Often a city will require some treatment of storm water from development sites. Let us assume that land is being developed for a small shopping area land near 134th Street & "0" Street, near the proposed east by-pass. There are many water quality parameters that are of concern, but for this problem we will focus on sediment. Sediment washes from pavement, roofs, and bare soil. There are several methods of removing sediment from storm water before it enters a stream. We will explore two of these: retention ponds and vegetative filter strips. Retention Pond: As stormwater enters a retention pond, organic compounds in the water will decay and sediment will settle to the bottom. Sediment settling in this case is a first-order reaction. The following data pertains to this problem: Detention pond surface area: 1.0 acres = 4,046 m Average water depth: 2 meter Mass of sediment that will flow to the pond in the design storm (e.g., 6 mo. summer storm): 486 kg (be sure to convert to mg for part a) "Allowable" sediment concentration to release to the nearby stream: 20 mg/L There is currently no flow into or out of the pond. Use mass balances to solve the following questions. a) Assuming the entire mass of sediment enters the pond during a storm, and that the pond is well-mixed (uniform sediment concentration throughout the pond), what is the initial concentration of sediment in the pond water in mg/L? b) If there is no discharge from the pond while the sediment settles, how long will it take for the concentration of sediment to decrease to a safe level (to then allow for discharge)? Assume that there is no flow into or out of the pond (batch reactor) and that the settling rate constant for sediment in the pond is k=0.05 1/days. Calculate the retention time required. The below equation (based on empirical data) can be used. C = Co e-(kt) where: C = Allowable sediment concentration (20 mg/L) Co = Sediment concentration in the pond after the storm (answer from part a) k = first-order reaction constant (0.05 1/day) vegetative Filter Strips c) Another option is to use a vegetative filter strip. There are many variants of this approach (including having a swale that the water must flow over), with different names being used. We are going to keep our approach simple here and just consider having a length of grass that the sediment will flow over. For stormwater, sediment, bacteria, and chemicals will be removed as it flows over the strip. A key issue is the width of the vegetative filter strip. Reduction of the water-borne sediment concentration across the strip is roughly first-order. The below equation (based on empirical data) can be used. C = Co e-(KL) where: C = Sediment concentration after passing over vegetative filter strip (20 mg/L) Co = Sediment concentration entering vegetative filter strip (answer from part a) K= first-order reaction constant (0.35 1/m) L = width of vegetative filter (meters) What is the minimum width of grass (in meters, m) that reduces the sediment concentration to 20 mg/L? d) Based on your answers to parts (b, c, and d), which option do you think might be the easiest to implement and maintain at the site? = Hint: if you need to manipulate an equation like Aout = Ain e-kt divide each side by Ain Aout/Ain = e-kt, take the In of each site: In (Aout/Ain) = In (e-kt) realize that taking in of e give you-kt: In (Aout/Ain) = -kt then solve for either kort, as is needed. Often a city will require some treatment of storm water from development sites. Let us assume that land is being developed for a small shopping area land near 134th Street & "0" Street, near the proposed east by-pass. There are many water quality parameters that are of concern, but for this problem we will focus on sediment. Sediment washes from pavement, roofs, and bare soil. There are several methods of removing sediment from storm water before it enters a stream. We will explore two of these: retention ponds and vegetative filter strips. Retention Pond: As stormwater enters a retention pond, organic compounds in the water will decay and sediment will settle to the bottom. Sediment settling in this case is a first-order reaction. The following data pertains to this problem: Detention pond surface area: 1.0 acres = 4,046 m Average water depth: 2 meter Mass of sediment that will flow to the pond in the design storm (e.g., 6 mo. summer storm): 486 kg (be sure to convert to mg for part a) "Allowable" sediment concentration to release to the nearby stream: 20 mg/L There is currently no flow into or out of the pond. Use mass balances to solve the following questions. a) Assuming the entire mass of sediment enters the pond during a storm, and that the pond is well-mixed (uniform sediment concentration throughout the pond), what is the initial concentration of sediment in the pond water in mg/L? b) If there is no discharge from the pond while the sediment settles, how long will it take for the concentration of sediment to decrease to a safe level (to then allow for discharge)? Assume that there is no flow into or out of the pond (batch reactor) and that the settling rate constant for sediment in the pond is k=0.05 1/days. Calculate the retention time required. The below equation (based on empirical data) can be used. C = Co e-(kt) where: C = Allowable sediment concentration (20 mg/L) Co = Sediment concentration in the pond after the storm (answer from part a) k = first-order reaction constant (0.05 1/day) vegetative Filter Strips c) Another option is to use a vegetative filter strip. There are many variants of this approach (including having a swale that the water must flow over), with different names being used. We are going to keep our approach simple here and just consider having a length of grass that the sediment will flow over. For stormwater, sediment, bacteria, and chemicals will be removed as it flows over the strip. A key issue is the width of the vegetative filter strip. Reduction of the water-borne sediment concentration across the strip is roughly first-order. The below equation (based on empirical data) can be used. C = Co e-(KL) where: C = Sediment concentration after passing over vegetative filter strip (20 mg/L) Co = Sediment concentration entering vegetative filter strip (answer from part a) K= first-order reaction constant (0.35 1/m) L = width of vegetative filter (meters) What is the minimum width of grass (in meters, m) that reduces the sediment concentration to 20 mg/L? d) Based on your answers to parts (b, c, and d), which option do you think might be the easiest to implement and maintain at the site? = Hint: if you need to manipulate an equation like Aout = Ain e-kt divide each side by Ain Aout/Ain = e-kt, take the In of each site: In (Aout/Ain) = In (e-kt) realize that taking in of e give you-kt: In (Aout/Ain) = -kt then solve for either kort, as is needed