Fluid Pressure in Piping

8/8/2019 Fluid Pressure in Piping

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FLUID PRESSURE IN PIPING

BY : SH. M . G. CHOUDHURY - VICE PRESIDENT PIPING

E-MAIL : [email protected]

SH. ANINDYA BHATTACHARYA ( ASSTT. MANAGER )


SH. HIMANSHU VARSHNEY ( ASSTT. MANAGER )


FLUID PRESSURE IN PIPING

1.0 INTRODUCTION :

Pipes are used for transporting fluid. The pipes have to contain the internal pressure of the fluid which

also travels at certain velocity as required by the specific application .This generates various stress and

strain in piping. The present article will deal with the effect of fluid pressure in detail with reference to

specific problems and particularly the effect of longitudinal pressure stress in piping systems. This is so

required as the circumeferential stress popularly known as HOOP STRESS is well documented in Code

and widely used by piping engineers but not much information is available on the effects of the

longitudinal stresses. The longitudinal stress also leads to some problematic situation and thorough

understanding of this mechanism is necessary.

2.0 PRESSURE EFFECT ON CURVED SURFACE :

The distribution of longitudinal and circumferential stresses in a pipe element can be shown from the

stand point of static equilibrium as :

Longitudinal Stress = PD / 4t

Circumferential Stress (Hoop Stress ) = PD / 2t

Where : P = Internal Pressure In the Pipe

D = Internal Diameter of the Pipe.



The above formula , Piping engineers use extensively and is given in Code in slightly modified form for

calculating pipe wall thickness.

3.0 GENERAL :

The Longitudnal Stress being part of sustained Stress condition is additive to other sustained stress suchas due to weight . Now Longitudnal force / Stress transfer sometimes involves lot of problems where

Expansion Bellows are involved .

In this chapter this specific problem will be investigated with reference to the use of Rubber Expansion

Bellows in water transfer systems.

4.0 CASE STUDY :

a) HYPOTHETICAL CASE :

First a hypothetical case is undertaken. Two systems are considered.Both are identical piping system and

pumping fluid like cooling water . However one has no Expansion Bellow and the other has a singleconvolution Rubber Expansion joint . For Rubber Expansion joint there will be three cases one with four

nos. 36 mm dia. Tie rods in loose condition , the other with tie rods loose but anchor immediately after

bellow and the other with tie rods in tightened condition specifically for the the outer nuts. The four cases

are given in sketch nos. I , II , III , IV. All the four sketches show the free body diagram of the piping

system . Some approximations have been adopted , like square corner approximation , non consideration

of eddy forces along diametrical plane of the elbows, no continuity restoration moments etc.

4.1.1. SKETCH - I ( NO BELLOW SYSTEM ):

The piping System is at static balance with the pressure forces at elbow being transmitted through the pipe

wall as longitudinal stress. This is the most common situation in piping and there is longitudinal strain in

piping. But the longitudinal strain in the present loading condition will be very minimal say less than

2.0mm for the 20 mtr. Leg. No thrust block or anchor etc. are required . Now this concept needs further

elaboration. There will be strain in the system. For example the 60 mtr. Leg will have longitudinal strain

of around 5 mm. These strains will actually generate some moments as the strain on one leg is actually a

cantilever deflection at the other leg and at the elbow end there will be end rotation moment to maintain

continuity of structure. A thrust block or a proper anchor could be provided at the elbow that would

eliminate this small value of longitudinal strain and rotation. However this is not necessary and in

traditional analysis packages also where all the forces, moments and stresses are derived from strain

values the longitudinal strain effects are generally ignored.

4.1.2 SKETCH – II ( BELLOW WITH LOOSE TIE ROD )

The free body diagram for the pressure thrust effect is drawn. The ( P.A - Kδ ) unbalanced force will

generate moment on the cantilever arm . The solution for δ will generate this equation.

δ = ( P.A - Kδ ) L3

/ 3 EI .

http://sketch-1.tif/







Solution of this equation will give the value of δ deformation. Following are the additional no-

menclature.

