# Flow in a swale

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Flow (Q) in an open channel, such as a swale, may be calculated using Manning's equation: ${\displaystyle Q=VA={\frac {R^{\frac {2}{3}}S^{\frac {1}{2}}}{n}}}$ Where: ${\displaystyle R={\frac {A}{P}}}$

Where:

• Q = the flow in the swale (m3/s)
• A = the cross sectional area of the swale (m2)
• P = the wetted perimeter of the swale (m)
• S = the longitudinal slope (m/m)
• n = Manning's coefficient or 'Manning's n' (dimensionless)

Manning's n of vegetated surfaces [1]
n value range Good condition turf grass Other
0.002 - 0.010 Where the average depth of flow is at ≥ 2 times the height of the vegetation Supple tree seedlings such as willow or cottonwood growing where the average depth of flow is at ≥ 3 times the height of the vegetation
0.010 - 0.025 Where the average depth of flow is between 1 - 2 times the height of the vegetation Moderately dense weeds, or tree seedlings growing where the average depth of flow is from 2 -3 times the height of the vegetation
0.025 - 0.050 Where the average depth of flow is about equal to the height of the vegetation 8- to 10-year-old willow or cottonwood trees inter-grown with some weeds and brush (none of the vegetation in foliage)
0.050 - 0.100 Where the average depth of flow is < 0.5 times height of the vegetation bushy willow trees about 1 year old inter-grown with weeds along side slopes (all vegetation in full foliage)

## References

1. Arcement, G.J., Schneider, R. Guide for Selecting Manning's Roughness Coefficients for Natural Channels and Flood Plains U.S.G.S. WATER-SUPPLY PAPER 2339, 1989 https://pubs.usgs.gov/wsp/2339/report.pdf