Time of Concentration Explained: Methods and Applications

Time of concentration (Tc) is one of the most important—and frequently misunderstood—parameters in drainage design. It fundamentally links watershed characteristics to rainfall intensity and determines peak flow rates.

What Is Time of Concentration?

Time of concentration (Tc) is the time required for water to travel from the hydraulically most distant point in the watershed to the outlet. When storm duration equals Tc, the entire watershed is contributing runoff to the outlet, producing the maximum peak discharge.

Why Tc Matters

1. Rainfall Intensity Selection

In the Rational Method, Tc determines storm duration, which determines rainfall intensity:

The relationship:

• Longer Tc → Longer duration → Lower intensity → Lower peak flow
• Shorter Tc → Shorter duration → Higher intensity → Higher peak flow

2. Hydrograph Timing

Tc is related to:

• Lag time: TL ≈ 0.6 × Tc
• Time to peak: Tp = D/2 + TL
• Hydrograph duration: Based on Tc

3. Design Storm Duration

Many regulations require storm duration = Tc for peak flow calculations.

The Segmented Flow Path Approach

The NRCS (TR-55) method divides the flow path into segments with different flow types:

1. Sheet Flow

Shallow flow over plane surfaces (parking lots, lawns, roofs).

Characteristics:

• Very shallow depth (<0.1 ft typically)
• Maximum length: 100-300 ft (depending on agency)
• Occurs at the top of watersheds

NRCS Kinematic Wave Equation:

Where:

• Tt = Travel time (hours)
• n = Manning’s roughness coefficient
• L = Flow length (feet)
• P2 = 2-year, 24-hour rainfall (inches)
• S = Slope (ft/ft)

Sheet Flow n Values:

2. Shallow Concentrated Flow

After sheet flow concentrates, but before it enters defined channels.

Characteristics:

• Depth typically 0.1-0.5 ft
• Flows in small rills, swales, or along curbs
• Velocity estimated from slope

NRCS Velocity Equations:

For paved surfaces:

For unpaved surfaces:

Where V is in ft/s and S is slope in ft/ft.

Travel Time:

Where L is in feet and Tt is in hours.

3. Channel Flow

Flow in defined channels, pipes, or streams.

Use Manning’s Equation:

Then:

Alternative Tc Methods

Several empirical equations exist for estimating Tc directly without segmenting the flow path.

Kirpich Equation (1940)

Originally developed for small agricultural watersheds in Tennessee:

Where:

• Tc = Time of concentration (minutes)
• L = Length of main channel (feet)
• S = Average slope (ft/ft)

Best for: Small agricultural watersheds, natural channels Limitations: Tends to underestimate for flat slopes; doesn’t account for surface type

FAA Method (1970)

Used for airport drainage:

Where:

• Tc = Time of concentration (minutes)
• C = Rational method runoff coefficient
• L = Length of overland flow (feet)
• S = Average slope (%)

Best for: Overland flow on airports, parking lots Limitations: Empirical; limited range of original data

Kerby-Hathaway Method

For overland flow:

Where:

• Tc = Time of concentration (minutes)
• L = Flow length (feet)
• nk = Kerby roughness coefficient
• S = Slope (ft/ft)

Kerby nk Values:

Izzard Method

For shallow sheet flow with laminar conditions:

Where cr is a retardance coefficient and i is rainfall intensity.

Comparison of Methods

Step-by-Step NRCS Velocity Method Example

Given:

A 50-acre commercial development with:

• Sheet flow: 150 ft over parking lot (n = 0.011), 2% slope
• Shallow concentrated flow: 800 ft along curb line, 1.5% slope
• Channel flow: 1,200 ft in concrete pipe (n = 0.013), 0.5% slope, 36” diameter
• P2 = 3.5 inches

Solution:

Segment 1: Sheet Flow

Segment 2: Shallow Concentrated Flow (Paved)

Velocity:

Travel time:

Segment 3: Channel Flow (36” Concrete Pipe)

Assuming half-full conditions:

• A = 3.53 ft²
• R = 0.75 ft
• n = 0.013

Velocity:

Travel time:

Total Tc:

Try the Time of Concentration Calculator →

Minimum Time of Concentration

Most agencies specify a minimum Tc:

• Common values: 5-10 minutes
• Rationale: Very short Tc produces unrealistically high intensities
• Application: Use actual calculated Tc if > minimum; use minimum if calculated < minimum

Effects of Development on Tc

Development typically reduces Tc:

Before and After Development

A typical site might have:

• Pre-development Tc: 45 minutes (grass, natural swales)
• Post-development Tc: 15 minutes (pavement, storm sewers)

This 3x reduction in Tc can increase rainfall intensity by 2x or more, dramatically increasing peak flow.

Common Mistakes

1. Sheet Flow Length Too Long

Limit sheet flow to 100-300 ft. Beyond this, flow concentrates regardless of what the topography shows.

2. Using Wrong n Values

Sheet flow n values are NOT Manning’s equation n values. Use the appropriate tables for each flow type.

3. Ignoring Minimum Tc

Don’t use calculated Tc values below 5 minutes without explicit approval.

4. Double-Counting Improvements

If pipes reduce Tc, don’t also use pre-development Tc elsewhere in the calculation.

5. Inconsistent Methods

Don’t mix methods (e.g., Kirpich for part, NRCS for another). Use one consistent approach.

6. Forgetting Channel Entry/Exit

Include time to reach and exit channels, not just channel travel time.

Summary

Time of concentration is critical because:

• It determines design rainfall intensity
• It affects peak flow directly
• Errors propagate through all calculations

Key points:

• Use segmented approach (sheet → shallow → channel)
• Respect maximum sheet flow lengths
• Apply appropriate minimum Tc
• Consider effects of development
• Be consistent with chosen method

References

1. Natural Resources Conservation Service. (1986). Urban hydrology for small watersheds (Technical Release 55). U.S. Department of Agriculture.

2. Kirpich, Z. P. (1940). Time of concentration of small agricultural watersheds. Civil Engineering, 10(6), 362.

3. Federal Aviation Administration. (1970). Airport drainage (Advisory Circular 150/5320-5B). U.S. Department of Transportation.

4. Kerby, W. S. (1959). Time of concentration for overland flow. Civil Engineering, 29(3), 174.

5. Izzard, C. F. (1946). Hydraulics of runoff from developed surfaces. Highway Research Board Proceedings, 26, 129-150.

6. McCuen, R. H. (2016). Hydrologic analysis and design (4th ed.). Pearson.

7. Federal Highway Administration. (2013). Urban drainage design manual (3rd ed., Hydraulic Engineering Circular No. 22). U.S. Department of Transportation.