For the Civil Engineering Stormwater modeling field, this spreadsheet calculates the time of concentration (based on TR-55 methodology and restricts sheet flow to include the first 300 LF). Please note that this spreadsheet is password protected and cell formulae cannot be seen.
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The time of concentration (Tc) is the time it takes for water to flow from the most remote point in a watershed to the outlet. The TR-55 methodology, developed by the USDA's Natural Resources Conservation Service (NRCS), provides a way to calculate Tc. The TR-55 method divides the flow path into three segments: sheet flow, shallow concentrated flow, and channel flow.
Here's how to calculate the time of concentration using the TR-55 method:
- Sheet flow (overland flow):
Tt_sheet = (L_sheet / 100) * (n_sheet / P) * (L_sheet^0.8 * S^0.5) / (I_sheet^0.4)
where: Tt_sheet = time of concentration for sheet flow segment (minutes) L_sheet = length of sheet flow segment (feet) n_sheet = Manning's roughness coefficient for sheet flow (dimensionless) P = rainfall intensity for a 10-year, 24-hour storm (in/hr) S = slope of the sheet flow segment (feet/feet) I_sheet = average rainfall intensity for the sheet flow segment (in/hr)
Typical values for Manning's n for sheet flow:
- Pavement: 0.011
- Lawns (flat): 0.15
- Lawns (moderate slope): 0.20
- Lawns (steep slope): 0.25
- Shallow concentrated flow:
Tt_shallow = L_shallow / (50 * V_shallow)
where: Tt_shallow = time of concentration for shallow concentrated flow segment (minutes) L_shallow = length of shallow concentrated flow segment (feet) V_shallow = flow velocity for shallow concentrated flow segment (ft/min)
Use this equation to estimate the flow velocity:
V_shallow = 16.1 * (S^0.5)
- Channel flow:
Tt_channel = L_channel / (60 * V_channel)
where: Tt_channel = time of concentration for channel flow segment (minutes) L_channel = length of channel flow segment (feet) V_channel = flow velocity for channel flow segment (ft/min)
Use the Manning's equation to estimate the flow velocity:
V_channel = (1.49 / n_channel) * (A_channel / P_channel)^(2/3) * S_channel^0.5
where: n_channel = Manning's roughness coefficient for channel flow (dimensionless) A_channel = cross-sectional area of flow (square feet) P_channel = wetted perimeter of the flow (feet) S_channel = slope of the channel (feet/feet)
- Add the times for each segment to find the total time of concentration:
Tc = Tt_sheet + Tt_shallow + Tt_channel
Remember that the TR-55 method has limitations and may not be suitable for all situations. Always consult local stormwater management guidelines or a professional engineer to ensure that your calculations are accurate and appropriate for your project.
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