CIVE 530 - OPEN-CHANNEL HYDRAULICS

LECTURE 10: THE HYDRAULIC JUMP (CHOW CHAPTER 15)

15.1  THE HYDRAULIC JUMP


  • The theory of the jump developed from nearly horizontal channels, where the effect of gravity is negligible.

  • The results appear to apply to most channels encountered in engineering problems.

  • For channels of large slope, this effect may not be negligible.

  • Practical applications of the jump are:

    • To dissipate energy in water flowing over dams, weirs, and other hydraulic structures, and to prevent scouring downstream from the structures.

    • To recover head or raise the water level on the downstream side of a measuring flume.

    • To increase weight on an apron and thus reduce uplift pressure under a masonry structure.

    • To increase the discharge of a sluice by holding back tailwater, since the effective head will be reduced if the tailwater is allowed to drown the jump.

    • To indicate special flow conditions, such as the existence of supercritical flow.

    • To mix chemical used for water purification.

    • To aerate water for city water supplies.

    • To remove air pockets from water-supply lines and thus, prevent air locking.

15.2  JUMP IN HORIZONTAL RECTANGULAR CHANNELS


  • A hydraulic jump will form in a channel if the upstream flow depth y1, the downstream flow depth y2, and the Froude number of the upstream flow F1 satisfy the equation:

    y2/y1 = (1/2) [(1 + 8F12)1/2 -1]

  • This equation is shown in the following figure:


    Fig. 15-1 (Chow)

15.3  TYPES OF JUMPS


  • Hydraulic jumps can be classified according to the upstream flow Froude number, as follows:

    • F1 = 1-1.7. Undular jump.

    • F1 = 1.7-2.5. Weak jump.

    • F1 = 2.5-4.5. Oscillating jump.

    • F1 = 4.5-9.0. Steady jump.

    • F1 > 9.0. Strong jump.


Fig. 15-2 (Chow)

15.4  BASIC CHARACTERISTICS OF THE JUMP


  • The energy loss in the hydraulic jump is:

    ΔE = E1 - E2 = (y2 - y1)3 / (4y1y2)

  • The relative energy loss is ΔE / E1:

    ΔE / E1 = 1 - (E2/E1)

  • The efficiency is E2 / E1:

    E2 / E1 = [(8F12 + 1)3/2 - 4F12 + 1] / [8F12 (2 + F12)]

  • Thus, the relative energy loss is also a dimensionless function of F1.

  • The height of the jump is:

    hj = y2 - y1

  • The relative height of the jump is:

    hj/E1 = (y2 / E1) - (y1 / E1)

    where y1 / E1 is the relative initial depth, and y2 / E1 is the relative sequent depth.

  • The relative height of the jump can be expressed as a function of F1:

    hj/E1 = [(1+ 8F12)1/2 - 3] / (F12 + 2)

  • Figure 15-3 shows all these jump characteristics as a function of F1.


    Fig. 15-3 (Chow)

  • The following conclusions are drawn:

    • The maximum relative height hj/E1 is 0.507, at F1 = 2.77

    • The maximum relative sequent depth y2/E1 is 0.8, which occurs at F1 = 1.73.

    • Experiments show that the transition from undular to weak jump occurs at this value of F1 (1.73).

    • When F1 = 1, the flow is critical and y1/E1 = y2/E1 = 0.67 = 2/3.

    • When F increases beyond 2, the changes in all characteristic ratios become gradual.

15.5 LENGTH OF JUMP


  • The length of the jump may be defined as the distance measured from the front face of the jump to a point on the surface immediately downstream from the roller.

  • This length cannot be determined easily by theory, but it has been experimentally investigated by many hydraulicians.

  • The experimental data can be plotted as L/y2 vs. F1, as shown in Fig. 15-4.

    Fig. 15-4 (Chow)

15.6 THE SURFACE PROFILE


  • The surface profile of a jump can be represented by dimensionless curves, as shown in Fig. 15-5.


    Fig. 15-5 (Chow)

  • Other measurements have shown that the actual length of the jump may be as much as 20% longer than that shown in Fig. 15-5.

 
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