water can jump!!!! hydraulic jump phenomena

Water Can Jump!!!!Hydraulic Jump Phenomena

Bader AnshasiMatthew Costello

Alejandra Europa CasanuevaRobert Zeller

IntroductionDue to excess kinetic energy (Fr>1)

Results in "jump" to a higher fluid heightIncrease in Potential EnergySeen both in nature and industry

Rapids, waterfallsDams, spillways

Primary function is to dissipate energyIncreased Turbulence

Reduce erosionReduce damage to structures

Examples

Hydraulic JumpTheory

Jump RequirementsOccurs 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 NumberFr =1 at critical flow

V = velocity, g = gravitational constant, y = depth

A hydraulic jump occurs because of Fr changes:

Fr1 >1 and Fr2 <1

PhenomenaFlow depth increases abruptly with the

formation of eddy currentsKinetic energy is converted to potential energy

Results in a change of height When eddies downstream of the jump break

up, the fluid entraps airThe fluid loses energy after a jump

Leading to many practical applications

Types of Hydraulic Jumps

No hydraulic JumpFr<1

Theoretically this would be a negative hydraulic jump, i.e. the fluid depth will decreaseOnly physically possible if some external force

accelerates the fluid at that point

Undular JumpFor (1 < Fr1<1.7)Characterized by:

Slight undulation Two conjugate depths are close Transition is not abrupt – slightly ruffled water

surface

Weak JumpFor (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 JumpFor (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 JumpFor (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 JumpFor (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 applicationsEngineers design hydraulic jumps to reduce

damage to structures and the streambedProper design can result in a 60-70% energy

dissipation Minimizes erosion and scouring due to high

velocitiesDams, weirs and other hydraulic structures

Other Practical ApplicationsRecover pressure head and to raise water

levels downstream of a canalMaintain a high water level for irrigation or

other water-distribution purposesMix chemicals in water purification Aerate water for city water supplies Remove air pockets from water to prevent air

locking in supply lines

Recreational ApplicationsTraveling down rivers/rapidsKayaking and canoeing: playboat/surf

hydraulic jumps

ConclusionAn 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%

DemonstrationRepresenting a hydraulic jump in your sink: Shallow

fluid A smooth flow pattern forms where the water hits Further away, a sudden hydraulic jump occursSpecific characteristics of this jump:

Water flows radially and it continues to grow shallowerIt slows down due to friction (decrease in Froude

number) up to the point where the jump occursFrom supercritical to subcritical flowDiameter of the jump decreases as water depth

increases.