Volumetric to linear expansion conversion for constrained fluids

[mwemag]

Does anyone know how to convert the value of volumetric thermal expansion into linear expansion, when the fluid is constrained in a channel?

I'm searching for fluids for a microactuation device, in which a linear micron-sized deflection is produced by the pressure of linear expansion. The expansive fluid would be constrained in a narrow channel and could only expand in one direction, like in a thermometer, but without an additional reservoir. The aim is to reach a linear expansion of approximately 30% by a temperature raise of 200 - 300 deg.C, which is possible for example with phase changing materials like paraffin, just that in my application it has to be a fluid.

Knowing the linear expansion coefficient, e.g. for solids, it is easy to calculate the expansion in percent, but the coefficient of fluids is mostly expressed as volumetric expansion, which is three times larger than the linear expansion. E.g. the volume thermal expansion coefficient of ethyl is 1630x10-6/degC. To convert this into linear expansion it must be divided by three, but I'm not sure whether this is also true when the fluid is constrained so that it can expand only in one direction. Rather I assume in this case the linear expansion would be half of the volumetric expansion, but I'm not sure.

Does Anybody know more?

 

[darai]

Volume of a cylinder: pi * Diameter * Diameter * Length / 4
This is all you need in addition to your coefficient.
See, your fluid increases in volume by so much, if it was constrained in a cylinder then the equation gives you he increase in length.
Assuming always of course it remains incompressible.