Ball in pipe turbulant problem

[ytcat]

Hello

I have a vertical pipe with floating ping pong ball in it.

I have fan at the bottom that that push the ball up.

The pipe parameters:
D=45mm
L=1.07m

Ball parameters:
D=40mm
M=2.7g

I tried to change fan speed to move the ball but becouse turbulance the ball is not steady, and so I can not control ball hight with fan speed.

I installed step motor at the top to open and close the hatch, it seems to be working.

I have now problem to calculate all of it.

If I look at the ball that floats in the air (inside the pipe) , the forces that I believe are effecting the ball are:
fg-weight force (down)
fd-drag force (up)
fb-buoyant force (up)

And I believe that there is a some turbulance force that pulls the ball down.

I can't use stocks equations becouse Re number is more than 2300 and I can't use bernoulli equations also becouse I have turbulance.

Eventually I need somehow to calculate the pressures ratio between two sides of the ball,

and develop formula for ball's hight.

Please help with this.

 

[eljose79]

Thank you for sharing your project with us. It is definitely an interesting experiment to study the behavior of a floating ping pong ball in a vertical pipe.

Based on the parameters you have provided, it seems like you are dealing with a low Reynolds number flow, which means that the flow is dominated by viscous forces rather than inertial forces. In this case, the Stokes' drag force equation can be used to calculate the drag force on the ball. This equation is valid for low Reynolds number flows and takes into account the size and shape of the object.

To calculate the buoyant force, you can use Archimedes' principle, which states that the buoyant force on an object is equal to the weight of the fluid it displaces. In this case, the fluid is air and the weight of the displaced air can be calculated using the ideal gas law.

As for the turbulence force, it is difficult to accurately calculate it as it depends on many factors such as the flow velocity and the shape of the object. However, it can be estimated using empirical correlations or through experimental measurements.

To calculate the pressure ratio between the two sides of the ball, you can use the Bernoulli equation. Although it is not valid for turbulent flows, it can still provide a rough estimate of the pressure difference.

To develop a formula for the ball's height, you will need to consider the forces acting on the ball and their balance. The net force on the ball should be zero for it to remain in a steady position. By equating the weight, drag, and buoyant forces, you can develop an equation for the ball's height.

I hope this helps you in your project. Good luck with your calculations and feel free to reach out if you have any further questions. Happy experimenting!