V.T. Chow, Open Channel Hydraulics, 1959 problem 9-8. for each reach computed in file below and placed here. = 5.436' yc = 2.688'

Transcription

1 V.T. Chow, Ope Chael Hydraulics, 959 problem 9-8 y c ad y for each reach computed i file below ad placed here WSE =47.0' 7.0' 70.0' y =.86' yc =.688' So =.0 y = 5.46' yc =.688' So =.0004 y =.70' yc =.688' So =.007 dowstream WSE = ',500',000' The rectagular chael above is 0 wide ad cosists of three reaches of differet slopes. The chael has a roughess coefficiet =.05 ad carries a discharge of 500 cfs. Determie: a. ormal ad critical depth for each reach b. water surface profile - must be doe usig hec-ras. c. Plot the etire water surface profile to some cosistet scale last save 0/7/00 / 0:40 AM / 5 0//00 / 8:7 AM

2 Determie the elevatio every 00' alog the structure. Begi with most upstream sectio SECTION : S o :=.0 S o :=.0 D := S o 00 D = Elev := 70 dist := 0, elev ( dist) := Elev S o dist elevatio at upper ed of reach = 70' elev ( 500 ) = 65 bottom elevatio at the lower ed of the uppermost reach Eve though the discharge is give as 500 cfs we will determie the discharge from the specific eergy behid the sluice gate E 0 := 4 Required specific eergy across sluice gate, assumig o losses y := water depth exitig from sluice gate b := 0 chael width Q := 500 sec Compute ormal depth i the uppermost reach of the chael S f :=.0, :=.05, iitial guess for y: y :=.5 Q.49 ( y b) = ( y b) S f Maigs equatio y + b solve for the ormal depth usig the root fuctio ormal_depth := rootq.49 ( y b) ( y b) ( y) + b S f, y ormal_depth =.86 - ormal depth o uppermost reach last save 0/7/00 / 0:40 AM / 5 0//00 / 8:7 AM

3 Now compute the critical depth for the etire system. This is idepedet of slope ad will be costat throughout system: Q y c b g y c = Froude umber ( ) Q g b y c := b y c =.688 critical depth, Fr =.0 g This depth combied with the ormal depth, computed earlier, tells us that the flow issueig from the sluice gate is i the supercritical rage. This meas there will ot be a critical sectio at the upstream ed of the system because the flow depth issueig from the sluice gate is already less tha critical ad will drop eve further as it moves dow reach. The appropriate upstream boudary coditio is the the kow water surface elevatio, 7' ad we will have a mixed water surface profile. SECTION S o :=.0004 Elevo := 65 D 004 := S o 00 D 004 = 0.04 dist := 0, elevatio at uppered of reach : elev ( 500 ) = 65 elev ( dist) := Elevo S o dist elev ( 500 ) = elevatio at lower ed of reach ormal_depth := rootq.49 ( y b) ormal_depth ( y b) ( y) + b = 5.46 > y c therefore flow subcritical S o, y Based o this we surmise that a hydraulic jump must occur somewhere o reach or. last save 0/7/00 / 0:40 AM / 5 0//00 / 8:7 AM

4 SECTION S o :=.007 Elevatio at upper ed of reach Elevo := 64.4 dist := 0, S o 00 = 0.7 elev ( dist) := Elevo S o dist Elevatio at lower ed of reach elev ( 000 ) = 6.9 y := 8 Q = 500 sec ormal_depth := rootq.49 ( y b) ( y b) ( y) + b S o, y ormal_depth =.70 ote that this is quite close to the critical depth of y c =.688 Thus, the water surface elevatio assumig ormal depth at the lower ed of the reach will be = 6.9 ormal_depth =.70 > y c =.688 therefore ormal depth flow regime will be subcritical However, the problem poits out that the depth at the lower ed of the profile is 66'. Thus we have a M- profile extedig back from this kow elevatio. Note: Flow ever reaches uiform coditios o reach for Q = 500 cfs. the reach is too short. Flow approaches critical depth o reach but stays just above it as it trasitios to a M- profile. last save 0/7/00 / 0:40 AM 4 / 5 0//00 / 8:7 AM

5 HEC - RAS water surface profile 500 cfs Problem 9-8 Chow 74 Leged 7 70 M- profile hydraulic jump WS 500 cfs Crit 500 cfs Groud Elevatio () M- profile y = 5.46' reach y =.70' reach y =.86' reach S- profile 64 y c =.688' Mai Chael Distace () last save 0/7/00 / 0:40 AM 5 / 5 0//00 / 8:7 AM