Water Can Jump!!!! Hydraulic Jump Phenomena Bader Anshasi Matthew Costello Alejandra Europa Casanueva Robert Zeller

Introduction Due to excess kinetic energy (Fr>1) Results in "jump" to a higher fluid height Increase in Potential Energy Seen both in nature and industry Rapids, waterfalls Dams, spillways Primary function is to dissipate energy Increased Turbulence Reduce erosion Reduce damage to structures

Examples

Hydraulic Jump Theory

Jump Requirements Occurs during “Rapidly Varied Flow” When flow depth changes rapidly in the direction of flow within a short length Flow changes from supercritical to subcritical condition

Froude’s Number “Rapidly Varied Flow” can be characterized by the Froude’s Number Fr =1 at critical flow 𝐹𝑟= 𝑉 𝑔𝑦 V = velocity, g = gravitational constant, y = depth A hydraulic jump occurs because of Fr changes: Fr1 >1 and Fr2 <1

Phenomena Flow depth increases abruptly with the formation of eddy currents Kinetic energy is converted to potential energy Results in a change of height When eddies downstream of the jump break up, the fluid entraps air The fluid loses energy after a jump Leading to many practical applications

Types of Hydraulic Jumps

No hydraulic Jump Fr<1 𝑦 1 𝑦 0 = 1+8 𝐹𝑟 2 −1 2 𝑦 1 𝑦 0 = 1+8 𝐹𝑟 2 −1 2 Theoretically this would be a negative hydraulic jump, i.e. the fluid depth will decrease Only physically possible if some external force accelerates the fluid at that point

Undular Jump For (1 < Fr1<1.7) Characterized by: Slight undulation Two conjugate depths are close Transition is not abrupt – slightly ruffled water surface

Weak Jump For (1.7<Fr1<2.5) Characterized by: Eddies and rollers are formed on the surface Energy loss is small The ratio of final depth to initial depth is between 2.0 and 3.1

Oscillating Jump For (2.5 <Fr1<4.5) Characterized by: Jet oscillates from top to bottom – generating surface waves that persist beyond the end of the jump Ratio final depth to initial depth is between 3.1 to 5.0 To prevent destructive effects this type of jump should be avoided

Stable Jump For (4.5<Fr1<9) Characterized by: Position of jump fixed regardless of downstream conditions Good dissipation of energy (favored type of jump) Considerable rise in downstream water level Ratio of final to initial depth is between 5.9 and 12.0

Strong or Rough Jump For (Fr1 > 9) Characterized by: Ratio of final to initial depth is over 12 and may exceed 20 Ability of jump to dissipate energy is massive Jump becomes increasingly rough Fr1 should not be allowed to exceed 12

Hydraulic Jump Applications

Practical applications Engineers design hydraulic jumps to reduce damage to structures and the streambed Proper design can result in a 60-70% energy dissipation Minimizes erosion and scouring due to high velocities Dams, weirs and other hydraulic structures

Other Practical Applications Recover pressure head and to raise water levels downstream of a canal Maintain a high water level for irrigation or other water-distribution purposes Mix chemicals in water purification Aerate water for city water supplies Remove air pockets from water to prevent air locking in supply lines

Recreational Applications Traveling down rivers/rapids Kayaking and canoeing: playboat/surf hydraulic jumps

Conclusion An ideal design for energy dissipation would result in a “Stable Jump” Characterized by a 4.5<Fr1<9 Position of jump is fixed Provides the most effective energy dissipation Protects the structures and streambed by reducing velocity Energy dissipation ranges from 45-70%

Demonstration Representing a hydraulic jump in your sink: Shallow fluid A smooth flow pattern forms where the water hits Further away, a sudden hydraulic jump occurs Specific characteristics of this jump: Water flows radially and it continues to grow shallower It slows down due to friction (decrease in Froude number) up to the point where the jump occurs From supercritical to subcritical flow Diameter of the jump decreases as water depth increases.