Homework # 3 (6 pages!) Introduction to Hydrogeology (GEO 346C), Spring 2010 Due: 2/19/2010 (5 pm) Instructor: Bayani Cardenas, cardenas@jsg.utexas.edu, EPS 3.160 TA: Travis Swanson, tswanson@mail.utexas.edu, John Nowinski, jnowinski@mail.utexas.edu EPS 3.102D Please show all work on a separate sheet of paper, Box answers and use reasonable significant figures. 1. (5 pts) Analysis of baseflow recession curves from a drainage basin has yielded a recession constant of 1.42x10-2 day -1 when discharge is in cubic feet and time is in days. (A) If recession begins with a discharge of 420 ft 3 /s and t is in days, what will be the flow after 30 and 70 d? (B) If recession begins with a discharge of 2300 ft 3 /s, what will be the flow in 5 d? 2. (5 pts) The flow of a river at the start of baseflow recession was 27 m 3 /s; after 7 d the flow declined to 6.5 m 3 /s. (A) What is the recession constant? (B) What would be the flow after 16 d? 3. (5 pts) Assume that the hydrograph in Figure 2.15 (in Fetter) has a drainage basin area of 700 mi 2. How long will overland flow continue after the flood peak passes [answer in days]? 4. (5 pts) A V-notch weir is placed in a road culvert to measure flow of a stream passing through the culvert. The value of H is 2.72 ft. Compute the discharge of the stream [answer in ft 3 ]. 5. (5 pts) The V-notch weir is replaced with a rectangular weir. If we want the backwater height H to remain the same under the same discharge conditions, what should be the length of the notch (L) [answer in ft]? 6. (5 pts) A university with flat-roofed buildings, numerous parking lots, and little open area has a drainage basin area of 37 ac. This university area is adjacent to a creepy old cemetery with an area of 45 ac. The 25-year rainfall event (the amount that would on average occur once in 25 years) has a precipitation intensity of 1.6 inches/hour. Assuming that most of the overland flow converges to one ditch, calculate the peak discharge for the ditch [answer in m 3 ]. 1
7. (5 pts) A winding natural stream with weeds has an average depth of 0.75 m and is 15 m across. The stream channel drops 0.25 m/ km. What is the stream s average flow velocity? 8. (10 pts) The table below shows measured stage or gage height and discharge measured at the same times for the Rio Not-so-Grande. Develop a rating curve for this river using MS Excel. Plot the gage height on the x-axis and the discharge as the dependent variable. Use the trendline tool in MS Excel to fit a function through the data. To do this, bring the mouse pointer/ arrow above any of the points on the plot and then do a right-click (sorry Mac users, I ve never tried this on a Mac and I m still trying to figure out the equivalent of right-click). Scroll down along the menu that appears and click on Add Trendline. You now have six functions to choose from that Excel can fit to the data. But before you choose one, click on the Options tab. Check the boxes for Display equation on chart and Diplay R-squared value on chart. The R 2 is a parameter that tells you how good the fitted equation is. The closer it is to 1, the better. Go back to the Type tab and pick the function you want to fit and then click OK. Try it for the different functions until you get the largest R 2. For each new function, you may have to recheck the boxes in Options. After you have chosen the best function that describes the stage-discharge relationship, delete the other ones. Turn in the final plot with the data points and the fitted function. Using this function (y=f(x)), you can now calculate the discharge (y) just by knowing stage (x). Compute the discharge if the gage height is 2.52 ft. gage height (ft) Q (ft 3 /s) gage height (ft) Q (ft 3 /s) 0.38 19.94 1.63 99.15 0.60 27.26 1.80 120.00 0.79 23.93 1.79 123.86 0.89 36.53 1.86 132.11 0.97 28.33 1.84 140.33 1.05 33.68 2.04 194.56 1.05 48.19 2.27 246.39 1.14 39.99 2.40 255.62 1.16 54.51 2.55 305.48 1.19 43.87 2.51 310.80 1.31 54.55 2.68 382.44 1.33 71.00 2.78 407.14 1.37 62.79 2.92 532.96 1.43 70.07 2.91 458.94 1.47 93.78 2.96 583.76 1.55 81.22 3.00 656.34 1.60 90.43 2
