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Q1: 1 . \quad \Delta \mathrm{S}=\mathrm{P}-(\mathrm{E}+\mathrm{T}+\mathrm{I}+\mathrm{Q}) \text { 2. } \quad \text { Average precipitation }=\left(\Sigma \mathrm{P}_{\mathrm{i}} \mathrm{A}_{i} / \Sigma \mathrm{A}_{\mathrm{i}}\right) \text { 3. } \quad Q_{p}=C I A \text { 4. } \quad f=f_{\mathrm{c}}+\left(f_{0}-f_{\mathrm{c}}\right) \mathrm{e}^{-\mathrm{kt}} \begin{aligned} &5 \text { . }\\ &F(t)=\int_{0}^{t} f d t=f_{c} t+\left[\frac{f_{0}-f_{c}}{k}\right]\left(1-e^{-k t}\right) \end{aligned} \text { 8. } \quad H=\frac{p}{\gamma}+z+\frac{v^{2}}{2 g} \text { 9. } E=y+\frac{Q^{2}}{2 g A^{2}} \text { 10. } y_{c}=\left(\frac{q^{2}}{g}\right)^{1 / 3} \text { 11. } \frac{Q^{2}}{g}=\left(\frac{A^{3}}{B}\right) \text { 12. } \quad F_{r}=\frac{V}{\sqrt{g D}} \text { 12a. } \quad \frac{y_{2}}{y_{1}}=\frac{\sqrt{1+8 F_{r 1}^{2}}-1}{2} \text { 13. } Q=\frac{C_{n}}{n} A R_{h}^{2 / 3} S_{0}^{1 / 2} \text { 14. Area }=\frac{h}{2}\left[y_{0}+2\left(y_{1}+y_{2}+y_{3}+\ldots \ldots+y_{n-1}\right)+y_{n}\right] \begin{aligned} &15\\ &T_{R}=\frac{D}{2}+t_{p} \end{aligned} \text { 16. } \quad Q_{p}=\frac{484 A}{T_{R}} \text { 17. } \quad t_{p}=\frac{l^{0.8}(S+1)^{0.7}}{1900 y^{0.5}} \text { 18. } \quad S=\frac{1000}{C N}-1 \begin{array}{ll} 19 . & B=1.67 \mathrm{~T}_{\mathrm{R}} \end{array} \text { 20. Snyder's method } \text { 21. } \quad t_{p}=C_{t}\left(L L_{c}\right)^{0.3} \text { 22. } \quad Q p=\frac{640 C_{p} A}{t_{p}} \text { 23. } \quad \mathrm{T}_{\mathrm{b}}=3=\mathrm{t}_{\mathrm{p}} / 8 \text { 24. } \quad I-Q=\frac{\Delta S}{\Delta t} \text { 25. } \quad \frac{I_{1}}{2}+\frac{I_{2}}{2}-\frac{Q_{1}}{2}-\frac{Q_{2}}{2}=\frac{S_{2}-S_{1}}{\Delta t} \text { 26. } \quad S=K[x I+(I-x) Q] \text { 27. } \quad S_{2}-S_{1}=K\left[x\left(I_{2}-I_{1}\right)+(1-x)\left(Q_{2}-Q_{1}\right)\right] \text { 28. } \quad Q_{2}=C_{0} I_{2}+C_{1} I_{1}+C_{2} Q_{1} \text { 29. } \quad C_{0}=\frac{-K x+0.5 \Delta t}{D} \text { 30. } \quad C_{1}=\frac{K x+0.5 \Delta t}{D} \text { 31. } \quad C_{2}=\frac{K-K x-0.5 \Delta t}{D} \text { 32. } D=K-K x+0.5 \Delta t \text { 33. } \quad\left(I_{n}=I_{n+1}\right)+\left(\frac{2 S_{n}}{\Delta t}-Q_{n}\right)=\left(\frac{2 S_{n+1}}{\Delta t}+Q_{n+1}\right) See Answer
Q2: 3. (20 points) Repeat problem 3 for Cairo in January, when the average net radiation is 40 W/m, the air temperature is14°C, the relative humidity is 65%, and the wind speed is2.0 m/s at a height of 2 m.See Answer
Q3: 8- Brutsaert (2005, Fig. 13.12) gives fits of five different probability distributions to maximum annual flood data for a basin in Arizona. What insights about the limitations and strengths of these five different probability models do you get from this plot? Be precise in your answer. See Answer
Q4: 9- Stream flow record lengths are generally short. To estimate exceedance probabilities, it is a common practice to fit frequency functions to annual flood data.Flood quantiles are computed from the fits of frequencies to different gauging stations in a homogeneous region on which regional quantile regressions are done.Obtain an empirical cumulative frequency function for the maximum annual flood date given below (Q in cfs) using (i) Weibull plotting position formula. (ii) Fit a log-Pearson type III distribution to this data. Show your calculations clearly (Seehttps://streamflow.engr.oregonstate.edu/analysis/floodfreq/index.htmhttps://streamflow.engr.oregonstate.edu/analysis/floodfreq/meandaily_example.htandmas a guide for your calculations) (iii) Calculate flood quantiles with 25 period and 125 yr return period from the two methods, and briefly discuss your reasons for differences/similarities in the computed values. See Answer
