What is sonic velocity?

How important is it for sizing PSV?

Also, what will happen if a PSV is OK in inlet/outlet dP and has adequate area but has a sonic velocity above 75%?

Thank you.

DJ

Simply stated, sonic velocity is the velocity of sound in that fluid (a gas/vapor). It is a maximum that can be achieved by the fluid.

As you know, flow is induced due to a pressure difference between the upstream condition and the downstream condition. Holding the upstream pressure constant, as you lower the downstream pressure, the fluid velocity will increase. At a certain downstream pressure, the fluid velocity will hit a maximum. Dropping the pressure any further will have no affect on this value. This is the point where the fluid has reached sonic velocity. Another term we tend to use here is critical or choked flow, given by the units such as lb/hr-sq. ft. or kg/hr-sq.m. Or we can also designate the pressure at this point as being the choked or critical pressure. I like to use the term "choked" because most engineers relate the word "critical" to the thermodynamic point of the vle curve.

How important is it for sizing PSV? For one thing, most of the formulas given in literature are based on the fluid reaching sonic velocity in the PSV throat. There are equations for the case where sonic velocity is not achieved and these are somewhat more complicated. Plus it is harder to certify the PSV if the flow has not reached sonic velocity. Another problem is when the fluid reaches sonic velocity at some point downstream of the PSV. This will create the largest pressure drop, which translates into a large back pressure. It can also cause extreme and damaging vibration in the piping.

Some people do not allow the velocity in the downstream piping to ever achieve a flow greater than 75% to 80% of sonic. You can do this by increasing the piping size but of course, you pay more for this as well. I don't necessarily subscribe to this limitation. I will size the pipe for sonic velocity but then choose the next larger standard pipe size. This will bring the velocity down somewhat. I then have the piping designers design the pipe for potential vibration if necessary.

Without going through a more detailed thesis, you can easily Google "sonic velocity" and start reading. You can pick up any fluids book or thermo book as well.

Phil, thanks for your reply. I try to understand your saying... and I still have few questions:

1. I quote your reply: "Simply stated, sonic velocity is the velocity of sound in that fluid (a gas/vapor). It is a maximum that can be achieved by the fluid."
Does this apply to liquid (ie. water, hydrocarbon, etc.) as well?

2. Sonic velocity is the maximum speed can be reached by a fluid. So...sonic velocity cannot be greater than 100%, am I right?

3. Assuming sonic velocity > 80% but the outlet dP is less than 50% (pilot operated valve)....does this meet the API Recommended Practice?

Regards,
DJ

There are two aspects here, and I am unclear as to which one is relevant for your case:

a) The flow through the PSV orifice is choked ( sonic velocity). This is desirable, and the equations to size the orifice is given in API 520 Part 1.

The flow through the tailpipe ( I assume exit; or downstream of the the PSV) is reaching 0.75 mach. As Phil pointed out, some companies have restrictions on the mach velocities allowed in tail pipes and main headers ( BTW this was a subject of my query a couple of years back, and was never closed out satisfactorily). 0.75 mach looks OK to me for a tailpipe.

For reference, please see my article on cheresources
Compressible Flow article

Regards
Rajiv

DJ,
You state

Velocities higher than sonic can be achieved by various means. Chief among them in our industry would be through the use of a converging-diverging nozzle. Despite this, the times when we would be interested in achieving supersonic velocities are few and far between, and we can therefore think of sonic velocity as a practical limit in most cases.

Sonic velocity in a liquid is much higher than sonic velocity in a gas or vapor. I have not seen of situations where achieving sonic velocity in liquid flow is a concern. That may just be my lack of opportunity. I would think that sonic velocities are reached inside modulating valves when pressure drops are high. I have never heard of reaching anywhere near sonic velocity in a liquid filled pipe. If such situations exist, I would be curious to hear more of them.

Your second question was addressed above.

I'll defer answering the third question to those more knowledgable than myself in code requirements.
Doug

Good follow-ups to my original response.

The Code and practices only say that the back pressure on the PSV must not affect the ability of the relief device to perform its required function. There are no definitive values set by Code or standards; there are only suggestions. Only the manufacturer can tell you how their relief device will function at a given back pressure.

One last thing....we need to clean up the terminology a little. You can't have sonic velocity of a given percentage, i.e. your statement, "Assuming sonic velocity > 80%..." is not correct. You can be within 80% of sonic velocity but sonic velocity can not be 80%.

Pardon my mistake for the terminology... I am still learning on how to think, write, and speak like an engineer. Sometimes my brain and my fingers do not cooperate well.

There are many relief devices in a plant. I believe they are not all come from the same manufacturer. Also, I am pretty sure they are not all purchased and installed at the same time. Looking at this situation, isn't there supposed to be some kind of general standard? Some numbers that cannot be violated and whatnot? When we size a PSV, we don't really know who we'll purchase it from. So, there must be some kind of rule of thumb.

My other question is... some people design a relief device per API. Others use ASME as their standard. Does it matter which one we follow?

Other readers may not aware of these contents by looking at the topic. Suggest xyz168 to open a new post for similar question.