What's the modulus of elasticity (or wave speed) of liquid sulphur? 1

[dbevil]

I'm in the process of designing a 113 kilometer long liquid sulphur pipeline and need to determine the transient pressures due to "waterhammer". To do this I need the modulus of elasticity of liquid sulphur in order to calculate the wave speed of the system. So far, I have not found any source for this information.

Anyone have this info?

 

[hacksaw]

113 km -> 70-75 miles. That's a pretty long line for liquid sulfur.

How do you plan to keep it liquified?

 

[TD2K]

South West (Western?) Research does a lot of work with sulphur, they might be able to give you leads on a couple of references.

 

[dbevil]

It will be kept liquid (heated) with a Skin Effect Heat Tracing (SEHT) technique used on several smaller pipelines and, of course, it's insulated.

 

[hacksaw]

the only data I've found: 3500 m/s at 115 deg C (just above the melting point).

in shorter runs (several hundred meters), water hammer was never a problem, even with quick opening/closing valves (rotary). The fluid viscosity seemed to dampen out any tendency for "shock waves" propagating very far.

 

[dbevil]

I found the bulk modulus (7.7 GPa)
at:

http://www.webelements.com/webelements/elements/text/S/phys.html

Which translates to a wave velocity of 2068 m/s.

Hacksaw,

I don't understand how viscosity could effect surge pressure, which is a function of fluid velocity, wave speed, density and the rigidity of the carrier pipe. I've never seen a relationship between viscosity and waterhammer. The modulus of elasticity of the carrier pipe is what dampens surge pressures and in a steel pipeline, it's very slight.

 

[hacksaw]

The modulus that you are looking at may be for solid phase.


The velocity data I located was specifically for liquid sulfur at 115 Deg C. The actual data was listed as 0.35 cm/microsecond.

There was no data for more common liquid sulfur temperatures. It is about mid-way between that of liquid iron and liquid sodium. your figure (2078 m/s) seems abit low.


The viscosity does not affect the speed of the pressure wave but it acts to dissipate the energy and smooth out the rate of pressure rise as the wave travels down the pipe. This limits the hammer effect.

The modulus of the pipe also limits the pressure rise as you've stated, but does so elastically. This elastic response returns the energy stored in deformation, to the pressure wave rather than dissapating it.

Have not observed any evidence of waterhammer in liquid sulfur, though we were concerned about it. That said, you application has so much momentum involved, that it cannot be ignored.

I'll keep you posted if more definitive sulfur props are located.

 

[hacksaw]

dbevil,

the velocity in liquid sulfur is a tough nut to crack, but here is some meaningful data, coutesy of J.K. Olsen

http://www.physics.utah.edu/~jared/aps4c2002.pdf

you should fine this right on the mark.

Good luck,

 

[hacksaw]

for those without adobe acrobat:

the velocity of sound in sulfur is 1440 m/s at 82 Deg C and 1290 m/s at 155 Deg C with a linear slope between the two points.

 

[dbevil]

Hacksaw,

The info was right on the money. I should be able to complete the analysis now and close the subject.

Thanks for the effort.

 

[chip1998]

dbevil, do you want modulus of elasticity of sulphur or bulk modulus. i think you need the later. Modulus of elasticity refers to the pipe material.

You need mudulus of elasticity and density of sulphur.