Q5: \text { 1. } \quad \Delta S=P-(E+T+I+Q) \text { 2. Average precipitation }=\left(\Sigma P_{i} A_{i} / \Sigma A_{i}\right) \text { 3. } \quad Q_{p}=C I A \text { 4. } f=f_{c}+\left(f_{0}-f_{c}\right) e^{-k t} F(t)=\int_{0}^{t} f d t=f_{c} t+\left[\frac{f_{0}-f_{c}}{k}\right]\left(1-e^{-k t}\right) \text { 8. } \quad H=\frac{p}{\gamma}+z+\frac{v^{2}}{2 g} \text { 9. } E=y+\frac{Q^{2}}{2 g A^{2}} \text { 10. } y_{c}=\left(\frac{q^{2}}{g}\right)^{1 / 3} \text { 11. } \frac{Q^{2}}{g}=\left(\frac{A^{3}}{B}\right) \text { 12. } \quad F_{r}=\frac{V}{\sqrt{g D}} \text { 12a. } \quad \frac{y_{2}}{y_{1}}=\frac{\sqrt{1+8 F_{r 1}^{2}}-1}{2} \text { 13. } Q=\frac{C_{n}}{n} A R_{h}^{2 / 3} S_{0}^{1 / 2} \text { 14. Area }=\frac{k}{2}\left[y_{0}+2\left(y_{1}+y_{2}+y_{3}+\ldots \ldots+y_{n-1}\right)+y_{n}\right] \text { 15. } \quad T_{R}=\frac{D}{2}+t_{p} \text { 16. } \quad Q_{p}=\frac{484 A}{T_{R}} \text { 17. } \quad t_{p}=\frac{l^{0.8}(S+1)^{0.7}}{1900 y^{0.5}} \text { 18. } \quad S=\frac{1000}{C N}-1 \text { 19. } \quad B=1.67 \mathrm{~T}_{\mathrm{R}} \text { 20. Snyder's method } \text { 21. } \quad t_{p}=C_{t}\left(L L_{c}\right)^{0.3} \text { 22. } \quad Q p=\frac{640 C_{p} A}{t_{p}} \text { 23. } \quad \mathrm{T}_{\mathrm{b}}=3=\mathrm{t}_{\mathrm{p}} / 8 \text { 24. } \quad I-Q=\frac{\Delta S}{\Delta t} \text { 25. } \frac{I_{1}}{2}+\frac{I_{2}}{2}-\frac{Q_{1}}{2}-\frac{Q_{2}}{2}=\frac{S_{2}-S_{1}}{\Delta t} \text { 26. } \quad S=K[x I+(I-x) Q] \text { 27. } \quad S_{2}-S_{1}=K\left[x\left(I_{2}-I_{1}\right)+(1-x)\left(Q_{2}-Q_{1}\right)\right] \text { 28. } \quad Q_{2}=C_{0} I_{2}+C_{1} I_{1}+C_{2} Q_{1} \text { 29. } \quad C_{0}=\frac{-K x+0.5 \Delta t}{D} \text { 30. } \quad C_{1}=\frac{K x+0.5 \Delta t}{D} \text { 31. } \quad C_{2}=\frac{K-K x-0.5 \Delta t}{D} \text { 32. } D=K-K x+0.5 \Delta t \text { 33. } \quad\left(I_{n}=I_{n+1}\right)+\left(\frac{2 S_{n}}{\Delta t}-Q_{n}\right)=\left(\frac{2 S_{n+1}}{\Delta t}+Q_{n+1}\right) See Answer
Q6: 5- The initial rate of infiltration for a watershed is estimated as 2.1 in/hr, the final capacity is 0.2in/hr, and the time constant, k, is 0.4 hr1. Use Horton's Equation to find: (A) The infiltration capacity at t = 2 hr and t = 6 hr. (4 pts) (B) The total volume of infiltration over the 6-hr period. (4 pts)See Answer
Q7: Determine: The discharge rate in a 1.52-m reinforced concrete pipe (RCP) (n = 0.013) on a slope of 0.005 flowing full. The discharge rate if the water depth is 0.91 m. Compute the water depth for discharge rate of 1.70 m³/s.See Answer
Q8: 1- Given an initial infiltration capacity fo of 3 in/hr and a time constant k of 0.29 hr^-1,use the Horton infiltration equation to compute the infiltration capacity as a function of time, fp(t), if the asymptotic infiltration capacity fe is 0.55 in/hr. For the first 10 hours, estimate the total potential volume of water infiltrated in inches.See Answer
Q9: A fully penetrating well with a diameter of 20 in penetrates an unconfined aquifer that is120 ft. thick. Two observation wells are located at 100 ft and 230 ft. from the well, and the measured draw downs are 22.0 ft. and 20 ft., respectively. Flow is steady and hydraulic conductivity is 1200 gal/d/ft. What is the steady sate rate of discharge from the well?See Answer
Q10: 3- The mean monthly temperature in °C from January to December in a year are 16.6,18.5, 23.3, 27.6, 28.4, 25.8, 24.4, 23.8, 23.5, 23.6, 20.2, 17.1. Calculate the annual potential evapotranspiration using the Thornthwaite Equation. Why we should adjust the PET calculated by the Thornthwaite Equation?See Answer
Q11: 7. An undeveloped watershed area of 1873 acres received 1.43 inches of rainfall from 10:00am to 10:30 am on January 25. The rain ended at 10:30 am. The interception loss was estimated to be 0.17 inches and the depression storage losses 0.06 inches. Soil data for infiltration is: fo = 0.51 in/hr; fc = 0.10 in/hr; k = 0.30/hr. The soil is dry at the start. (15 pts) A) Determine the direct runoff from the rainstorm in inches B) Determine the direct runoff from the watershed in acre-ftSee Answer
