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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:**1. (15 points) Water requirements to bring the level to the fixed from a Class A pan and rainfall observations for a monitoring station are as follows: Estimate the evaporation for each day.а. b. If the pan coefficient is 0.70, estimate the lake evaporation in inches and acre-feet for a nearby reservoir with a surface area of 250 acres.See Answer**Q3:**2. (15 points) For Cairo, Egypt in July, the average net radiation is 185 W/m2, the air temperature is 28.5°C, the relative humidity is 55%, and the wind speed is 2.7 m/s at a height of 2 m. Calculate the open water evaporation rate in mm/day using the energy method (E,), the aerodynamic method (E), and the combined method.See Answer**Q4:**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**Q5:**4. (20 points) Glacier melting forms an important water resource for some parts of the world. Estimate the maximum annual yield of water in acre-feet from a 1 mi?surface area glacier in Nepal (latitude of 30° N) across a year, assuming clear skies (i.e., using R values from Table4.4 in the notes) and that the glacier surface has properties typical of old snow.See Answer**Q6:**5. (20 points) If the average temperature on a day in June was25°C at a humid location with a latitude of 40° N, and the measured solar radiation was R, = 23 MJ/m?/day, calculate the net radiation for a field with an albedo of 0.23.See Answer**Q7:**6. (20 points) Estimate the reference evapotranspiration in mm/day using the FAO Penman-Monteith Equation for a location where the net radiation was 20 MJ/m2/day, the mean temperature was 28°C, the dew point was 21°C, and the mean wind speed at a height of 10 m was 1.5 m/s. FAO suggests using the following formula to estimate the wind speed at 2 m based on measurement at a different height z(m):See Answer**Q8:**\text { 3. } \quad Q_{p}=C i ASee Answer**Q9:**\begin{aligned} &5\\ &T=\frac{1}{P} \end{aligned}See Answer**Q10:**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**Q11:**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**Q12:**7- Using the total direct runoff hydrograph given below, derive a unit hydrograph for the 1715-ac drainage area. See Answer**Q13:**3- (A) The mean annual precipitation (P) is 700 mm. The mean annual potential evapo-transpiration(PET) is 200 mm. Estimate total runoff, runoff coefficient and actual evaporation. (4 pts) (B) Now, assuming the size of the watershed storage equal to 400 mm, and assuming that rainfall and ET occurs at different times, with rainfall preceding ET; estimate the total runoff and actual evapo-transpiration. (3 pts) (C) Now, assuming the size of the watershed storage equal to 100 mm, and assuming that rainfall and ET occurs at different times, with rainfall preceding ET; estimate the total runoff and actual evapo-transpiration. (3 pts)See Answer**Q14:**\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**Q15:**6.19. A 6-ac basin is to be developed into 2 ac of commercial development(C 0,95) and 4 ac of park (C 0.2), as sketched in Figure P6-19 . Using the tabulated IDF information, what should be the design flow at the inlet? See Answer**Q16:**Q=2 \pi K b \frac{h_{2}-h_{1}}{\ln \left(r_{2} / r_{1}\right)}See Answer**Q17:**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**Q18:**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**Q19:**Calculate the plotting position of the following maxima flows in m/s: 150, 310, 280, 160, 480, 550, 600, 225 See Answer**Q20:**\text { 4. } f=f_{\mathrm{c}}+\left(f_{0}-f_{\mathrm{c}}\right) \mathrm{e}^{-\mathrm{k}}See Answer

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