Vortex & Vortices

Vortices--conservation of angular momentum and fluid dynamics.

Demonstration:  Tornado in a Tube Connector & Using the fly wheel and spinning platform.
Also can show turblence in a flame projected onto a screen.
 
Author: Bob Fiero--borrowing from various sources.
 
Principles:
vorticies
angular momentum
fluid dynamics/kinetics
torque
right hand rule
 
Standards:

Conservation of Energy and Momentum

  1. The laws of conservation of energy and momentum provide a way to predict and describe the movement of objects. As a basis for understanding this concept:
    1. Students know how to calculate kinetic energy by using the formula E=(1/2)mv2 .
    2. Students know how to calculate changes in gravitational potential energy near Earth by using the formula (change in potential energy) =mgh (h is the change in the elevation).
    3. Students know how to solve problems involving conservation of energy in simple systems, such as falling objects.
    4. Students know how to calculate momentum as the product mv.
    5. Students know momentum is a separately conserved quantity different from energy.
    6. Students know an unbalanced force on an object produces a change in its momentum.
    7. Students know how to solve problems involving elastic and inelastic collisions in one dimension by using the principles of conservation of momentum and energy.
    8. * Students know how to solve problems involving conservation of energy in simple systems.
 
Materials:    
             
Tornado Tube Connector
2 two liter bottles
Optional:  lamp oil, food coloring or anything that allows the
               vortex to be more visible.
Also other demo equipment:  fly wheel (hand held) with turntable.
 
 
Procedure: How does it work?
  1. Fill one of the 1-liter bottles with water. Connect the empty bottle to the first with the Tornado Tube, so it looks like an hourglass. Tip this "hourglass" upside down, swirl the bottles, and in seconds a beautiful "tornado" appears.

Explanation: What does it teach?        

Use this experiment to introduce students to kinetic energy and potential energy as well as the atmospheric conditions needed to create a tornado vortex.. Help students discover how air pressure and density work together to create an incredible force of nature. Learn about the science of vortex energy, the swirling, twisting and spiraling action that can be found everywhere in nature.

is the angular momentum of the particle,

is the position vector of the particle relative to the origin,

is the linear momentum of the particle, and

is the vector cross product

 

A vortex (plural: vortices) is a spinning, often turbulent, flow of fluid. Any spiral motion with closed streamlines is vortex flow. The motion of the fluid swirling rapidly around a center is called a vortex. The speed and rate of rotation of the fluid are greatest at the center, and decrease progressively with distance from the center.

Examples: sunspot activity, wingtip vortices, wake of object moving through a liquid, black hole accretion disc, hurricanes (water spouts, cyclones, etc.), liquid down a drain, hypothetical wormhole junctures, high pressure nozzles, hovering bats, Bose–Einstein condensates, superconductors over magentic field, binary star orbits, spiral galaxies, and optical vortices.vortices_hires.jpg
 
Karman vortex, a repeating pattern of spinning vortices caused by the unsteady separation of flow over bluff bodies. They appeared over AlexanderSelkirk Island in the southern Pacific Ocean – off the coast of Chile – rising voluptuously from the surrounding waters and creating a stunning spiral effect.
 
 
 
In fluid dynamics, vortex stretching is the lengthening of vortices in three-dimensional fluid flow, associated with a corresponding increase of the component of vorticity in the stretching direction—due to the conservation of angular momentum.[1]

Angular momentum (also known as moment of momentum) of a particle about a given origin is defined as:

       L = r X P      

L is the angular momentum of the particle,

r is the position vector of the particle relative to the origin,

P  is the linear momentum of the particle, and

is the vector cross product

The conservation of angular momentum explains the angular acceleration of an ice skater as she brings her arms and legs close to the vertical axis of rotation. By bringing part of mass of her body closer to the axis she decreases her body's moment of inertia. Because angular momentum is constant in the absence of external torques, the angular velocity (rotational speed) of the skater has to increase.

Vortex stretching is at the core of the description of the turbulence energy cascade from the large scales to the small scales in turbulence. In general, in turbulence fluid elements are more lengthened than squeezed, on average. In the end, this results in more vortex stretching than vortex squeezing. For incompressible flow—due to volume conservation of fluid elements—the lengthening implies thinning of the fluid elements in the directions perpendicular to the stretching direction. This reduces the radial length scale of the associated vorticity. Finally, at the small scales of the order of the Kolmogorov microscales, the turbulence kinetic energy is dissipated by viscosity.

However, in fluid dynamics the internal areas can flow or rotate faster than the relative peripheral area at the same time. Reason is that a fluid can shear indefinitly on itself. Their bits translate along circular pathways giving it a strange irrotational characteristic.

Vorticity is a concept used in fluid dynamics. In the simplest sense, vorticity is the tendency for elements of the fluid to "spin."

More formally, vorticity can be related to the amount of "circulation" or "rotation" (or more strictly, the local angular rate of rotation) in a fluid. The average vorticity ωav in a small region of fluid flow is equal to the circulation C around the boundary of the small region, divided by the area A of the small region.

In physics, fluid dynamics is a sub-discipline of fluid mechanics that deals with fluid flow—the natural science of fluids (liquids and gases) in motion. It has several subdisciplines itself, including aerodynamics (the study of air and other gases in motion) and hydrodynamics (the study of liquids in motion). Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and reportedly modeling fission weapon detonation. Some of its principles are even used in traffic engineering, where traffic is treated as a continuous fluid.

Fluid dynamics offers a systematic structure that underlies these practical disciplines, that embraces empirical and semi-empirical laws derived from flow measurement and used to solve practical problems. The solution to a fluid dynamics problem typically involves calculating various properties of the fluid, such as velocity, pressure, density, and temperature, as functions of space and time.

Historically, hydrodynamics meant something different than it does today. Before the twentieth century, hydrodynamics was synonymous with fluid dynamics. This is still reflected in names of some fluid dynamics topics, like magnetohydrodynamics and hydrodynamic stability—both also applicable in, as well as being applied to, gases.
ngular momentum is a quantity that is useful in describing the rotational state of a physical system. For a rigid body rotating around an axis of symmetry (e.g. the fins of a ceiling fan), the angular momentum can be expressed as the product of the body's moment of inertia and its angular velocity (\mathbf{L} = I \boldsymbol{\omega}). In this way, angular momentum is sometimes described as the rotational analog of linear momentum.

Angular momentum is conserved in a system where there is no net external torque, and its conservation helps explain many diverse phenomena. For example, the increase in rotational speed of a spinning figure skater as the skater's arms are contracted is a consequence of conservation of angular momentum. The very high rotational rates of neutron stars can also be explained in terms of angular momentum conservation. Moreover, angular momentum conservation has numerous applications in physics and engineering (e.g. the gyrocompass).
Formally, the angular momentum of a point object is defined as the cross product of the object's position vector and linear momentum vector (\mathbf{L} = \boldsymbol{r} \times m\boldsymbol{v}). Angular momentum is a pseudovector whose magnitude is given by L = rmvsinθ where θ is the angle between the object's position vector and velocity vector. The direction of the angular momentum can be determined by applying the right-hand rule. The angular momentum of a system of particles (e.g. a rigid body) is the sum of angular momenta of the individual particles.
 
References:
SteveSpangelerScience.com
Wikipedia
Various Articles
  
 
Video: Basic Animated Model of a Vortex

Video: Basic Hurricane Model
 
 
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