/cm<sup>3</sup> for sand) − * ''C'' = Typical constant for spherical solids (0.4) and (1.0) for sand grains}} Line 167:
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→Detention time
===Detention time===
===Detention time===
A detention time of 24 hours should be targeted in all instances. Where this necessaitates a very low outflow, a [[Flow control#Vortex valve|vortex valve]] or similar is recommended over an [[orifice]] or pipe restiction. The detention time is approximated by the drawdown time.
A detention time of 24 hours should be targeted in all instances. Where this necessitates a very low outflow, a [[Flow control#Vortex valve|vortex valve]] or similar is recommended over an [[orifice]] or pipe restiction. The detention time is approximated by the drawdown time.
The drawdown time in the pond can be estimated using the classic falling head orifice equation which assumes a constant pond surface area<ref name="MOE"/>. This assumption is generally not valid, and a more accurate estimation can be made if the equation is solved as a differential equation. This is easily done if the relationship between pond surface area and pond depth is approximated using a linear regression:
The drawdown time in the pond can be estimated using the classic falling head orifice equation which assumes a constant pond surface area<ref name="MOE"/>. This assumption is generally not valid, and a more accurate estimation can be made if the equation is solved as a differential equation. This is easily done if the relationship between pond surface area and pond depth is approximated using a linear regression:
===Settling Velocity of Particulates===
===Settling Velocity of Particulates===
The process of sedimentation is enacted when solids "settle" to the bottom of a sedimentation practice, from suspension in moving or retained water (in this case a dry pond BMP). Due to dry ponds having grassy channels and slopes they are able to over time decrease the velocity of incoming stormwater flow that enters the practice. This combined with the agility of the practice to allow for temporary storage and ponding of water (24 - 48 hr) allows excess sediments (sand, silts, clay and small aggregates) and associated pollutants to settle and be retained within the BMP (Weiss et al. 2010)<ref>Gulliver, J.S., A.J. Erickson, and P.T. Weiss (editors). 2010. "Stormwater Treatment: Assessment and Maintenance. University of Minnesota, St. Anthony Falls Laboratory. Minneapolis, MN. https://stormwaterbook.safl.umn.edu/</ref>. These sediments should be removed periodically to maintain as designed performance of the feature. The following calculations are for measuring the settling velocities of various solids.
====Stoke's Law for settling solids====
Stoke's Law measures solids settling in stormwater features and is applicable to fines, clay, silt, and sand in water. <br>
* ''ρ'': mass density of water (1000 kg/m<sup>3</sup>
* ''ρ'': mass density of water (1000 kg/m<sup>3</sup>
* ''v'': kinematic viscosity of water at (1 mm<sup>2</sup>/s)}}
* ''v'': kinematic viscosity of water at (1 mm<sup>2</sup>/s)}}
<br>
====Ferguson & Church (2004)<ref>Ferguson, R.I. and Church, M. 2004. A simple universal equation for grain settling velocity. Journal of sedimentary Research, 74(6), pp.933-937. for settling solids. http://geoweb.uwyo.edu/geol5330/FergusonChurch_GrainSettling_JSR04.pdf</ref>====
Ferguson & Church's calculation meanwhile allows for designers to include the relationship between settling velocity and particle diameter size. A relationship for settling velocity that incorporates larger particles, such as sands with Reynolds Number (RE) > 10. The equation becomes Stokes' Law when particles have smaller diameters and allows for a constant drag coefficient to be applied for larger particle diameters.
<math>V = \frac{gRd^2}{18v + (0.75CgRd^3)^\frac{1}{2}}</math>
{{plainlist|1=Where
* ''V'' = settling velocity of particles (m/s)
* ''g'' = gravitational acceleration constant (9.81 m/s<sup>2</sup>)
* ''d'' = diameter of the solid (spherical) (µm)
* ''v'' = kinematic viscosity of water (1 mm<sup>2</sup>/s)
* ''R'' = Specific gravity for solid in question (i.e. 1.58kg/cm<sup>3</sup> for sand)
* ''C'' = Typical constant for spherical solids (0.4) and (1.0) for sand grains}}
See the table below for average settling velocities of different particle size ranges and particle types based on MOEE (1994)<ref>MOEE (1994). Stormwater management practices planning and design manual. Ministry of Environment and Energy, Ontario, Canada. </ref> and from Muschalla, 2014<ref>Muschalla, D., Vallet, B., Anctil, F., Lessard, P., Pelletier, G. and Vanrolleghem, P.A., 2014. Ecohydraulic-driven real-time control of stormwater basins. Journal of hydrology, 511, pp.82-91.</ref>
{| class="wikitable" style="width: 900px;"
|+'''Visual Indicators Framework - Bioretention/Swales'''
|-
!<br>'''Size Fraction (i)'''
!<br>'''Particle size range (µm)'''
!<br>'''Average settling velocity of particles in size fraction i, V<sub>si</sub> (m/s)'''
!<br>'''Fraction of total mass contained in size fraction i (%) - MOEE'''
!<br>'''Fraction of total mass contained in size fraction i (%) - measured'''
|-
|'''1'''
|x ≤ 20
|2.54E-06
|20
|83.4
|-
|'''2'''
|20 ≤ x ≤ 40
|1.30E-05
|10
|9.1
|-
|'''3'''
|40 ≤ x ≤ 60
|2.54E-05
|10
|4.4
|-
|'''4'''
|60 ≤ x ≤ 130
|1.27E-04
|20
|4.1
|-
|'''5'''
|130 ≤ x ≤ 400
|5.93E-04
|20
| -
|-
|'''6'''
|400 ≤ x ≤ 4000
|5.50E-03
|20
| -
|-
|}<br>
===Excess flow control===
===Excess flow control===