You can calculate sheet flow, specifically its time of concentration ($T_t$), using a specific equation commonly applied in hydrological analysis, particularly in the headwaters of streams.
Sheet flow is a type of overland flow that occurs as a shallow, uniform layer of water flowing across relatively smooth land surfaces, like parking lots, cultivated fields, or turf grass, before it concentrates into rills or channels. It is often considered the initial phase of surface runoff in areas located at the headwater of stream systems.
Calculating Sheet Flow Time of Concentration
The reference provided gives a specific equation used to describe sheet flow, focusing on calculating the time of concentration ($T_t$). The time of concentration is the time it takes for water to travel from the hydraulically most distant point of the watershed to the outlet.
The equation provided for calculating $T_t$ for sheet flow is:
$T_t = \frac{0.007(nL)^{0.8}}{(P_2)^{0.5}s^{0.4}}$
Where:
- $T_t$: Time of concentration for sheet flow (in hours).
- $n$: Manning's roughness coefficient (dimensionless) for overland flow. This value represents the resistance to flow due to the surface type (e.g., smooth pavement, short grass, dense forest).
- $L$: Flow length (in feet). This is the horizontal distance water travels as sheet flow from the watershed boundary to the point where concentrated flow begins.
- $P_2$: Two-year, 24-hour rainfall depth (in inches). This is a standard rainfall intensity used in many hydrological design calculations.
- $s$: Land slope (in feet per foot or m/m). This is the average slope of the land surface along the flow path.
Understanding the Variables
Let's look closer at the variables:
- Manning's Roughness ($n$): This is crucial as different surfaces impede flow differently.
- Smooth surfaces like pavement have low 'n' values, leading to faster flow.
- Vegetated surfaces like grass or forest floor have higher 'n' values, slowing the flow.
- Example: Pavement might have n ≈ 0.011, while dense grass might have n ≈ 0.24.
- Flow Length ($L$): Sheet flow typically occurs over relatively short distances before concentrating. The standard maximum length considered for sheet flow calculation is often around 100 to 300 feet (30 to 90 meters), depending on the methodology used. Beyond this length, flow usually becomes concentrated.
- Rainfall Depth ($P_2$): This accounts for the intensity of the rainfall event being analyzed. Higher rainfall can sometimes affect overland flow dynamics, though its influence is represented here by a standard design value.
- Land Slope ($s$): Steeper slopes lead to faster flow. The slope is usually determined by surveying the land surface along the flow path.
Practical Considerations
- This equation is specifically for the sheet flow portion of the flow path. Total time of concentration for a watershed might include time for sheet flow, shallow concentrated flow, and channel flow.
- Accurately determining the flow length ($L$), slope ($s$), and appropriate Manning's 'n' value are critical for a correct calculation.
- Hydrology manuals and engineering guidelines (like those from the Natural Resources Conservation Service - NRCS) often provide tables for typical Manning's 'n' values for various surface types and guidance on determining flow length and slope.
Using this formula allows engineers and hydrologists to estimate how quickly runoff travels over initial smooth or vegetated surfaces within a watershed's headwaters, which is a vital component in designing drainage systems and predicting flood responses.
