What is the Time of Concentration (Tc)?
In hydrology and civil engineering, the Time of Concentration (Tc) is defined as the time required for water to flow from the most hydraulically remote point in a watershed to the outlet. It is a critical parameter used in rainfall-runoff modeling and the design of stormwater management systems, such as gutters, culverts, and detention ponds.
Understanding the Kirpich Formula
The Kirpich Formula is one of the most widely used empirical methods for estimating Tc in small, rural watersheds. It was developed by P.Z. Kirpich in 1940 and relies on two main variables: the length of the flow path and the average slope of the channel. The formula is expressed as:
Tc = 0.0078 × L0.77 × S-0.385
Where L is the length in feet and S is the slope in feet per foot. Note that if you are using the formula for paved surfaces or concrete channels, an adjustment factor (typically 0.4 for concrete) may be required.
How to Use This Calculator
To calculate the time of concentration using our tool, follow these steps:
- Flow Length: Measure the longest flow path from the ridge to the drainage outlet in feet.
- Average Slope: Determine the change in elevation divided by the flow length. For example, a 10-foot drop over 500 feet results in a slope of 0.02.
- Calculate: Click the button to see the step-by-step breakdown of the exponential calculation.
FAQs
Why is Tc important for the Rational Method?
The Rational Method (Q = CiA) requires the rainfall intensity (i). This intensity is usually selected from an IDF curve based on a duration equal to the Time of Concentration. If your Tc is inaccurate, your peak flow estimation (Q) will be incorrect, leading to potentially dangerous under-design or costly over-design.
Does slope significantly affect Tc?
Yes, because the slope appears with a negative exponent in the denominator, a steeper slope significantly decreases the time it takes for water to reach the outlet, thereby increasing peak discharge.