Mathematical equation of a Jet Stream of Air

AI Thread Summary
The discussion revolves around creating a control system for a vertical jet stream of air to suspend a ping pong ball using a valve to adjust air pressure. The main challenge is developing a mathematical equation or transfer function that accurately represents the jet stream dynamics, as traditional equations like Bernoulli's may not apply due to the open environment. The user seeks guidance on the physics and mathematics involved, particularly in transitioning from time domain equations to the Laplace domain for control system design. Suggestions include using empirical data for PID tuning instead of relying solely on theoretical models. Overall, the conversation highlights the complexities of modeling fluid dynamics for control systems in non-enclosed environments.
Uridan
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Hi,

First of all, Happy new year to you all, I hope you enjoyed it as much as I did :), but its back to work for me now :(.
I am an electronics Student and doing a project about control systems to control a vertical jet stream of air coming out of a pipe.

My basic setup is a motor that blows out air from a pipe and a ping pong ball will eventually flout inside the low pressure of air stream coming out of the pipe, then a valve will be controlled to control the height of the ping pong ball.

I need help in understanding the physics and Maths behind the jet stream of air coming out of the pipe, since I need an equation that represents the jet stream of air. This will eventually be converted into laplace domain and used as the transfer function for my control system.

I have required some books about Thermodynamics and aerodynamics etc.. but can't come any close to a conclusion. I know about Bernoulli's equation and the pressure changes in the jet stream of air and why the ball eventually flouts inside it, but I have no clue in how I may find a mathematical equation that explains the behavior of this jet stream of air coming out the pipe.

Any help would be greatly appreciated :)

Thanks
Uridan
 
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Vertical jet stream of air

Hi,

Is there a way to find the transfer function of a vertical jet stream of air coming out of a pipe? The problem is that the stream of air is not inside a pre set volume, such as a wind tunnel. I don't thing that Bernoulli's equation is good since the pressure of the stream of air will change according to the pressure in the room.

Thanks
Uridan
 
Control system for a jet stream of air

Hi fellow engineers,

I have a problem, how can I come out with a proper transfer function of a vertical jet stream of air coming out of a pipe to be able to use it in my design of a PID controller and Phase compensator ?

The thing is that I have no clue about Thermodynamics and such, I'm just electrical and electronics guy :).

Thanks
Uridan
 
Equation for a vertical jet stream of air

Homework Statement



Got a small problem regards the Mathematical equation for a vertical jet stream of air. We all know that when air is coming out of a pipe it will create a pressure change, i.e the pressure will be lower at the center of the stream of air than the outside pressure (room pressure), I can't seem to find a way to be able to find the transfer function/mathematical relationship/topology of this jet stream of air.


Homework Equations



Bernolli's equation is : v^2/2 + P/p + g*h

Where P=Pressure , p= density

Which pressure is it referring to ? because the jet stream of air is being release in atmospheric pressure, (pressure found in the room).

p.s I am an electronics student and don't have any knowledge on Thermodynamics etc. I am using this for a PID controller and a phase compensator design.

Thanks
Uridan
 


Uridan said:
Hi fellow engineers,

I have a problem, how can I come out with a proper transfer function of a vertical jet stream of air coming out of a pipe to be able to use it in my design of a PID controller and Phase compensator ?

The thing is that I have no clue about Thermodynamics and such, I'm just electrical and electronics guy :).

Thanks
Uridan

Transfer function from what to what? What control variables do you have over the stream of air? What is its response to the control variables? Are you just able to control some pressure? Are you trying to suspend something in the air stream? What is the air stream used for?
 


Hi Berkeman

My system is to control a valve which will allow an amount of volumetric air to pass through the pipe, so basically I am changing the pressure of air going out of the pipe.

I am to suspend a ping pong ball by the jet stream of air and control its height by controlling the valve.

To be able to do so I must find a transfer function for my model in s domain, thus the original equation must be in time domain, so I can obviously calculate my P or PI or PID controller needed to control the valve for such parameters.

Basically I am using Bernoulli's equation but some variables do not apply since I am not working inside a wind tunnel with a pre set volumetric change, and I've read that I must use some kind of Euler's equation but I got lost there and then lol.

Thanks
Uridan
 


I can't help you from a math standpoint, but something in your post bothers me. Doesn't the presence of the pipe (ie: ducted fan) automatically result in a pre-set volume?
 


Uridan said:
Hi Berkeman

My system is to control a valve which will allow an amount of volumetric air to pass through the pipe, so basically I am changing the pressure of air going out of the pipe.

I am to suspend a ping pong ball by the jet stream of air and control its height by controlling the valve.

To be able to do so I must find a transfer function for my model in s domain, thus the original equation must be in time domain, so I can obviously calculate my P or PI or PID controller needed to control the valve for such parameters.

Basically I am using Bernoulli's equation but some variables do not apply since I am not working inside a wind tunnel with a pre set volumetric change, and I've read that I must use some kind of Euler's equation but I got lost there and then lol.

Thanks
Uridan

Would it be permissible to use empirical data to set the PID loop up? Sounds like a pretty complicated simulation to figure it out computationally. I think I'll move this to the ME forum to get some better views. This is more of an ME question than an EE question.
 


Just make your controller ad-hoc. Tune the gains until the thing works. There is no reason as to why you need a transfer function in this situation.
 
  • #10
Ack. Multiple thread posts merged into one. Please don't multiple post, Uridan.
 
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