Does Bernoulli's Principle Apply to Aerodynamics at Different Heights?

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Discussion Overview

The discussion revolves around the application of Bernoulli's principle in the context of aerodynamics, specifically regarding the behavior of a ping pong ball in a tube with a slit as it is influenced by varying heights and airflow. Participants explore the relationship between pressure, drag forces, and the dynamics of the ball's motion within the tube.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant inquires about the effect of a slit on the side of the tube on the ping pong ball, suggesting that the drag force from the fan counteracts the ball's weight and questioning whether the slit leads to a decrease in pressure.
  • Another participant questions whether static pressure decreases with height according to Bernoulli's principle, as potential energy increases, and seeks clarification on the relationship between the ball's height and the airflow volume.
  • A third participant notes that the air is not significantly compressed and maintains a constant temperature, arguing that the potential energy from hydrostatic head is negligible when buoyancy is equal to the surrounding atmosphere.

Areas of Agreement / Disagreement

Participants express differing views on the application of Bernoulli's principle and the effects of height on pressure, indicating that multiple competing perspectives remain unresolved.

Contextual Notes

Participants have not reached consensus on the relationship between pressure changes and height in this specific scenario, and assumptions regarding the behavior of the air and the ball's buoyancy are not fully clarified.

SamJ96
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Homework Statement
Hi everyone. I have a ping pong levitation system with a ping pong ball in a tube being pushed by a dc motor fan. Can anyone describe the force effect of a slit on the side of the tube on the pin pong ball? I know there is a drag force applied by the fan going against the balls weight, but I don't know how the slit effects the motion. Is it a decrease in pressure? Can anyone quantify it within a force diagram? The setup and FBD i have currently are attached. Cheers
Relevant Equations
F=m*a[ball]=-m*g+0.5*Cd*p*A*(v[air]-v[ball])-F[slit]
What is F[slit]?
20211206_141444.jpg
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Welcome to PF.
SamJ96 said:
Can anyone describe the force effect of a slit on the side of the tube on the pin pong ball? I know there is a drag force applied by the fan going against the balls weight, but I don't know how the slit effects the motion. Is it a decrease in pressure?
The pressure under the ball, and the flow past the ball, support the ball. For a fixed size ball in a fixed size tube, that pressure, flow and force, should be a constant no matter what height the ball 'floats' in the tube.

As the ball rises, more of the slot is uncovered, so more air can escape through the slot, before reaching the ball.

The height of the ball is therefore a function of the volume of air being blown into the tube by the fan.
 
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Hi Baluncore,
Thank you very much for your answer. Just wondering, doesn't the static pressure decrease based on Bernoulli's principle as the the potential energy increases with height? Also, is the function that relates the balls height with the air volume blown into the tube different from the force equation that I showed, or is my force equation completely wrong? Thank you once again.
 
SamJ96 said:
Just wondering, doesn't the static pressure decrease based on Bernoulli's principle as the the potential energy increases with height?
The air is not being significantly compressed, and can be taken as the same temperature throughout the experiment. PE of hydrostatic head is not significant when the fluid has buoyancy equal to the surrounding atmosphere.
 
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