Dear Piyush,
Here I give a sample Force Time History for slug flow problems:

Solution to slug flow problems can be obtained by first carrying out the two-phase flow(thermal) analysis and then pipe stress (dynamic) analysis.
In two-phase flow analysis , the flow pattern may be predicted from the correlations proposed by Baker[Oil Gas J.,53-12,185-190,192,195(1954)] as shown in fig. 1 . These flow regimes can be obtained by generating Baker Charts for all the piping segments. Further two-phase flow analysis is carried out only for the segments where slug formation is predicted by Baker chart.
Two-phase flow analysis must further be extended to get liquid slug length, gas length and liquid slug velocity.
Unbalanced force due to Slug impact is equal to change in momentum with respect to time. It can be calculated by the formula :
F = dp/dt = rho. sq.V . A [(1- COS theta)/2]1/2
Where rho– Fluid Density
V – Slug Flow Velocity
A – C/S Area
theta– Bend Angle
Duration of loading(TL) can be obtained by dividing the liquid slug length by liquid slug velocity.
Rise time(TR) and fall time(TF) are difficult to calculate and are generally assumed.
These parameters would be sufficient to get the Force-Time History for single occurance. In order to include the second occurrence of slug loading calculate the periodicity of slug.
Periodicity of slug(TP) can be calculated by dividing the “length of liquid slug + gas length” by slug velocity.
A sample time History is given here for proper understanding of the subject.


GAS LENGTH = 0.072 * 90/10 = .648 m
DURATION OF LIQ SLUG = 0.072/13.75 = 0.0052 Sec=5.2ms
PERIODICITY OF SLUG=(0.072+0.648) /13.75=0.052 Sec=52 ms


0 (0) 0
0.52(0.52) F
5.72(0.52+5.2) F
6.22(0.52+5.2+0.52) 0
52 0
52.52 F
57.72 F
58.24 0

Navendu Shrivastava