# Free energy? increasing speed of a fluid in a nozzle

I have a tube 1 m long and 1 m wide with an ideal fluid inside with a pressure of 1 bar.

I conect that tube of 1*1m with another tube of 1m long and 0.5m wide and this connected to another tube of 1 m and 0.25 m wide and so on

So i have a tube in wich every 1 m of lenght the wideness of the tube is half, 1m. 0.5, 0.25, 0.125... and so on

The fluid starts with a speed of 1 m/s and a pressure of 1 bar, when it goes to the next part of the tube the speed doubles and the pressure halfs because the section is half

So as the ideal fluid goes along the narrowing tube every meter doubles the speed and halfs the pressure

So the pressure will go: 1 bar, 0.5, 0.125 and so on and the speed of the fluid will go: 1m/s, 2, 4 ,8 ,16 ,32,...

So with a presure of 1 bar and a initial speed of 1 m/s i can get an ideal fluid to go as fast as i want

So can someone explain me whats wrong with this assumption because kinetic energy cant be created

This is a thought experiment with an ideal fluid so plz dont tell me it wouldnt be posible because of friction, its an ideal fluid

ZapperZ
Staff Emeritus
I have a tube 1 m long and 1 m wide with an ideal fluid inside with a pressure of 1 bar.

I conect that tube of 1*1m with another tube of 1m long and 0.5m wide and this connected to another tube of 1 m and 0.25 m wide and so on

So i have a tube in wich every 1 m of lenght the wideness of the tube is half, 1m. 0.5, 0.25, 0.125... and so on

The fluid starts with a speed of 1 m/s and a pressure of 1 bar, when it goes to the next part of the tube the speed doubles and the pressure halfs because the section is half

So as the ideal fluid goes along the narrowing tube every meter doubles the speed and halfs the pressure

So the pressure will go: 1 bar, 0.5, 0.125 and so on and the speed of the fluid will go: 1m/s, 2, 4 ,8 ,16 ,32,...

So with a presure of 1 bar and a initial speed of 1 m/s i can get an ideal fluid to go as fast as i want

So can someone explain me whats wrong with this assumption because kinetic energy cant be created

This is a thought experiment with an ideal fluid so plz dont tell me it wouldnt be posible because of friction, its an ideal fluid

First of all, you need an external force to maintain the pressure. So this isn't a "free" energy (and from now on, please try to avoid using that term because that would only raise warning flags all over).

Secondly, why would you even need to demonstrate this with all those different size diameters? Just putting a finger partially over a water hose is a sufficient demonstration. What you need to consider is the TOTAL ENERGY per second that crosses the cross-sectional surface of the pipe. You are moving the SAME volume per unit time. But since the pipe with a smaller diameter has a smaller cross-section, then the unit volume of water has to move faster. So same volume, same pass per unit time being moved by the same force, so work done is the same no matter what the pipe diameter is. No free energy.

Zz.

russ_watters
Mentor
Just something else to point out here:

This is a relatively simple fluid dynamics concept. When you start thinking about such things, you may want to take a step back and consider the possibility that others have thought about the same issues and simply research what they found.

We don't mean to sound harsh here, but the words "free energy" do set off loud warning bells for us.

So.....

What you are musing about is Bernoulli's Principle:
Bernoulli's Principle states that in an ideal fluid (low speed air is a good approximation), with no work being performed on the fluid, an increase in velocity occurs simultaneously with decrease in pressure or gravitational energy.

This principle is a simplification of Bernoulli's equation, which states that the sum of all forms of energy in a fluid flowing along an enclosed path (a streamline) is the same at any two points in that path.
http://en.wikipedia.org/wiki/Bernoulli's_principle

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Yes that was exactly what my teacher answered me when i asked him about converging nozzles, pressure which is potential energy decreases transforming in kinetic energy, speed of the fluid

But i still dont understand it so i have another question:

I have a tube of constant wideness and to get the ideal fluid to a speed of 1 m/s I need a pump that gives a pressure of 1 bar

what would happen if in the end of the 1 m section tube i put a converging nozzle with the narrower section of .125m?

Obviously the fluid will come out at a speed of 4 m/s

But if the mass of ideal fluid per unit of time is the same however the section how is it possible it increases its speed 4 times if the pump works at the same rate?

Same energy spent by the pump, same amount of mass but 4 times more speed just by putting the nozzle

And that taken into account the nozzle is just 4 times smaller if I made the nozzle 1 million times smaller the speed at which the water came out would be awesome and all with the pump working at the same rate

I dont believe in creation of energy so plz explain me how with the pump working at the same rate i can get an ideal fluid as fast as I want making tiny the nozzle and i can always make the nozzle even smaller

ZapperZ
Staff Emeritus
Yes that was exactly what my teacher answered me when i asked him about converging nozzles, pressure which is potential energy decreases transforming in kinetic energy, speed of the fluid

But i still dont understand it so i have another question:

I have a tube of constant wideness and to get the ideal fluid to a speed of 1 m/s I need a pump that gives a pressure of 1 bar

what would happen if in the end of the 1 m section tube i put a converging nozzle with the narrower section of .125m?

Obviously the fluid will come out at a speed of 4 m/s

But if the mass of ideal fluid per unit of time is the same however the section how is it possible it increases its speed 4 times if the pump works at the same rate?

Same energy spent by the pump, same amount of mass but 4 times more speed just by putting the nozzle

And that taken into account the nozzle is just 4 times smaller if I made the nozzle 1 million times smaller the speed at which the water came out would be awesome and all with the pump working at the same rate

I dont believe in creation of energy so plz explain me how with the pump working at the same rate i can get an ideal fluid as fast as I want making tiny the nozzle and i can always make the nozzle even smaller

You have 2 cylinders. One has a cross-sectional diameter 1/2 of the other one. How much longer is that cylinder to have the SAME volume? This is the same length that has to flow through per unit time to preserve the same volume flowing through in that time.

Zz.

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russ_watters
Mentor
The simple answer is you can't do that without increasing the pressure at the pump. When you speed up the flow, you convert static pressure to velocity pressure (as the equation shows), so if you want to end up with the same volume flow rate, you need more pressure at the pump.

The wik link provides all the derivations and even has a picture of what you are describing (though reversed). Please read it (or google for other explanations).

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