Exploring Angular Speed in Water Vortices

In summary, the smaller the hole in the cap the faster the water speed (L = r x p). However, the larger the hole the faster the water goes. The rate of rotation of the ball around the vortex is related in any way to the size of the exit hole.
  • #1
gianamar
4
0

Homework Statement


In a water vortex formed in a plastic bottle, what is the relationship between the angular speed of the water and the diameter of the hole in the cap? I would have expected that according to the conservation of angular momentum, the smaller the hole the faster the water speed (L = r x p). However, I've been trying to test this relationship out but seem to get that the larger the hole the faster the water goes.

Homework Equations


L = r x p = I \omega
 
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  • #2
Please describe your experimental set up in detail.
 
  • #3
First I drilled holes of different diameters into bottle caps. Then, I held a 2L bottle with the bottom cut off, upside-down, in place with a clamp stand and filled it around 2/3 of the way up with water, covering the hole in the cap. I swirled the bottle to create a vortex and once the vortex was established, I dropped a small plastic ball into the water and used a stop-motion camera to film the experiment. However, the number of revolutions of the plastic ball per second increased as I used caps with larger diameters, whilst I expected that the angular frequency would decrease to conserve the angular momentum of the vortex.
 
  • #4
Where is the plastic ball when you measure its rotation rate? It's not going through the hole yet, right?
Outside of the central vortex, you should have irrotational flow (yes?). That means the rotation rate is in inverse ratio of the radius, so it matters at what radius the ball sits. I don't see how the size of exit hole in the cap is going to affect the vortex higher up in the bottle (much). Maybe I still don't have the right picture.
 
  • #5
No, the plastic ball doesn't go through the hole - it is dropped in from the top of the apparatus when the vortex is formed.
 
  • #6
gianamar said:
No, the plastic ball doesn't go through the hole - it is dropped in from the top of the apparatus when the vortex is formed.
Then why should the rate of rotation of the ball around the vortex be related in any way to the size of the exit hole?
You didn't completely answer my question about the position of the ball. Where does it sit radially? Is it always near the wall of the bottle?
 

1. What is angular speed in water vortices?

Angular speed in water vortices refers to the rotational velocity of the water particles within a vortex. It is typically measured in radians per second and is influenced by factors such as the size and shape of the vortex, as well as the speed and direction of the surrounding flow.

2. How is angular speed in water vortices measured?

Angular speed in water vortices can be measured using various techniques, including visual observation, particle tracking, and Doppler velocity measurements. These methods allow researchers to track the movement of individual water particles and calculate their angular velocity.

3. What is the significance of exploring angular speed in water vortices?

Exploring angular speed in water vortices can provide valuable insights into the dynamics of fluid flow and the formation of vortices. This knowledge can be applied in various fields, such as oceanography, meteorology, and engineering, to better understand and predict the behavior of natural and man-made vortices.

4. What factors can affect the angular speed in water vortices?

Several factors can influence the angular speed in water vortices, including the initial velocity and direction of the surrounding flow, the viscosity and density of the water, and the shape and size of the vortex core. Turbulent conditions and external forces can also impact the angular speed.

5. What are the potential applications of studying angular speed in water vortices?

The study of angular speed in water vortices has many potential applications, such as improving the design and efficiency of turbines and propellers, understanding the behavior of ocean currents, and predicting the formation and strength of hurricanes and tornadoes. It can also help in the development of new technologies for mixing and stirring fluids in industrial and medical processes.

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