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Related Concept Videos

Hydraulic Jump01:29

Hydraulic Jump

A hydraulic jump is a sudden rise in fluid depth in open channels, occurring when high-velocity (supercritical) flow transitions to low-velocity (subcritical) flow. This phenomenon requires an upstream Froude number greater than 1, as flows with Fr1<1 remain subcritical, making a hydraulic jump impossible due to the need for negative head loss, which violates thermodynamic principles.The characteristics of a hydraulic jump depend on the upstream Froude number and are classified as...
Hydraulic Jump: Problem Solving01:16

Hydraulic Jump: Problem Solving

To analyze a hydraulic jump in a rectangular channel with a flow speed of 6 meters per second, follow these steps:Calculate Effective Upstream Velocity:When the downstream gate closes, a hydraulic jump forms, traveling upstream at 2 meters per second. This wave speed combines with the initial channel flow velocity, creating an effective upstream velocity.Identify Flow Velocities Before and After the Hydraulic Jump:Upstream of the hydraulic jump, the effective flow velocity includes both the...
Design Example: Creating a Hydraulic Model of a Dam Spillway01:21

Design Example: Creating a Hydraulic Model of a Dam Spillway

Scaled hydraulic models of dam spillways provide a practical way to replicate and study the intricate flow dynamics of these structures. Often built to a 1:15 ratio, these models allow for observing critical water behavior, such as velocity distribution, flow patterns, and energy dissipation.
Design Example: Designing Water Slide01:18

Design Example: Designing Water Slide

When designing a water slide, controlling the speed of water flow is crucial for rider safety while maintaining an exciting experience. As water flows down the slide, gravity causes it to accelerate, with its speed at the bottom depending on the height from which it starts. The higher the slide, the more potential energy the water has at the top, which is converted into kinetic energy as it descends, increasing its speed.
Bernoulli's principle determines the water's velocity along the slide.
Typical Model Studies01:30

Typical Model Studies

Fluid mechanics model studies often utilize scaled-down systems to predict fluid behavior in full-scale environments, such as river flows, dam spillways, and structures interacting with open surfaces. Maintaining Froude number similarity in river models is crucial, as it replicates surface flow features like wave patterns and velocities.
Hydrostatic Pressure Force on a Curved Surface01:04

Hydrostatic Pressure Force on a Curved Surface

Hydrostatic pressure on curved surfaces is a fundamental concept in fluid mechanics with broad applications in the civil engineering field. When fluid is in contact with a curved surface, as in a reservoir, dam, or storage tank, it exerts pressure that varies in magnitude and direction along the curved surface. To assess the total hydrostatic force exerted by the fluid on a curved structure, engineers typically isolate the fluid volume adjacent to the surface and analyze the forces acting on...

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Related Experiment Video

Updated: May 22, 2026

A Modeling and Simulation Method for Preliminary Design of an Electro-Variable Displacement Pump
09:04

A Modeling and Simulation Method for Preliminary Design of an Electro-Variable Displacement Pump

Published on: June 1, 2022

Model for polygonal hydraulic jumps.

Erik A Martens1, Shinya Watanabe, Tomas Bohr

  • 1Group for Biophysics and Evolutionary Dynamics, Max Planck Institute for Dynamics and Self-Organization, 37073 Göttingen, Germany. erik.martens@ds.mpg.de

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 17, 2012
PubMed
Summary

A new model explains polygonal hydraulic jumps using fluid dynamics principles. It predicts polygonal shapes based on a single dimensionless number, offering insights into fluid flow instabilities.

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Area of Science:

  • Fluid Dynamics
  • Nonlinear Phenomena

Background:

  • Polygonal hydraulic jumps were previously observed.
  • Type-II hydraulic jumps feature a "roller" separation eddy.

Purpose of the Study:

  • To develop a phenomenological model for polygonal hydraulic jumps.
  • To analyze the forces governing jump shape and stability.

Main Methods:

  • The model incorporates mass conservation and radial/azimuthal force balances.
  • Linearization and a truncated nonlinear model were used for analysis.
  • Time-dependent terms were included to study linear stability.

Main Results:

  • A parameter relationship for nearly circular polygonal states was derived.
  • A simplified model analytically predicts polygonal shapes similar to experimental observations.
  • Instability of the circular state was found for small Bond numbers.

Conclusions:

  • The model successfully describes polygonal hydraulic jump formation.
  • The dimensionless number φ is key to polygon existence.
  • The study provides a framework for understanding fluid flow instabilities.