Free energy? increasing speed of a fluid in a nozzle

In summary, to get an ideal fluid to go as fast as you want it to go, you need an external pump that gives it a pressure and a speed.
  • #1
lerts
5
0
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 which every 1 m of length 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 what's wrong with this assumption because kinetic energy can't be created

This is a thought experiment with an ideal fluid so please don't tell me it wouldn't be posible because of friction, its an ideal fluid
 
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  • #2
lerts said:
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 which every 1 m of length 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 what's wrong with this assumption because kinetic energy can't be created

This is a thought experiment with an ideal fluid so please don't tell me it wouldn't 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.
 
  • #3
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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  • #4
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 don't 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 don't believe in creation of energy so please 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
 
  • #5
lerts said:
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 don't 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/sBut 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 don't believe in creation of energy so please 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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  • #6
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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1. What is free energy and how is it related to fluid speed in a nozzle?

Free energy refers to the potential energy available in a system that can be converted into useful work. In the case of a fluid in a nozzle, the free energy is related to the kinetic energy of the fluid, which is directly proportional to its speed in the nozzle. This means that as the fluid speed increases, the amount of free energy available also increases.

2. How is the speed of a fluid increased in a nozzle?

The speed of a fluid in a nozzle can be increased through the principle of conservation of energy. This involves using a pump or compressor to increase the pressure of the fluid, which in turn increases its speed as it flows through the nozzle. The shape and size of the nozzle also play a role in determining the velocity of the fluid.

3. Can the speed of a fluid in a nozzle continue to increase indefinitely?

No, the speed of a fluid in a nozzle cannot continue to increase indefinitely. The fluid will eventually reach a maximum speed known as the critical velocity, where the pressure and velocity of the fluid are in equilibrium. Any further increase in pressure will not result in a corresponding increase in speed.

4. What are some practical applications of increasing fluid speed in a nozzle?

Increasing fluid speed in a nozzle has many practical applications, such as in jet engines, where the high-speed flow of air through the nozzle produces thrust. It is also used in hydraulic systems to power machinery and in rocket engines to generate thrust for space exploration. Additionally, it is used in industrial processes such as water jet cutting and spray painting.

5. Are there any potential drawbacks to increasing fluid speed in a nozzle?

One potential drawback of increasing fluid speed in a nozzle is the energy required to maintain high fluid velocities. This can result in higher operating costs for machinery and equipment. Additionally, the high-speed flow of fluids can cause erosion and wear on the nozzle and other components, which may require frequent maintenance and replacement.

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