A Modified Manning’s Equation for Estimating Flow Rate in Grass Swales under Low Inflow Rate Conditions

Abstract

As green infrastructure has evolved, grass swales have become integral components of stormwater management. Manning’s equation is commonly used to describe the hydraulic characteristics of grass swales. However, due to flow loss from infiltration, grass swales often deviate from the assumptions of Manning’s equation, potentially leading to significant errors in grass swale flow rate calculations. In this study, we systematically investigated changes in flow rates in grass swales under various constant inflow rate conditions. The results indicated that the suitability of using Manning’s equation to estimate flow rate in grass swales varies with inflow rate. At an inflow rate of 3.00 m3/h, the discrepancy between the measured and the estimated flow rates by Manning’s equation was the smallest, ranging from −0.24 to 0.19 m3/h. At lower inflow rates (1.00 to 2.00 m3/h), Manning’s equation underestimated the flow rates by 0.16 to 0.47 m3/h; at higher rates (4.00 m3/h), it overestimated the flow rates by 0.01 to 0.61 m3/h. Considering infiltration losses as the primary cause of these errors, we proposed an improved Darcy’s formula for estimating the infiltration rates in grass swales, along with a modified Manning’s equation for more accurate flow rate calculations. The modified Manning’s equation provides enhanced accuracy in calculating flow rates in grass swales compared to the traditional version.

Keywords

• Darcy’s formula
• infiltration loss
• grass swales
• flow rate
• low-impact development