Problem 1: An intensity-duration-frequency (IDF) curve is a mathematical function that relates the rainfall intensity with its duration and frequency of occurrence. These curves are commonly used in engineering for urban drainage design. The following data for rainfall intensity (in/hr) corresponds to an area in Knoxville, Tennessee Return Period (years) duration (min) 12.62 8.63 5.52 10 50 100 200 500 8.17 6.54 5 10 15 30 60 90 120 4 2.6 1.54 1.1 10.04 10.86 11.65 8 9.23 6.76 7.27 7.77 5.09 5.57 6.05 3.45 3.83 4.24 2.1 2.37 2.67 1.53 1.75 1.98 Rainfall intensity (in/hr) 9.98 8.38 6.66 4.78 3.06 2.32 a) Plot the data for 10 yr-retum period in Mathcad. The duration, in minutes, is plotted in the horizontal axis and the rainfall intensity, in in hr, is plotted in the vertical axis. b) Fit the data with the specialized function Intio). Determine the trendline equation and value: Infit(x, y) Returns a vector containing the coefficients for a logarithmic curve of the form a ln(x) + b that best approximates the data in v and ry, ) Using the equation, find the rainfall intensity for a specific stor duration (for example 20 min). d) Write a program that receives as input parameter a specific storm duration in the range of 5 to 120 min, and also a retum period in the range of 10 to 500 years. The program will perform the appropriate calculations and retum as an output the rainfall intensity I (inlur) for this area in Knoxville, Tennessee. Use regression and linear interpolation to find to most accurate answer. e) Test your program using the following data. Determine the rainfall intensity for each case, duration return period (min) fyr) 5 10 20 100 25 300 Create a neat design worksheet, using program from question 1 and program from question 2, to design storm water drain pipelines. Determine the less expensive pipe that satisfy each of the following design criteria using your design worksheet: Storm duration (min) 8 20 25 Criteria 1 Criteria 2 Criteria 3 Return period (years) 100 200 300 Catchment area (acres) 8.5 8.5 10 Runoff Pipe coefficient slope 0.9 0.005 0.85 0.001 0.85 0.010 Pipe diameter (in) ? ? ? Problem 1: An intensity-duration-frequency (IDF) curve is a mathematical function that relates the rainfall intensity with its duration and frequency of occurrence. These curves are commonly used in engineering for urban drainage design. The following data for rainfall intensity (in/hr) corresponds to an area in Knoxville, Tennessee Return Period (years) duration (min) 12.62 8.63 5.52 10 50 100 200 500 8.17 6.54 5 10 15 30 60 90 120 4 2.6 1.54 1.1 10.04 10.86 11.65 8 9.23 6.76 7.27 7.77 5.09 5.57 6.05 3.45 3.83 4.24 2.1 2.37 2.67 1.53 1.75 1.98 Rainfall intensity (in/hr) 9.98 8.38 6.66 4.78 3.06 2.32 a) Plot the data for 10 yr-retum period in Mathcad. The duration, in minutes, is plotted in the horizontal axis and the rainfall intensity, in in hr, is plotted in the vertical axis. b) Fit the data with the specialized function Intio). Determine the trendline equation and value: Infit(x, y) Returns a vector containing the coefficients for a logarithmic curve of the form a ln(x) + b that best approximates the data in v and ry, ) Using the equation, find the rainfall intensity for a specific stor duration (for example 20 min). d) Write a program that receives as input parameter a specific storm duration in the range of 5 to 120 min, and also a retum period in the range of 10 to 500 years. The program will perform the appropriate calculations and retum as an output the rainfall intensity I (inlur) for this area in Knoxville, Tennessee. Use regression and linear interpolation to find to most accurate answer. e) Test your program using the following data. Determine the rainfall intensity for each case, duration return period (min) fyr) 5 10 20 100 25 300 Create a neat design worksheet, using program from question 1 and program from question 2, to design storm water drain pipelines. Determine the less expensive pipe that satisfy each of the following design criteria using your design worksheet: Storm duration (min) 8 20 25 Criteria 1 Criteria 2 Criteria 3 Return period (years) 100 200 300 Catchment area (acres) 8.5 8.5 10 Runoff Pipe coefficient slope 0.9 0.005 0.85 0.001 0.85 0.010 Pipe diameter (in)