CVE 372 HYDROMECHANICS EXERCISE PROBLEMS OPEN CHANNEL FLOWS

Transcription

1 CVE 72 HYDROMECHANICS EXERCISE PROBLEMS OPEN CHANNEL FLOWS ) A rectagular irrigatio chael of base width m, is to covey 0.2 m /s discharge at a depth of 0.5 m uder uiform flow coditios. The slope of the chael is a) Fid the chael roughess. b) At the ed of a dry period, it has bee observed that there is a chage i the roughess of the base, such that the same discharge, 0.2 m /s, could be coveyed at a depth of 0.80 m, uder uiform flow coditios. Calculate the base roughess. ( Note that side wall roughess do ot chage.) (a) (b) y = 0.5 m y = 0.8 m b = m =? 2) For a rectagular ope chael the followig iformatio is give: Discharge, Q=25 m /s, cross-sectio width, b = 0 m, Maig roughess coefficiet = 0.025, chael bottom slope S o = Determie: a) Uiform flow depth, y. (For the first iteratio assume y = 0 m) b) State of the flow. c) Resistace to the flow, τ. y b

2 ) Water flows with a velocity of 2 m/s i a rectagular chael m wide at a depth of m. What is the chage i depth ad i water surface elevatio produced by a gradual upward chage i bottom elevatio (upstep) of 60 cm? What would be the depth ad elevatio chages if there were a gradual dowstep of 5 cm? What is the maximum size of upstep that could exist before upstream chages would result? Neglect head losses 4) Two braches of differet sectios ad discharges merge ad cotiue to flow i a mai chael with trapezoidal sectio as show i the figure below. a) Fid the discharge i brach A, b) Fid the discharge i brach B, c) Fid the depth of flow i the mai chael. Brach A A A B C C Mai Chael Brach B B =0.025 S A =0.002 y A =.5 m b=25 m =0.05 =0.025 =0.0 =0.0 y C =? b=0 m S C = =0.0 Sectio A-A. Sectio C-C. =0.02 =0.02 =0.05 y B =.5 m =0.05 =0.05 =0.02 =0.02 m 50 m 0 m 50 m S B =0.006 Sectio B-B. 2

3 5) Water flows i a rectagular ope chael havig a width of 2 m with a flow rate of 0 m /s as show i the figure. If the flow depths before ad after the step are give as y = m, y 2 = 2 m, determie; a) State of flow at upstream ad dow stream sectios. b) Step height z =? c) Draw the specific eergy versus flow depth (E-y) curve ad show the values of y, y 2, y c, E, E 2, ad z o the curve. upstream dowstream y = m Q = 0 m /s y 2 = 2 m y z =? (2) b = 2 m () 6) Water is flowig at a velocity of 4 m/s ad depth of 5 m i a chael of rectagular sectio of 4 m wide. a) At dowstream if there is a smooth expasio i width to 5 m; determie the depth i the expaded sectio. b) Fid the maximum allowable cotractio i the width without ay chokig. c) If the width is cotracted to m, what is the miimum amout by which the bed must be lowered for the upstream flow to be possible as specified? u=4 m/s b =4 m b 2 =5 m y =5 m y 2 =? m

4 7) For the horizotal rectagular chael show what is the miimum specific eergy required for the discharge to be Q = 6 m /s Q=6 m/s b =5 m b 2 = m b =4 m z= m 8) A hydraulic jump is to be formed i a trapezoidal chael width a base width of 6 m ad side slopes of 2H:V. The dowstream depth is 2.4 m ad the discharge is 27 m /s. Fid the upstream depth, the head loss, ad the horsepower dissipated i the jump. 9) Water flows i a rectagular chael of 5 m wide as show i figure below. Calculate a) the force o the step. b) the head loss through the jump q = 5. m /s/m y = 5.56 m y 2 =? y = 4.0 m z=0.5m 0) A hydraulic jump occurs over a sill located i triagular chael with water flowig as show. The iverse side slopes are m = m 2 =, the drag coefficet C D =0.40, ad the height of the sill z = 0. m. Determie the discharge Q if y =0.50 m ad y 2 =.8 m. Note that the force o the sill is give by 2 Fsill = CDρU A sill, where ρ = 000 kg/m, A sill = frotal area of the sill. 2 4

5 Frotal area z = 0. m y =0.5 m z =0. m y =.8 m w =2m () (2) ) Classify the chael bottom slopes ad sketch the possible flow profiles. Assume o eergy loss i the chael. NDL CDL NDL 5

6 2) Water flows at a discharge of 6 m /s i a rectagular chael of 5 m wide. A hydraulic jump forms uder the sluice gate. After the jump, the chael smoothly expads to a width of 6 m. At the expaded sectio, the depth of flow is 4.5 m. Determie a) the cojugate depths of the jump b) water depth before sluice gate c) head loss through the jump d) the force o the walls of the expaded sectio e) the force o the sluice gate y y y 4= 4.5 m y b =5 m b 4 =6 m ) Water flowig at the ormal depth i a rectagular cocrete chael (=0.0) that is 2.0 m wide ecouters a obstructio, as show i the Figure, causig the water level to rise above the ormal depth at the obstructers ad for some distace upstream. The water discharge is 26 m /s ad the chael bottom slope is The depth of water just upstream from the obstructio is 4.55 m. Fid the distace upstream to the poit where the water surface is at the ormal depth. Show the water surface profile o a graph. Q 6

7 4) A trapezoidal mai chael carries 0 m /sec discharge ad it will be built with cocrete liig. If this chael has a slope of ad =0.025, z= fid the sectio dimesios. Miimum allowed velocity is 0.7 m/sec. 5) Desig a ulied trapezoidal caal o a sady soil whose particle size, D, is 0 mm ad is very agular. Take =0.02, z=2, S 0 = The desig discharge is.5 m /sec. 6) A ulied caal is costructed i a slightly rouded coarse ocohesive soil which has a average particle diameter of 20 mm. The caal has z = 2, = 0.02, So = 0.006, b = 2.5 m ad θ = o (agle of repose from Fig. 9). Determie the greatest discharge which ca be coveyed without causig erosio i the caal. Use tractive force approach. 7