Two equations govern the flow of runoff on a slope. The first is the continuity equation (conservation of mass) and the second is an equation describing conservation of momentum. The continuity equation is just the water balance for the slope or any small portion of the slope and can be given as: p - fp = RO where i = rainfall rate, fp = infiltration capacity, and RO = runoff rate, all expressed as a depth per time, e.g. mm h-1 . Since Q= VA, the Q for each unit width = i*1*depth*length of slope. The momentum, or flow equation we often use is Manning's equation: V = 1.49 R2/3 S0.5.n
Application:
You have been asked to determine the rate and depth of flow from a parking lot at a shopping mall and recommend the size of the gutter needed to accommodate the runoff from the lot. The lot is 300 feet by 500 feet. The overland flow portion is the 300 feet and has a slope of 2.0%. Flow will enter the gutter along the 500 feet at the bottom of the overland flow. The gutter has a slope of 1.0 % and a rectangular cross section with a bottom width of 1.5 foot.
Determine the following:
1. The discharge, q, along the 300 feet of overland flow,
2. The depth, d, of flow along the 300 feet of overland flow, and
3. The discharge, Q, and depth of flow in the gutter.
Someone spills a container of gasoline at the farthest corner of the parking lot during the storm. Estimate the average time for the gasoline to reach the outlet of the gutter.
Procedure:
1. Use a 1/2-hour duration, 10-year recurrence interval storm for the exercise. Assume that the rainfall occurs at a uniform intensity during the 1 hour duration. You can use the IDF (Intensity-Duration-Frequency) curves for Region 2 in Precipitation in Connecticut available at www.ctiwr.uconn.edu under Publications/special reports. or http://digitalcommons.uconn.edu/ctiwr_specreports/36/ for the direct link.
2. Determine the discharge along the slope of the lot in cfs per foot of width across the lot for every 10 foot increment. Using Manning's equation, determine the depth of flow down the lot, i.e. from the top to the entrance to the gutter, again at 10 ft increments. The surface of the lot is older, rough asphalt which has an 'n' value = 0.10 for shallow flow. NOTE: this ‘n’ maybe higher than typically given, but we assume at first that the flow is very shallow.
3. Determine the discharge along the gutter and calculate the depth needed for the gutter at its outlet. The gutter is made from concrete which has an 'n' value = 0.04.
4. In the design of storm water control systems, engineers often will add "freeboard" to the calculated depth of a channel to account for blockage, changes in 'n', etc. Determine if 0.5 feet of added depth to the gutter will accommodate the 100-year, 1/2-hour storm.
5. Using the velocities calculated from Manning's, determine the time it takes for the gasoline to reach the outlet of the gutter. State any assumptions involved in your calculations.