Q12: Problem 5.4. The figure shown below illustrates a basin with an established set of precipitation gages in the region. The annual observed precipitation for each gage is listed in the following table. a) Compute the areal average annual precipitation using arithmetic average approach.an b) Compute the areal average annual precipitation using a Thiessen polygon approach by constructing the polygons by hand and "counting squares" for each polygon area. Make sure to be very precise in the construction of the polygons.Consider only the area inside the basin for the weights. c) Calculate the percent difference between the two estimates. d) Discuss the difference in the two annual averages you find for the watershed. Which method do you think provides the most representative mean areal precipitation estimate over the basin? Why? So which method should generally be employed for estimating mean areal precipitation?See Answer
Q13: The rain gages in the urban watershed below, which has a basin areaof 28 km2, measure the following cumulative precipitation during a 1-hour storm event: The basin is in an arid environment where there is no baseflow. Themeasured hydrograph at the stream outlet resulting from the storm ismeasured to be: a) Compute the mean areal rainfall during the storm (in units of cm)using the Theissen polygon method. Note: You can simply re-usethe areal weights calculated previously. b) Using the trapezoidal method for integration, what is the totalstormflow runoff (in units of cm) for the storm? Plot the hydrograph. c) Generate the 1-hr unit hydrograph (i.e. corresponding to 1 cm ofrunoff) for this basin based on the hydrograph shown above and youranswer to part b). Your answer should be in the form of a tabulatedhydrograph (time and flow) and should have units of m3s-1/cm. d) Using your unit hydrograph and the superposition principleconstruct the predicted hydrograph for a 3 hour storm with aeffective cumulative precipitation (i.e. stormflow runoff) of 9 mm. Plothe predicted hydrograph. What is the predicted peak flow for thistorm and the time-to-peak?See Answer
Q14: Refer to the previous question. Is there a HEC-RAS model available to download for location of the Erickson Alumni Center?See Answer
Q15: 9.31. Estimate the maximum amount of rainfall that can be expected in 1 h.See Answer
Q16: 1. (40 points) Given the following inflow and outflow hydrographs, use the Muskingum method with a nonlinear regression to estimate the values of K and X by minimizing the total mean squared error as shown in class. Plot: a) the inflow using a dashed line, b) the observed outflow using square hollow markers with no line, and c) the simulated outflow using a solid line on a single chart in MS Excel. Include a legend. See Answer
Q17: 9.32. Maximum precipitation amounts can be estimated using Equation 9.42D, and observed precipitation maxima are listed in Table 9.6Compare the predictions given by Equation 9.42D with the observations in Table 9.6 D.See Answer
Q18: 9.21. Using the NRCS method for constructing the cumulative rainfall distribution, compare the normalized 24-h rainfall distributions (i.e.,P/P24) given by each of the three sources of data in Problem 9.9.See Answer
Q19: 02Take the outflow hydrograph you have just calculated as the inflow for the reachimmediately downstream. Using the Muskingum method, calculate the outflow for thereach. The first stage of your calculations requires you to use the following data,recorded previously in the reach as another storm event passed through. Note that theflow in the reach downstream of the reservoir includes a compensation flow of 1m³/s,which is provided continuously through a low-level outlet in the dam (i.e. not over thespillway). Your calculations should also include this. You may assume that this outflowhas no impact on the water surface elevation. See Answer
Q20:Problme 4: For the rainfall event shown below, find the runoff/rainfall excess (a) in the first and fourth intervals, (b) at the end of the rainfall event, and (c) in every interval. The soil in the area is dry. It is an agriculture land, Meadow/Woods; the hydrologic soil group is C and is in Poor condition. See Answer

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