Enhanced swales: Sizing

These sizing equations are suggested for use in calculating the capacity of swales which have a larger proportion of surface flow. i.e. grass swales, rather than bioswales. 
In many cases the length of swale required will exceed the available space, so that an underground infiltration trench or a dry pond will be a preferred solution. 
thumb|500px| Plan, profile, and section views of a trapezoidal channel grass swaleAtlanta Regional Commission (ARC). 2001. Georgia Stormwater Management Manual.
Atlanta, GA. https://www.lex-co.com/Departments/PublicWorks/GSMMVol2.pdf
===Triangular channel===
Sizing a triangular channel for complete volume retention:
L=\frac{151,400Q_{p}^{\frac{5}{8}}m^{\frac{5}{8}}S^{\frac{3}{16}}}{n^{\frac{3}{8}}\left (\sqrt{1+m^{2}} \right )^{\frac{5}{8}}q}
===Trapezoidal channel===
Sizing a trapezoidal channel for complete volume retention:
L=\frac{360,000Q_{p}}{\left\{ b+2.388\left[\frac{Q_{p}n}{\left(2\sqrt{1+m^{2}-m}\right)S^{\frac{1}{2}}}\right ]^{\frac{3}{8}}\sqrt{1+m^{2}} \right \}q}
==Sizing and spacing of check dams==
Check dams are a feature of enhanced grass swales. They promote infiltration and evaporation by promoting limited ponding. 
To design check dams into a swale:
#The height of each dam is determined by the depth of ponded water that will infiltrate in a specified period (often 48 - 72 hours). The infiltration may be through the turf grass or other plants directly into the native soil or some soil amendments may be proposed in the design.
#The gradient between the top of the lower check dam and the bottom of the upper one is called "compensation gradient" which is the future or final effective gradient of the swale. It is formed when material carried by flowing water fills the check dams to spillway level. 
#Dams are usually installed between 10-20 m along the swale. The spaces between check dams can be determined according to the compensation gradient and the effective height of the dams. They are distributed such that the crest of each dam is at approximately the same elevation as the toe of the upstream dam. If the slope along the swale varies, so should the distance between the dams.
#The compensation gradient of enhanced swales must be < 1 % (0.5 % preferred).
The objective of these design recommendations are to maximize the distribution of ponded water along the whole BMP. Detailed design may require iteration of the dam heights and distances along each section of a long swale.
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To estimate the depth of water that can be infiltrated into a surface within a given time: 
y=f'\times t
 
 
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After surveying the longitudinal profile of the swale, the number of check dams for the swale can be calculated by using the following equation:
Number\ of\ dams= \frac{L\left ( S_{i}-S_{e} \right )}{h}
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*The first check dam should be constructed on a stable point in the gully such as a rock outcrop, the junction point of the gully to a road, the main stream or river, lake or reservoir. 
*If there is no such stable point, a counter-dam must be constructed. The distance between the first dam and the counter-dam must be at least two times the effective height of the first check dam.
*The points where the ensuing check dams are to be built are determined according to the compensation gradient and the effective height of the check dams. 
*The effective height of the second check dam is determined by taking into account the depth of the swale, the depth of the spillway and the maximum height of the check dam. 
*In this way, all the other proposed check dam points can be calculated.
When spacing check dams, give preference to the narrowest parts of the swale in order to reduce construction costs. 
In this case, to establish the compensation gradient between the proposed check dams, proportionately increase the foundation depth of the upper check dam when the space between the lower and upper check dam is extended. 
When the space is shortened, decrease the foundation depth. 
As the foundation depth is increased, the total height of the check dam (effective height plus foundation depth) should not exceed the permissible, maximum total height.
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===Example Calculation===
An enhanced swale of 42 m has an existing longitudinal slope of 6 %. The underlying soil has been amended to infiltrate at 16 mm/hr (after safety correction applied); the regulatory authority requires that ponded water must not remain for over 48 hours.
The maximum height of the check dams (h) to prevent extended ponding is::
h=16\ mm/hr\times 48\ hrs = 768\ mm 
But the maximum recommended depth of check dams is 0.6 m (600 mm). 
(As an aside, these will drain in \frac{600\ mm}{16\ mm/hr}=37.5\ hrs)
The current vertical distance along the swale is::
42\ m\times \left ( \frac{6}{100} \right )=2.52\ m
The desired effective slope to slow flow is 0.5%. The vertical distance along the swale with compensation gradient is::
42\ m\times \left ( \frac{0.5}{100} \right )=0.21\ m
The number of check dams required is::
\frac{\left ( 2.52\ m\times 0.21\ m\right )}{0.6\ m}=3.85
This is rounded up to 4 dams, creating 5 ponding zones::
\frac{42\ m}{5}=8.4\ m
 
So the four check dams will be 0.6 m high and spaced every 8.4 m along the swale. These are fairly close together, but this construction is achievable and the dimensions are not remarkable, given the change in gradient is an order of magnitude.
category:modeling