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# Bernoulli Vs Crane Tp410 Equation 3-19

4 replies to this topic

### #1 Greggreg

Greggreg

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Posted 18 April 2011 - 10:55 AM

Good afternoon,

Problem 1:
I am studying rupture disc sizing. I would like to determine the relieving capacity of a relieving pipe. For example for a case of tube rupture in an U heat exchanger with gas in the tube side and cooling water in the shell side.
To determine the relieving capacity I consider the water from the shell side. I did a literature study but I don't know which equation I have to use. I can't decide between Bernoulli's theorem and Crane TP 410 equation 3-19. I think that in equation 3-19 from Crane, the difference of height is not considered and it seems me strange unless that the difference of height is included in the resistance coefficient K.

Problem 2:
Resolving the Bernoullli's equation I can find an equation like the equation 3-19 from Crane but with a coefficient of "K+1" at the denominator of the square root. Is this normal??

Best regards,

Greg

### #2 paulhorth

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Posted 18 April 2011 - 05:19 PM

Greg,

You have two flow problems to solve. First, the flow of gas through the ruptured tube into the shell side, and second, the flow of liquid from the shell side through the rupture disc. To prevent the shellside pressure from rising, which is the purpose of the rupture disc, the VOLUMETRIC flow of liquid out must be at least equal to the VOLUMETRIC flow of gas in, at the relevant pressure.

The first flow problem will probably be critical flow, considered as through an orifice (considering the tube rupture to be at the tubesheet) or a nozzle - the orifice assumption is more conservative and gives a larger flow. You can use a textbook equation for critical flow through an orifice. Remember, there are two broken ends so take double the flow.
The second problem is liquid flow through a pipe and fittings. Just treat it as you would any other length of pipe in the plant, and include static head.Find the size of pipe which takes the required volumetric flow of liquid for the given upstream and downstream pressure and the length.

I lost my copy of Crane some time ago, so I can't check the equation 3-19, but I didn't like Crane's presentation because it is empirical and conceals the origin of the relationships and assumptions used.
In contrast, Bernoulli is simply an energy balance, which is true regardless of the fluid or the system, so long as no energy or mass is added or removed (such as with a heater, pump or compressor). That is, p1 + rho 1 (v1 )squared/2 + rho 1 .g.h1 = p2 + rho 2 (v2) squared/2 + rho 2 .g.h2 for any flowing fluid system between points 1 and 2. However, this does not account for friction loss, where kinetic energy is turned into heat and thus the pressure falls. For this you deduct the frictional pressure loss DPf = K. rho.(v)squared/2.

This is where the dreaded Crane comes in. Crane gives values for K for various fittings. For straight pipe, K = f. L/D. Use this to size the liquid outlet line.

Paul

Edited by paulhorth, 18 April 2011 - 05:23 PM.

### #3 Greggreg

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Posted 19 April 2011 - 05:06 AM

I have another question to rise.

To calculate the relieving gas flow rate you suggest me to use a two orifices assumption. I knew this assumption, more conservative than the assumption with frictionnal losses (rupture at the tubesheet, one flow from the tubesheet and one flow from the tube). Nevertheless API 521 suggests to use the second assumption (the less conservative) knowing the first assumption provides a larger flow rate.
So, don't you think that the more conservative assumption will lead to oversize the relieving pipe?

Greg

### #4 fallah

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Posted 19 April 2011 - 06:50 AM

Greg,

In most cases considering one orifice with the size of exchanger tube would be adequate.

Fallah

### #5 paulhorth

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Posted 19 April 2011 - 08:25 AM

Greg,

You are right, it is more rigorous to calculate the flow from one orifice plus one ruptured tube. My proposal to use an orifice and take double the flow is quicker and more conservative (and was also quicker to describe in my post!). In my experience, there is not much reduction in flow when you do it the other way, so it won't make a lot of difference if any for the outlet piping (which comes in finite steps of size anyway) but by all means make the calculation to check if this is true.

On the subject of outlet piping, the sizing approach which we have discussed is suitable for liquid service. For gas service there is an alternative approach, where the rupture disc carrier is like a blowdown orifice taking most of the pressure drop, and seeing critical velocity, while the tailpipe downstream is sized for the usual criterion of 0.7 Mach and so is larger than the rupture disc. This is assumed in the British rupture disc standard BS 2915. In all cases the piping should be checked for slugging forces if liquid is followed by gas or two-phase flow. Erosion velocity can be tolerated since the flow is hopefully short-term.

Paul