time of concentration calculator

Understanding the "time of concentration" (Tc) is fundamental in hydrology and hydraulic engineering. It's a critical parameter used in storm sewer design, flood plain management, and various other water resource planning applications. Essentially, Tc represents the time required for runoff to travel from the hydraulically most distant point of a watershed to its outlet.

An accurate estimation of Tc is crucial because it directly influences the peak discharge calculation in a watershed. A shorter Tc often leads to a higher, more intense peak flow, which can impact the sizing of drainage structures and flood control measures. Conversely, a longer Tc suggests a more attenuated and spread-out hydrograph.

Methods for Calculating Time of Concentration

Several methods exist for calculating time of concentration, each with its own assumptions and applicability. The choice of method often depends on the watershed characteristics, available data, and regulatory requirements. Common methods include:

• Kinematic Wave Equation: Often used for sheet flow over short distances.
• Kirpich Equation: An empirical formula suitable for rural watersheds.
• Federal Aviation Administration (FAA) Method: Utilized for airport drainage design.
• NRCS (SCS) TR-55 Method: A widely accepted method that breaks down flow into three segments: sheet flow, shallow concentrated flow, and open channel flow. This is the method employed by our calculator.

The NRCS (SCS) TR-55 Method Explained

The TR-55 method, developed by the Natural Resources Conservation Service (formerly Soil Conservation Service), provides a standardized approach for estimating Tc. It assumes that runoff travels through distinct flow regimes, and the total Tc is the sum of the travel times for each segment.

1. Sheet Flow

Sheet flow is runoff over plane surfaces, usually occurring in the upper reaches of a watershed. It's characterized by very shallow depths and often occurs across lawns, fields, or paved areas before converging into small channels. The maximum length for sheet flow is typically limited to 300 feet (91 meters) in the TR-55 method.

The equation for sheet flow travel time (T_sheet) in hours is:

Tsheet = [0.007 * (n * L)0.8] / [P20.5 * S0.4]

• L (Length): Length of the sheet flow path in feet.
• n (Manning's Roughness): A dimensionless coefficient representing the surface roughness. Higher 'n' values indicate rougher surfaces (e.g., dense grass, woods), which impede flow.
• P2 (2-Year 24-Hour Rainfall): The 2-year, 24-hour rainfall depth in inches for the area. This value can be obtained from local rainfall atlases or NOAA data.
• S (Slope): The average land slope of the sheet flow path in feet per foot.

2. Shallow Concentrated Flow

As sheet flow progresses, it often converges into small rills and rivulets, forming shallow concentrated flow. This type of flow occurs in swales, ditches, or along property lines where defined channels haven't yet formed. The velocity of shallow concentrated flow is typically estimated using empirical relationships based on the surface type and slope.

The velocity (V_shallow) in feet per second is:

Vshallow = k * S0.5

The travel time (T_shallow) in minutes is:

Tshallow = L / (Vshallow * 60)

• L (Length): Length of the shallow concentrated flow path in feet.
• k (Velocity Factor): A coefficient dependent on the surface type:
  • k = 16.1 ft/s for unpaved surfaces (e.g., grassed waterways, bare soil).
  • k = 20.3 ft/s for paved surfaces (e.g., streets, driveways).
• S (Slope): The average land slope of the shallow concentrated flow path in feet per foot.

3. Open Channel Flow

Finally, runoff may enter well-defined channels, such as streams, rivers, or engineered ditches. For these segments, Manning's equation is typically used to calculate the flow velocity, and subsequently, the travel time.

The velocity (V_channel) in feet per second is:

Vchannel = (1.49 / n) * R2/3 * S0.5

The travel time (T_channel) in minutes is:

Tchannel = L / (Vchannel * 60)

• L (Length): Length of the open channel flow path in feet.
• n (Manning's Roughness): A dimensionless coefficient representing the roughness of the channel material.
• R (Hydraulic Radius): The ratio of the channel's cross-sectional area (A) to its wetted perimeter (P_w), in feet. R = A / Pw.
• S (Slope): The average bed slope of the open channel in feet per foot.

Importance of Accurate Time of Concentration

An accurate Tc is paramount for:

• Hydrologic Modeling: It's a key input for rainfall-runoff models used to predict watershed response.
• Stormwater Management Design: Directly impacts the sizing of culverts, storm drains, detention basins, and other infrastructure.
• Flood Forecasting: Helps in predicting the timing and magnitude of flood peaks.
• Erosion Control: Influences the design of measures to mitigate soil erosion.

Using the Calculator

Our Time of Concentration Calculator simplifies the TR-55 method. Simply input the required parameters for each flow segment (sheet, shallow concentrated, and open channel flow) in the designated fields. Ensure your units are consistent (feet for length, feet/foot for slope, inches for rainfall, etc.). The calculator will then provide the individual travel times for each segment and the total time of concentration in minutes.

Limitations and Assumptions

While the TR-55 method is widely used, it relies on several assumptions:

• Homogeneous Flow Conditions: Assumes relatively uniform conditions within each flow segment.
• Empirical Relationships: Many coefficients (like Manning's 'n' and 'k' values) are empirically derived and may vary based on local conditions.
• Maximum Sheet Flow Length: The 300-foot limit for sheet flow is a guideline; in reality, sheet flow might occur over longer or shorter distances.
• No Storage Effects: The method doesn't explicitly account for significant storage effects (e.g., wetlands, ponds) within the flow path, which can increase Tc.

Always use engineering judgment and consult local regulations and design manuals when applying these calculations.