9. (10 pts) The figure below shows the hydrograph of a stream, which is partially fed by baseflow, with several precipitation events. Compute the ground-water recharge that occurs between the first and second precipitation events. 3
10. (10 pts) The figure below is the hydrograph of a river with a long summer baseflow recession. Compute the volume of annual recharge that occurs between runoff year 1 and runoff year 2. 4
11. (15 pts) The annual minimum and maximum discharge of the Alibangbang River for the period 1900 to 1977 is given in the Table below. Your task is to make recommendations to water resource managers on two problems: A) The Alibangbang 3-eyed shiner is an endanger fish living in the river. The fish population will drop to very dangerous levels or even disappear if the flow in the river drops below 2 m 3 /s. What are the odds of this happening, i.e., what is the percent chance or probability that the discharge will drop below this critical level? On average, what is the interval in years between two of these discharge events occurring in the Alibangbang River? B) There is an important grass species that grows only along the floodplains of the Alibangbang River; it is the main food of the endangered Vacca foeda. The grass in the flooplains get wiped out when the floods in the Alibangbang River exceeds 2500 m 3 /s. What are the chances of this flood occurring and what is the recurrence interval for a flood of such magnitude? There are outliers in both the minimum and maximum discharge data. In your analysis, do not consider the 3 largest values of the min Q data and the 2 largest values in the max Q data. Turn in your plots for P and R generated in MS Excel. Ask Bayani, Travis or John for help with the spreadsheet work if you can t figure things out. Year Min. Q Max. Q Year Min. Q Max. Q Year Min. Q Max. Q 1900 7.3 2991 1926 5 553 1952 2.3 100 1901 4.5 310 1927 3.2 408 1953 2 414 1902 5.8 936 1928 3.9 464 1954 3 27392 1903 5 363 1929 3.8 176 1955 2.8 758 1904 3 2013 1930 2.7 785 1956 2.1 208 1905 14.2 1314 1931 5.1 240 1957 3.3 1073 1906 11.6 2516 1932 5.3 324 1958 3.6 1075 1907 5 327 1933 6.7 126 1959 3.9 1328 1908 5.9 1901 1934 3.8 229 1960 2.9 134 1909 4.2 727 1935 3.6 2359 1961 2.4 411 1910 4.3 2851 1936 4.9 559 1962 1.7 503 1911 5.3 755 1937 5 78 1963 2.2 88 1912 3.4 512 1938 5.3 881 1964 1.8 1037 1913 3.8 1761 1939 3.9 162 1965 2.9 436 1914 6.4 1873 1940 4.6 157 1966 2.9 433 1915 10.2 1453 1941 5.7 523 1967 2.6 60 1916 5.7 2711 1942 7.4 264 1968 2.6 626 1917 4.1 176 1943 5.4 313 1969 2.3 172 1918 2.9 1448 1944 4.4 250 1970 1.7 62 1919 3.5 243 1945 3.9 774 1971 2 2490 1920 6.3 1219 1946 4.2 1817 1972 3.3 123 1921 7.4 517 1947 4.2 171 1973 2.4 93 1922 6.2 2152 1948 3.1 1434 1974 1.6 16128 1923 4.2 358 1949 4 2753 1975 6 274 1924 3.6 1816 1950 2.8 1255 1976 3.9 1660 1925 3.8 1705 1951 2.6 229 1977 4.5 170 5
Bonus (5pts extra credit): Every homeowner in Hyde Park, Austin, TX saw the movie An Inconvenient Truth. After viewing, everyone installed Green roofs on their homes which have a runoff coefficient of 0.20. The roofing material that they replaced had an average coefficient of 0.95. For a given rainfall event and a single property, what would be the percent (%) change in peak runoff discharge? 6