Valoración global e interpretación de la función pulmonar

5.33. An alternating-block analysis indicated the following rainfall distribution for a 70-min storm: Rainfall Interval (mm/h) 1 7 2 25 3 45 4 189 5 97 6 44 7 18

where each interval corresponds to 10 minutes. If infiltration can be described by the Horton parameters: fo = 600 mm/h, fc = 30 mm/h, k = 0.5 min−1, and the depression storage is

4 mm, use the Horton method to determine the distribution of runoff, and hence the total runoff.

5.34. An area consists almost entirely of sandy loam, which typically has a saturated hydraulic conductivity of 11 mm/h, average suction head of 110 mm, porosity of 0.45, field capacity of 0.190, wilting point of 0.085, and depression storage of 4 mm. The design rainfall is given as:

Interval Average rainfall (min) (mm/h) 0–10 20 10–20 40 20–30 60 30–40 110 40–50 60 50–60 20

Use the Green-Ampt method to determine the runoff versus time for average initial moisture conditions, and contrast the depth of rainfall with the depth of runoff. Assume that the initial moisture conditions are midway between the field capacity and wilting point.

5.35. Repeat Problem 5.34 for a sandy clay soil with a depression storage of 9 mm. (Hint: Use Table 5.12 to estimate the soil properties.)

5.36. Derive the NRCS curve-number model for the infiltration rate given by Equation 5.71. Explain why this infiltration model is unrealistic.

5.37. Drainage facilities are to be designed for a rainfall of return period 10 years and duration 1 hour. The IDF curve is given by

i = 203 (t + 7.24)0.73

where i is the average intensity in cm/h and t is the storm duration in minutes. The minimum infiltration rate is 10 mm/h, and the area to be drained is primarily residential with lot sizes on the order of 0.2 ha (0.5 ac). Use the NRCS method to estimate the total amount of runoff (in cm), assuming the soil is in average condition at the beginning of the design storm.

555 5.38. Repeat Problem 5.37 for the case in which heavy rainfall occurs within the previous five days

and the soil is saturated.

5.39. Use Equation 5.71 to calculate the average infiltration rate during the storm described in Problem 5.37. Compare this calculated infiltration rate with the given minimum infiltration rate of 10 mm/h.

5.40. Data from a double-ring infiltrometer indicate that a soil in a catchment has the following Horton parameters: fo = 250 mm/h, fc = 44 mm/h, and k = 0.13 min−1. Observations also

indicate that the catchment has an average depression storage of 6 mm. If the catchment is located where the 10-year 24-hour rainfall is 229 mm and can be described by the NRCS Type II distribution, estimate the curve number for the site. Use hourly time increments in your analysis. Would the curve number be different for a 20-year 24 hour rainfall? Is the dependence of the curve number on the rainfall amount physically reasonable?

5.41. An undeveloped parcel of land in south Florida has a water table elevation 1.22 m below land surface, and an estimated cumulative water storage of 21 cm is recommended for use in the curve-number method. Consider the 1-day and 3-day storm events given in Tables 5.51 and 5.52, both of which have a total rainfall amount of 31.1 cm.

Table 5.51: 1-Day Storm Event

Time Rainfall Time Rainfall Time Rainfall (h) (cm) (h) (cm) (h) (cm) 0 0.0 0.5 0.2 8.5 4.8 16.5 27.6 1.0 0.3 9.0 5.3 17.0 27.9 1.5 0.5 9.5 5.9 17.5 28.2 2.0 0.6 10.0 6.6 18.0 28.5 2.5 0.8 10.5 7.4 18.5 28.8 3.0 1.0 11.0 8.4 19.0 29.0 3.5 1.2 11.5 9.9 19.5 29.3 4.0 1.4 12.0 20.4 20.0 29.6 4.5 1.6 12.5 22.7 20.5 29.8 5.0 1.9 13.0 23.9 21.0 30.0 5.5 2.2 13.5 24.7 21.5 30.2 6.0 2.6 14.0 25.4 22.0 30.4 6.5 3.0 14.5 26.0 22.5 30.5 7.0 3.4 15.0 26.4 23.0 30.7 7.5 3.8 15.5 26.9 23.5 30.9 8.0 4.3 16.0 27.4 24.0 31.1

Table 5.52: 3-Day Storm Event

Time Rainfall Time Rainfall Time Rainfall (h) (cm) (h) (cm) (h) (cm) 0 0.0 1 0.2 25 3.54 49 8.44 2 0.27 26 3.75 50 8.66 3 0.41 27 3.95 51 8.93 4 0.55 28 4.16 52 9.24 5 0.69 29 4.34 53 9.62 6 0.82 30 4.55 54 10.1 7 0.98 31 4.75 55 10.7 8 1.1 32 4.96 56 11.3 9 1.3 33 5.17 57 12.1 10 1.4 34 5.37 58 13.1 11 1.5 35 5.58 59 14.4 12 1.7 36 5.76 60 23.2 13 1.8 37 5.97 61 25.7 14 1.9 38 6.17 62 26.9 15 2.1 39 6.38 63 27.6 16 2.2 40 6.58 64 28.3 17 2.35 41 6.79 65 28.7 18 2.51 42 7.00 66 29.1 19 2.65 43 7.20 67 29.6 20 2.79 44 7.41 68 30.0 21 2.93 45 7.59 69 30.2 22 3.06 46 7.80 70 30.5 23 3.20 47 8.00 71 30.8 24 3.34 48 8.21 72 31.1

Assuming that the infiltration capacity of the soil is a constant, plot the relationship between curve number and infiltration capacity for both the 1-day and 3-day storm. Use these results to determine the infiltration capacity corresponding to the 21 cm of available storage. If the actual infiltration capacity of the soil is 4 cm/h, estimate the curve numbers that should be used for the 1-day and 3-day storms.

