1. HYDROLOGY Lecture 8 Measurements-2
Assoc.Prof. dr.tarkan erdik

2. 1. Rating Curve
Rating curve shows the stage-discharge relation of a stream cross-section

3. Control section is a cross-section where rating curve is obtained
Control section is a cross-section where rating curve is obtained. Narrow and deep cross sections are preferred.
Power function
Q=K(h-ho)n
Lineer function
Logarithmic scale
Logarithmic scale

4. Rating curve might change due to change of control section
Rating curve might change due to change of control section. Dredging, vegetation, bridge construction and sedimentation are possible reasons. Once or twice a year a check must be made, especially after floods.
Extrapolation must be made at high waters

5. The rating curve equation is given below
The rating curve equation is given below. The red ones in the equation are constants and they are obtained at the control section.
Question: How can we find the constants in red if we measure Q and h at the certain control section?
Reply: we have to logarithmically transform both of the axes

6. Q=K(h-ho)n
Log Q=Log K + n Log(h-ho)
Lets denote Log Q=Y, Log K=a, Log(h-ho)=x
Y=a+nx This is a lineer equation

7. Example: The following measurements are made at the gaging station below
h (m)
0.2
0.3
0.4
0.5
0.6
0.8 1
1.5 2
2.5
Q (m3/s)
6.9
9.9
15.2
22.5 32 66
116
279
486
720

8. n=2.58
Log K =1.7977
K= =63
Q=63(h- -0.2)2.58 =63(h+0.2)2.58

9. Please calculate the discharge if stage is 2.8m
Q=63( )2.58 =1073 m3/s

10. Daily streamflows are plotted versus time to obtain the hydrograph.
24 hour
Time (Hour)
Periodicity is observed

11. Computation of Daily Flows
When stage is measured once, a,b,c represent measurements on the previous day, that day and the next day
When stage is measured twice.
Measurement at 8:00 on the next day
Measurement at 16:00 on that day
Measurement at 16:00 on previous day
Measurement at 8:00 on that day

14. 1.Estimation of Flows at Ungaged Sites
Flows at an ungaged site of a stream are estimated using the data at anoter site on the same stream or on a neighboring stream. In order to do that you have to make an assumption flows are proportional to the drainage areas of the sites. Flood sicharges can be estimated assuming that they are proportional to An, where n<1 (such as n= ).

15. 2. Flow Duration Curve
Flow duration curve is obtained by plotting the flows on the vertical axis, and the percentage of time the flow is equal to or exceeeds a certain value on the horizontal axis
(t1+t2)/T
Percentage of time Q t1 t2
Discharge (m3/s)
Time

16. Discharge that is exceeded
in %25 of time
Discharge that is exceeded
in %50 of time
Discharge that is exceeded
in %90 of time
The discharge in 50% of time can be taken when calculating firm energy of HEPP

17. Example: Please calculate the flow duration curve for the station D02A161 below
AGENCY
STATION
DATE (Month, Day, Year)
STREAMFLOW (m3/s)
DSI
D02A161 76 72 86 80 77
105 75 73 98 60 48 45

18. Percent Exceeded (m/n+1)
Example: Please calculate the flow duration curve for the station D02A161 below
Data should be sorted from largest to smallest
n=total number of data, 15 in this example
AGENCY
STATION
DATE (Month, Day, Year)
STREAMFLOW (m3/s)
Rank (m)
Percent Exceeded (m/n+1)
DSI
D02A161
105 1
6.25% 98 2
12.50% 86 3
18.75% 80 4
25.00% 77 5
31.25% 76 6
37.50% 7
43.75% 75 8
50.00% 9
56.25% 73 10
62.50% 72 11
68.75% 12
75.00% 60 13
81.25% 48 14
87.50% 45 15
93.75%

19. 76 m3/s of discharge is exceeded in 40% of time

20. 2. Flow Mass Curve Total flow volume can be computed as
In practice, total flow volume
Where Qi is the average discharge in the time interval (month, year)

21. Variation of total flow volume in time
What is flow mass curve?
Variation of total flow volume in time
What is the slope of tangent at a certain point?
Discharge
The slope of the line OM is
average discharge
the required storage capacity providing continuosly average flow
The vertical distance between AB and CD is

22. A reservoir should be designed for the constant reservoir release of 2000 ac-ft per month
Points A1, A2, A3, and A4 define the beginning of low-flow periods whereas points B1, B2, B3, and B4 define the end of the low-flow periods.
10 months
20000 AF

23. Please design reservoir with a constant release of 1000 AF/month
Storage capacity 2
20000 AF
Storage capacity 1

24. Q1: Design reservoir capacity by MASS CURVE ANALYSISDt St
(Months)
(106 m3) 1 40 35 2 50 3 60 4 5 25 6 30 7 20 8 13 9 27 10 55 11 76 12 14 15 16 17 18 19

25. Q1: Design reservoir capacity by MASS CURVE ANALYSISDt St
∑(Dt)
∑(St)
(Months)
(106 m3) 1 40 35 2 50 80 85 3 60
120
145 4
160
180 5 25
200
205 6 30
240
235 7 20
280
255 8 13
320
268 9 27
360
295 10 55
400
350 11 76
440
426 12
480
481
520
521 14
560
551 15
600
576 16
640
596 17
680
631 18
720
681 19
760
741