E4 Questions on Gradually varied flow: Flow Transitions.

  1. E4.1

    A wide channel consists of two long reaches. The upstream reach has a bed slope of 1 in 100 and the downstream reach has a bed slope of 1 in 1500. The Chezy C for both lengths can be assumed constant and equal to 45. Determine the profile that occurs when the flow per unit width is 7.5m3/s/m7.5m^{3}/s/m and determine whether a hydraulic jump occurs and if one occurs which reach of the channel it occurs.
    (Answers: yn1=1.406my_{n1}=1.406m, yn2=3.467my_{n2}=3.467m, yc=1.79my_{c}=1.79m. Jump in reach 1.)

  2. E4.2

    A long wide channel consists of an upstream section with a bed slope of 0.025 and a downstream section with a bed slope of 0.0002. The Chezy C is constant for the whole of the channel and equal to 40 in SI units. When the discharge in the channel is 3m3/s/m3m^{3}/s/m. width demonstrates that a hydraulic jump occurs. Determine in which reach of the channel the jump occurs. Complete your answer with a free-hand sketch of the final profile and label each of the gradually varied profiles.
    (Answer: yn1=0.609my_{n1}=0.609m, yn2=3.041my_{n2}=3.041m, yc=0.972my_{c}=0.972m, yn1conjugate=1.459my_{n1\;conjugate}=1.459m, yn1conjugate=0.187my_{n1\;conjugate}=0.187m )

  3. E4.3

    A wide channel has three reaches each with a different slope. Each can be considered to be long and at the downstream end of the three reaches there is a free outfall. For a specific case, the Chézy C value for all reaches is 32 and the flow per unit width is 1m3/s/m1m^{3}/s/m. The upstream reach has a slope of 1-in-500, the middle reach has a slope of 1-in-50 and the downstream reach has a slope of 1-in-2,000. Determine which flow profile occurs.
    (Answer: yn1=0.787my_{n1}=0.787m, yn2=0.366my_{n2}=0.366m, yn3=1.250my_{n3}=1.250m, yc=0.467my_{c}=0.467m, yn2conjugate=0.586my_{n2\;conjugate}=0.586m, yn3conjugate=0.119my_{n3\;conjugate}=0.119m )

  4. E4.4

    A wide channel has two reaches with different bed slopes changing from so=0.01s_{o}=0.01 to So=0.0005S_{o}=0.0005. Both reaches have the same cross-section shape and bed roughness of n=0.03n=0.03. Sketch the critical flow depth ycy_{c} line, uniform flow depth yny_{n} lines, and water surface profile in the channel and identify the type of water surface profile, if the flow discharge per unit width is q=0.8m3/s/mq=0.8m^{3}/s/m.
    (Answer: yn1=0.425my_{n1}=0.425m, yn2=1.043my_{n2}=1.043m, yc=0.403my_{c}=0.403m, M1 profile )

  5. E4.5

    A wide channel consists of three long reaches. The upstream reach has a bed slope of 1 in 500, the middle reach a slope of 1 in 50, and the downstream reach slope of 1 in 1,750. The Chezy C for all three lengths can be assumed constant and equal to 27. Determine the profiles that occur if the flow per unit width is 0.75m3/s/m0.75m^{3}/s/m.
    (Answer: yn1=0.728my_{n1}=0.728m, yn2=0.338my_{n2}=0.338m, yn3=1.105my_{n3}=1.105m, yc=0.386my_{c}=0.386m, yn2conjugate=0.438my_{n2\;conjugate}=0.438m, yn3conjugate=0.087my_{n3\;conjugate}=0.087m. Jump in reach 2 (middle). )