δ = Bellow elongation.

I = Moment of inertia of the pipe.

E = Modulus of elasticity.

K = Bellow stiffness in longitudinal direction.A= Cross sectional area of pipe

L = Lever arm. ( 60 mtr. In this direct case)

P= internal pressure in the pipe

Solving this equation will give quite a large value of δ as the stiffness of a rubber expansion bellow (K)

is very small. The bellow will deform and the 60 mtr. pipe arm will move. Solving the equation will

give a very high value of deflection leading to the failure of the bellow. The moment generated on the 60

mtr. leg of the piping will generate a large bending stress. So this is a wrong installation. The solution

for δ assumes frictionless support or weightless pipe. Comprehensive analysis will also show high δ

value leading to bellow failure.

4.1.3 SKETCH – III ( WITH LOOSE TIE RODS BUT ANCHOR IMMEDIATELY AFTER

BELLOW)

At this situation the pressure thrust is totally taken at the anchor. Now if we consider an anchor of

infinite rigidity then the free body diagram for pressure thrust effect will look like as shown in Sketch

III.

This is a very ideal case of use of rubber expansion bellows. The thrust effect will be completely taken

by the anchor. Any thermal effect or vibration effect will be isolated. However it has been seen that

normally there is a large thrust value for installion with rubber bellows and these require to be designed

upstream. As an example in the case of a Condenser Circulating Water System these thrust values

were taken care of while designing of the pump house itself. That means proper anchor with the

consequent loading was considered in the design of the pump house itself. Absence of a properly

anchor designed a can result in problems afterwards.

4.1.4 SKETCH – IV ( BELLOW WITHOUT ANCHOR BUT TIGHTENED TIE RODS )

In this case there are 4 nos. of 36mm bolts. The force gets transmitted as longitudinal stresses through

the pipe wall and longitudinal strain will be the sum of the strain due to the piping portion and the

strain due to the bolt portion. Theoritically the large diameter bolts can take the tensile loads of the

system. This system should be alright without anchors. This system will be identical as that of the

piping system without the rubber expansion bellow. However problems at different times occur with this

type of installation. This is because of the following reasons:

The tie rod are strong in tension but considerably weak in any other conditions of loading such as moment

or torsion. The installion will not have an inherent fail safe rigidity and malfunctions are known to occur

in various cases because of improper tie rods, non uniform tightening of bolts , thick soft washers beingused by mistake etc. One of the examples of failure due to improper installation is that at the Patalganga

Captive Power Station. There the bellows with proper tie rods were theoretically alright , but failed due to

improper installation and afterwards the bellows were removed and the system is running ok for the past

9 years. However there are installation of pumping systems with rubber bellows where no failure has been

observed.

4.1.5 ACTUAL CASE - SKETCH – V










An actual case as presently encountered in an installation is shown. No proper design of anchor

was done upstream of the project. This installation has lined pipe. This installation will run alright with

I type of piping. The bellows can be removed with a spool. The spool can be first punchmarked and then

lined and fitted up . The system will also run with proper anchor being put in around the location of first

elbow which is basically of case III type. The inner nut will definetely be kept loose . Case II type

installation will lead to problem. Case IV type installation with tightened outer nut bellows but withoutanchor is not recommeneded in this case as with this type of configuration of the piping there will be

possibility that the tie rod bolts will be subjected to loading conditions other than tensile loads. In this

case the solution was done based on case III type approach.

5.0 CONCLUSION

The example of Water System which has been given earlier is better to be designed without bellows.

But whenever large diameter pipes are encountered such as normally seen in Power house Condenser

Cooling water system use of Bellows is recommended and anchor support design should be considered

in

the pump house design itself. Although theoretically alright the tie rod load transfer may fail due to

improper installation and is not a recommended solution.

6.0 ATTACHEMENTS:

Sketches I, II, III, IV, V, VI.

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Fluid Pressure in Piping