DLF calculation using PSV module

There are three rupture discs mounted on an equipment as shown in attachment titled as "picture.pdf".
The process data sheet is also attached titled as "data sheet.pdf".
Using relief load synthesis module we have worked out forces and the exit velocity. (Here we got higher flow rate than the one given in data sheet for liquid service.)
Refer file "liquid_1".pdf
Using this exit velocity we have worked out the time for pressure wave to travel upto exit. The minimum of three pipe lengths , i.e. 13 m is considered. We get a pressure ramp time of 0.5 sec . We have worked out a DLF based as shown in attachments "profile.pdf" and "dlf.pdf."
We run modal to get minimum frequency. For that frequency we worked out DLF . It is around 1.2
Since we are doing static equivalent analysis , modeled the force calculated from "liquid_1.pdf"by applying DLF of 1.2
Force applied at exit 45 deg bend.
Is this approach logical ?
Regards,
bag_piper

DLF of 1.2 is correlated with the pressure ramp you've considered, but I don't understand the pressure ramp time of 0.5 sec is an assumption or it is a result of calculation?

The ramp up time is worked out based on the time taken for pressure wave to reach the exit of pipe. The length from the rupture location to pipe end is 13 m as mentioned above. The velocity is 25.6 m /s . Hence distance divided by velocity works out to time = 0.5 sec. This way the ramp time is worked out.Is this method of working out ramp time correct ? we had apprehensions and hence the topic is put in discussion forum.
regards,
bag_piper

Let's try with a more familiar example. I use a whistle and I'm able to "ramp a signal up" in 0.2 seconds. You are at 700 m distance and you can hear the signal in about 2 seconds. Do you expect to receive my signal as 2 seconds gradual increase in loudness?

In your example, PSV has a dynamics between set pressure (when it opens) to set pressure+ overpressure (when it is fully opened) and this fact generates a perturbation which travels with a specific velocity to the opened end of piping. Ideally the perturbation will reach that point in the same "shape" as it was generated; in case the dispersion is important that shape will be modified. For gases the theory is far more complicated and has been developed by Helmholtz, Kirchhoff, Rayleigh and many others.

In short ,is there a method to work out the time required for force to reach maximum value of 5493 N ,from zero ? Also how to work out the time when force will remain stable and time taken to diminish ?

We were trying to work out the DLF .

Regards,
bag_piper

In fact you cannot do it accurately.
You can presume the dynamics of reaction force has the same ramp up time as the PSV.
To the second question, the time when PSV is fully opened depends on the quantity to be released- probably you'll never know it.

IMO opinion, you are not on a conservative approach and the question is why you try to avoid a DLF of 2 or a DLF established by a zero ramp-up?