Curved Tube For Constant Pressure Increase?

[person123]

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.

 

[Nidum]

I don't understand . Draw some pictures .

 

[boneh3ad]

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.

 

[Redbelly98]

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

V_disp = [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 V_disp.

Setting PV = constant, you can then solve for the tube cross-sectional area A(x).

 

[CWatters]

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?

 

[Baluncore]

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.

 

[Redbelly98]

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?

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.