Curved Tube For Constant Pressure Increase?

In summary: Overall, it seems like a promising concept to achieve a more constant rate of pressure increase in the tube. In summary, the conversation discusses the concept of designing a tube that increases pressure at a more constant rate by curving it inward towards the base. The idea is to decrease the amount of compressed air by decreasing the size of the tube, but there may be practical limitations such as designing a piston that can match the changing cross-sectional area of the tube. Another suggestion is using a buoyant cylinder in a liquid to achieve a more linear increase in force. However, this would also depend on other factors such as drag forces.
  • #1
person123
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My design concept stems from the fact that the pressure in a tube increases exponentially based on the length of the tube compressed. I would like to design a tube that increases pressure at a more constant rate. I would imagine that a tube curved inward toward the base would achieve this. As the air in the tube is being compressed by a greater distance, less air would be compressed since the size of the tube decreases. This would decrease the amount of pressure needed. However, I am not all sure if this would work, and I would be curious to hear your opinions on it.
 
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  • #2
I don't understand . Draw some pictures .
 
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  • #3
Also I am not sure where you are getting your exponential claim from. For an isothermal system, the pressure is inversely proportional to the volume.
 
  • #4
boneh3ad said:
Also I am not sure where you are getting your exponential claim from. For an isothermal system, the pressure is inversely proportional to the volume.
True enough. Ignoring this misuse of the term "exponential", I've actually worked it out for the isothermal case.

Disclaimer: the resulting shape is physically impossible to manufacture, so this all amounts to a purely theoretical exercise.

I'll just set things up, without working through to the final solution. Setting aside the issue of designing a piston that must change in size to match the changing cross-sectional area of the tube during the piston's stroke...

We want the pressure to increase linearly from its initial value P0 when the piston is at position x = 0, so:

P = P0 + ax, where a is a constant.

The volume V displaced by the piston, as a function of x, is

Vdisp = [Integral]A dx,
where A(x) is the cross-sectional area of the tube.

The volume V of gas in the tube is then the initial volume V0, minus the displaced volume Vdisp.

Setting PV = constant, you can then solve for the tube cross-sectional area A(x).
 
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  • #5
Redbelly98 said:
Setting aside the issue of designing a piston that must change in size to match the changing cross-sectional area of the tube during the piston's stroke...

Use water or oil for the piston?
 
  • #6
person123 said:
I would like to design a tube that increases pressure at a more constant rate.
A buoyant cylinder being pushed axially down into a liquid will present a force that rises linearly as the depth is increased. Changing the cross sectional area of the cylinder where it enters the liquid will change the rate of force increase.
 
  • #7
CWatters said:
Use water or oil for the piston?
What can keep a liquid piston like that contained, so that the increasing pressure within the cylinder doesn't blow it completely away?

Baluncore said:
A buoyant cylinder being pushed axially down into a liquid will present a force that rises linearly as the depth is increased. Changing the cross sectional area of the cylinder where it enters the liquid will change the rate of force increase.
Ah, interesting idea. Provided that the piston does not move so fast that drag forces become appreciable. It would depend on the specific application, of course.
 
Last edited:

1. What is a curved tube for constant pressure increase?

A curved tube for constant pressure increase is a type of instrument used in fluid mechanics to maintain a constant pressure of fluid as it flows through the tube. It is designed in a curved shape to allow for a gradual increase in pressure without causing turbulence in the flow.

2. How does a curved tube for constant pressure increase work?

The curved shape of the tube causes the fluid to change direction gradually, allowing for a smooth increase in pressure. This is achieved through the principle of Bernoulli's equation, which states that as the fluid's speed increases, its pressure decreases. The gradual increase in speed in the curved tube results in a gradual decrease in pressure, thus maintaining a constant pressure throughout the tube.

3. What are the advantages of using a curved tube for constant pressure increase?

Using a curved tube for constant pressure increase allows for a more controlled and accurate measurement of fluid pressure. It also reduces the risk of turbulence in the flow, which can affect the accuracy of the measurement. Additionally, it can be used for a wide range of fluid types and pressures.

4. Are there any limitations to using a curved tube for constant pressure increase?

One limitation of using a curved tube for constant pressure increase is that it can only maintain a constant pressure within a certain range. If the pressure difference is too high, the flow may become turbulent, affecting the accuracy of the measurement. Another limitation is that the curved shape may cause a slight pressure drop, which should be accounted for in the measurement.

5. How is a curved tube for constant pressure increase calibrated?

To calibrate a curved tube for constant pressure increase, a known pressure source is used to create a pressure difference across the tube. The resulting flow rate is measured and compared to the expected flow rate. Any discrepancies can then be adjusted by changing the curvature of the tube or using a different pressure source.

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