5.42. A proposed 20-ha development includes 5 ha of parking lots, 10 ha of buildings, and 5 ha of grassed area. The runoff from the parking lots and buildings are both routed directly to grassed areas. If the grassed areas contain Type A soil in good condition, estimate the runoff from the site for a 180 mm rainfall event.

5.43. Repeat Problem 5.42 for the case where the runoff from the buildings, specifically the roofs of the buildings, is discharged directly onto the parking lots. Based on this result, what can you infer about the importance of directing roof drains to pervious areas?

557 5.44. Repeat Problem 5.42 using an area-weighted curve number. How would your result change

if the roof drains are directly connected to the parking lot?

5.45. Discuss why it is preferable to route rainfall excesses on composite areas rather than using weighted-average curve numbers.

5.46. Consider a site that is I percent impervious in which the curve number of the impervious area is 98, and the curve number of the pervious area is CNp. If the all of the impervious

area is directly connected to the drainage system, show that the composite curve number of the site, CNc, is given by

CNc= CNp+

I

100(98 − CNp)

5.47. Consider the site described in Problem 5.46, with the exception that only a portion of the impervious area is directly connected to the drainage system. Show that the composite curve number of the site, CNc, is then given by

CNc = CNp+

I

100(98 − CNp)(1 − 0.5R)

where R is the ratio of the unconnected impervious area to the total impervious area. 5.48. A catchment with a grass surface has an average slope of 0.8%, and the distance from the

catchment boundary to the outlet is 80 m. For a 30-min storm with an effective rainfall rate of 70 mm/h, estimate the time of concentration using: (a) the kinematic-wave equation, (b) the NRCS method, (c) the Kirpich equation, (d) the Izzard equation, and (e) the Kerby equation.

5.49. What is the maximum flow distance that should be described by overland flow?

5.50. Find α and m in the kinematic wave model (Equation 5.85) corresponding to: (a) the Manning equation, and (b) the Darcy-Weisbach equation.

5.51. An asphalt pavement drains into a rectangular concrete channel. The catchment surface has an average slope of 1.0%, and the distance from the catchment boundary to the drain is 30 m. The drainage channel is 60 m long, 20 cm wide, 25 cm deep, and has a slope of 0.6%. For an effective rainfall rate of 50 mm/h, the flowrate in the channel is estimated to be 0.02 m3_/s.

Estimate the time of concentration of the catchment.

5.52. The surface of a 2-ha catchment is characterized by a runoff coefficient of 0.5, a Manning n for overland flow of 0.25, an average overland flow length of 60 m, and an average slope of 0.5%. Calculate the time of concentration using the kinematic-wave equation. The drainage channel is to be sized for the peak runoff resulting from a 10-year rainfall event, and the 10-year IDF curve is given by

i = 150 (t + 8.96)0.78

where i is the average rainfall intensity in cm/h and t is the duration in minutes. The minimum time of concentration is 5 minutes. Determine the peak runoff rate.

5.53. A 20-ha townhouse development is to be drained by a single drainage inlet. The average runoff coefficient for the site is estimated to be 0.7, Manning’s n for overland flow is 0.25, the average overland flow length is 100 m, and the average slope of the site towards the inlet is 0.6%. The site is located in an area with an IDF curve given by

i = 1020 (t + 8.7)0.75

where i is the rainfall intensity in mm/h and t is the duration in minutes. What is the peak runoff rate expected at the drainage inlet? If an error of 10% is possible in each of the assumed site parameters, determine which parameter gives the highest peak runoff when the 10% error is included, and which gives the lowest peak runoff when the error is included. Consider that the 10% error occurs simultaneously in all the drainage parameters, what would be the design peak discharge at the inlet?

5.54. Explain why higher runoff coefficients should be used for storms with longer return periods. 5.55. Suppose that the catchment described in Problem 5.52 contains 0.5 ha of impervious area that is directly connected to the storm sewer. If the runoff coefficient of the impervious area is 0.9, the Manning n for overland flow on the impervious surface is 0.035, the average flow length is 30 m, and the average slope is 0.5%, then estimate the peak runoff.

5.56. A 4.2-km2 catchment with 0.5% pond area has a curve number of 79, a time of concentration of 3 h, and a 24-h Type II precipitation of 10 cm. Estimate the peak runoff.

5.57. A 1-km2 catchment with 3% pond area has a curve number of 70, a time of concentration of 1.7 h, and a 24-h Type I precipitation of 13 cm. Estimate the peak runoff.

5.58. A 10-ha single-family residential development in Atlanta is estimated to have a curve number of 70 and a time of concentration of 15 minutes. There are no ponds or swamps on the site, and the 10-year IDF curve is given by

i = 2029 (t + 7.24)0.73

where i is the rainfall intensity in mm/h, and t is the storm duration in minutes. Estimate the peak runoff from the site, and determine the equivalent runoff coefficient that could be used with the rational method to estimate the peak runoff.

5.59. The 15-min unit hydrograph for a 2.1-km2 urban catchment is given by

Time Runoff Time Runoff (min) ( m3_{/s) (min) ( m}3_/s) 0 0 210 0.66 30 1.4 240 0.49 60 3.2 270 0.36 90 1.5 300 0.28 120 1.2 330 0.25 150 1.1 360 0.17 180 1.0 390 0