Manning formula and resistance to the flow 07122020

Manning formula and resistance to the flow 07/12/2020 Dr. Jean A. Cunge 1

Manning formula and resistance to the flow • 07/12/2020 Dr. Jean A. Cunge 2

Manning formula and resistance to the flow • 07/12/2020 Dr. Jean A. Cunge 3

Manning formula and resistance to the flow • 07/12/2020 Dr. Jean A. Cunge 4

Manning formula and resistance to the flow • 07/12/2020 Dr. Jean A. Cunge 5

Manning formula and resistance to the flow • 07/12/2020 Dr. Jean A. Cunge 6

Manning formula and resistance to the flow observed n= 0. 043 k=23 d= 1. 12 m 07/12/2020 Dr. Jean A. Cunge 7

Manning formula and resistance to the flow observed n= 0. 043 k=23 d= 1. 12 m 07/12/2020 Dr. Jean A. Cunge 8

Manning formula and resistance to the flow • 07/12/2020 Dr. Jean A. Cunge 9

Manning formula and resistance to the flow observed n= 0. 073 k=14 d= 25 m 07/12/2020 Dr. Jean A. Cunge 10

Manning formula and resistance to the flow • 07/12/2020 Dr. Jean A. Cunge 11

Manning formula and resistance to the flow observed n= 0. 024 k=42 d= 0. 032 m 07/12/2020 Dr. Jean A. Cunge 12

Manning formula and resistance to the flow INFLUENCE OF THE RIVER BANKS! VEGETATION => INCREASE OF TURBULENCE AND RESISTANCE WHAT ABOUT WINTER WHEN VEGETATION IS NOT THERE? NOT THE SAME VALUE FOR n !!!!! 07/12/2020 Dr. Jean A. Cunge 13

Manning formula and resistance to the flow The conclusions are that • Strickler formula for the value of the coefficient is limited • Manning coefficient cannot be defined but from measurements or guessed by experienced • Hydraulic radius concept is important for compact cross-sections (banks!) 07/12/2020 Dr. Jean A. Cunge 14

Manning formula and resistance to the flow USING GLOBAL HYDRAULIC RADIUS CONSIDER A CASE OF COMPLEX CROSS-SECTION: 07/12/2020 Dr. Jean A. Cunge 15

Manning formula and resistance to the flow y Complex cross-section. If calibration done for the elevation y = h, Can Manning -Strickler coefficient thus obtained be extrapolated to higher flows? 07/12/2020 Dr. Jean A. Cunge 16

Manning formula and resistance to the flow USING GLOBAL HYDRAULIC RADIUS FIRST CASE: (i) kstr = const FOR THE WHOLE SECTION AND CONVEYANCE K COMPUTED IN FUNCTION OF THE STAGE 07/12/2020 Dr. Jean A. Cunge 17

Manning formula and resistance to the flow Suppose constant value everywhere kstr = 35 y m 5. 0 If the flood peak is at y=5. 00 m just above another widening of the cross-section can conveyance K be extrapolated? ? 4. 0 3. 0 y= 1. 00 m y = 1. 05 m y = 3. 00 m y= 3. 05 m y = 4. 00 m 2. 0 1. 0 5000 07/12/2020 10000 Dr. Jean A. Cunge K= 657 K= 415 K= 8090 K = 5166 K = 14473 15000 K cusec 18

Manning formula and resistance to the flow USING GLOBAL HYDRAULIC RADIUS SECOND CASE: (ii) CONVEYANCE IS K KNOWN (COMPUTED AS A SUM OF CONVEYANCES CALCULATED SLICE BY SLICE) AND then global kstr IS COMPUTED 07/12/2020 Dr. Jean A. Cunge 19

Manning formula and resistance to the flow depth kstr Conveyance K=f(y) Strickler coefficient computed from conveyance kstr = K/(A R 2/3) where A and R are global for the cross-section 07/12/2020 Dr. Jean A. Cunge 20

Manning formula and resistance to the flow The conclusion: • Strickler or Manning formulas using global hydraulic radius are valid only for compact cross-sections • If modelling software uses global hydraulic radius calibration values cannot be extrapolated to higher stages. • Hydraulic radius concept is valid only for compact cross-sections (banks!) 07/12/2020 Dr. Jean A. Cunge 21

Manning formula and resistance to the flow References Manning, R. , « Flowof Water in Open Channels and Pipes » , Transactions of the Institution of Civil Engineers of Ireland, Vol. 20, 1890. Strickler, A. , « Beiträge zur Frage der Geschwindigkeitsformel und der Rauhigkeitszahlen für Ströme, Kanäle und geschlossene Leitungen » . Eidg. Wasserwirtschaftsamt Bern, Mitteilung 1923, S. B. , 83, N° 23 (1924) 07/12/2020 Dr. Jean A. Cunge 22