1. ERT 246 Hydrology & Water Resources Engineering Siti Kamariah Md Sa’at School of Bioprocess Engineering, UniMAP

2. Unit Hydrograph Cont.

5. More Example:  Two storm each of 6-hr duration and having rainfall excess values of 3.0cm and 2.0 cm respectively occur successively. The 2-cm ER rain follows the 3-cm rain. The 6-hr UH for the catchment is the same as given in previous example. Calculate the resulting DRH.

9. Unit Hydrograph of Different Durations  Under condition where lack of adequate data in developement of unit hydrograph  D-hour unit hydrograph is used to develop unit hydrographs of differing durations nD  Two method available: 1.Method of superposition 2.The S-Curve

10. Method of superposition  If a D-h unit hydrograph is available, and its desired to develop unit hydrograph of nD, its is easily accomplished by superposing n unit hydrographs with each graph separated from the previous on by D-h.

11. D = 2-Hr Unit Hydrograph Adjusted Net Rainfall one inch over basin QpQp

12. Change UH Duration Consider 1 hr UH Add and Lag two UH by one hour Sum and divide by 2 Results in 2 hr UH

13. Example  Given the ordinates of a 4-hr unit hydrograph as below derive the ordinates of a 12-hr unit hydrograph for the same catchment Time (hr) 048121620242832364044 Ordinates of 4-hr UH 020801301501309052271550

16. Equilibrium Hydrograph Uniform Rain Inflow = Outflow Equiv to summing n hydrographs in T Produces S curve One Hydrograph

17. S-Curve  Also known as S-hydrograph  Hydrograph produced by continous effective rainfall at a constant rate for infinite period.  Curve obtained by summation of an infinite series of D-h UH spaced D-h apart.

19. S-Curve Construction  Obtained by adding a string of D-h UH each lagged by D-hours from one another.  If Tb= base period of the UH, addition of only Tb/D UH are suffcient to obtained S-curve  U(t) = S(t)-S(t-D) or U(t) = S(t)+S(t-D) Where  S(t-D)= S-curve addition at time t  S(t) = Ordinate of D-h UH at time t

20. S-Curves for UH

21. S-Curves Convert 2 hr Unit hydrograph to 3-hr Lag each 2-hr UH by Duration D Add to produce S-curve S-curve

22. Lag by D’ and subtract both curves Lag S Curves in time, subtract them, and multiply by D/D’

23. 3 hr. Unit Hydrograph from a 2 hr. UH (D/D’) 3 HR UH

24. Example  Solve previous example with S-curve method:

26. Hydrograph Convolution 1 2 3 312 Add up the ordinates of all three to produce storm hydrograph STORM HYDRO Add and Lag Method

27. Multi-PeriodStorm P g - F = Net Rainfall RF units = UH duration (i.e. 1 hour) Adjust UH by Net RF Add and Lag UH Produce Storm Hydrograph UH STORM NET RF

28. Development Effects on UH NaturalPartialFully Developed

29. Synthetic UH Developed for basin that were ungaged Based on data from similar gaged basins Most methods are very similar in nature Revolutionized ability to predict hydro response

30. Synthetic UH Methods Methods to characterize ungaged basins Use data and relationships developed from gages Variety of approaches but most based on T p and Q p England and U.S. led the efforts to standardize UH

31. Synthetic UH Methods Snyder’s Method (1938) Clark Method (1945) Nash (1958) SCS (1964, 1975) Espey-Winslow (1968) Kinematic Wave (1970s)

33. Snyder’s Method  Synder (1938)- based on study of large catchment in eastern US developed a set of empirical equation for synthetic UH.  The equation are use in USA and with some modification in many other countries.

34. Lag time  The most important characteristic of basin due to storm- basin lag (lag time)  Lag time- time difference between the centroid of the input (rainfall excess) and the output (DRH)  Represent time of travel of water from all parts of watershed to the outlet during a given storm.

35. Snyder’s Method 5 to 7 points

36. SCS Method  Dimensionless UH  Based on a study of large number of UH  Developed by US Soil Conservation Services (SCS)

39. SCS Methods Triangular UH Dimensionless UH

40. SCS Triangular UH Example 1 inch of RF over 1.6 hr duration

41. 2-hr Duration UH Example Q p at 400 cfs at 10 hr with 24 hr T b Six Hours of Uniform Rainfall = 0.25 in/hr 1.5 Inches Total Rain 2 4 6 8 10 12 14 16 18 20 22 24 26 30 100 200 300 Time in Hours 400

42. SCS RAINFALL RUNOFF CURVES

43. Unit Hydrograph Applications

44. Land Use 1 Land Use 2 Unit Hydrograph Changes Land Use will alter UH Peak and Timing

45. Kinematic Wave Overland Collector Channels Main Stream Manning’s Eqn

46. Kinematic Wave

47. Basin hydrographs- routed & combined to produce storm hydrograph Basin hydrographs- routed & combined to produce storm hydrograph