Fluid Forces in Piping Systems

Stress calculations are essential to piping system design, but stress calculations are only as accurate as their input driving forces. Force calculations are complex for static systems, and fluid systems are rarely static. Further, a transient acting on the fluid (valve closure, pump trip, check valve slam, etc.) creates pressure and velocity waves which directly impact the load on the pipe. These waves similarly affect momentum and frictional losses as flow through the pipe changes, impacting forces further.

**Problem:**

The complexity of calculating forces due to fluid transients leads to simplified methods that can severely miscalculate the force. Often, pressure is considered the dominant driver of force considered in these analyses, an overly simplified approach which neglects real physical effects internal to the pipe. As with most fluid transient analyses, engineers should not speculate on whether such simplifications are acceptable for their system.

**Calculation Method:**

Incomplete methods may generate misleading or incorrect force values. Remove all doubt by computing the true force with the Acceleration Reaction Method for any liquid or gas piping system. Learn about the Acceleration Reaction Method and see how it is not difficult to utilize if the results of a transient fluid simulation are available.

**Authors: Scott A. Lang, PE and Trey W. Walters, PE**, Applied Flow Technology, USA; Presented at the ASME PVP Pressure Vessels & Piping Conference, July 2022

ABSTRACT

Changes in the operation of piping systems – like valve closures or pump starts – propagate pressure waves that travel at acoustic velocity throughout the fluid. These pressure waves have considerable effect on forces, potentially generating dynamic loads upwards of 10,000 lbf (50 kN) in common configurations. Some estimation methods used in industry for estimating transient forces neglect terms that may be important in some cases. Calculating forces due to these transients without simplification for transient liquid or gas flow is presented here in detail.

CONCLUSION

The authors have seen numerous erroneous reaction calculations. Often, the incomplete Endpoint Pressure Method is used due to its apparent simplicity. To be emphatically clear: the Endpoint Pressure Method is very often incorrect in realistic situations, and the authors do not recommend its use under any circumstances. The complete Acceleration Reaction Method presented here is not excessively difficult to utilize if the results of a transient fluid simulation are available. Instead of speculating on the importance of the correct force, the fundamental approach is recommended for any liquid or gas piping system.

ABSTRACT

Part 1 of this series discussed in detail how to accurately calculate the reactions induced by pressure transients that travel at acoustic velocity in either liquid or gas piping systems. Part 2 applies these methods to a variety of realistic examples to further illustrate their use and to demonstrate areas in which traditional or simplified methods may impart significant error.

CONCLUSION

Calculating transient forces on a piping assembly may at first glance appear to be a straightforward task. However, the complexities of control volume definition, accurate bookkeeping of signs, and challenging determination of some transient terms creates complication. This complication leads some engineers to use methods such as the Endpoint Pressure Method as an attempt to streamline the problem. Unfortunately, this method is incomplete, and in some cases dramatically misestimates the force values. Determining the true forces may be accomplished by careful application of Newton’s Second Law. The authors strongly recommend the use of the Acceleration Reaction Method described herein, even for simple systems. Without taking the time to make this calculation, the engineer can never be sure if the force values from an incomplete method are valid.

*Below is an excerpt from Part 1: Fundamentals. Use the links above to view the full papers. *

**1. INTRODUCTION**

**1.1 Motivation**

Many advanced techniques exist for determining stress and strain on piping systems. Safe use of these tools is only possible if the driving forces are determined accurately. Force calculations rapidly become complex even in static systems and fluid systems are rarely static. Pressure is often considered the dominant driver of force and thus the only effect of interest, an overly simplified approach which neglects real physical effects.

Fluid transients make the situation even more complex. Sudden changes in system operation – like valve closures or pump starts – propagate pressure waves throughout the entire system which directly impact the load that must be carried by piping. Pressure waves are strongly coupled to velocity waves, which means momentum and frictional losses are also transient. These must all be considered for a full representation of transient force.

The complexity of calculating forces due to fluid transients has led to, at worst, the effect being neglected entirely or being handled by simple correction factors. Even those aware of the transient nature often consider only pressure terms. In some cases, such simplifications are reasonable, but in other cases the simple approach considerably miscalculates the actual forces. Beyond the desire of the design engineer to avoid excessive stresses, limits for occasional loads are specified in standards such as ASME B31. ASME B31.1-101.5.1 specifically indicates that loads due to fluid transients shall be considered [1]. Similar statements are made in ASME B31.3 and B31.4 [2] [3]. To ensure the code is met, a method with high confidence should be used.

**The authors are of the opinion that, as with most fluid transient analyses, engineers should not speculate on whether such simplifications are acceptable for their system and should instead remove all doubt by computing the true force with the method outlined herein.**

**1.2 Historical Background**

The fundamentals that will be discussed here are not new. In fact, the approach taken is entirely based on simple principles such as Newton’s Laws. Applying these laws correctly to an assembly of piping under transient conditions has, however, not been adequately described in a plain manner to the knowledge of the authors.

Discussion of component reactions due to specific effects, such as the reaction due to flow around a bend, or shear due to wall friction, can be found in nearly any introductory fluids textbook [4]. These cases are often considered in academic isolation, making application in the field challenging. Great care must be taken to maintain a consistent system of forces and account for all terms of interest – something introductory texts do not cover.

A true accounting of the transient force must consider all transient terms, not just component forces that exist at the control volume boundaries. Across an acoustic, mass flows are not equal, and the temporal effect must be considered. Accounting for these transient behaviors is a complicated step often omitted from a typical analysis but is not a new concept; the method was noted in some detail in [5]. Unfortunately, the theory found in [5] was used primarily to develop a simple estimation, which can introduce significant error [6].

One of the most common approaches to calculating transient forces is to first determine accurate transient flow results and then simply use transient pressures at the control volume boundaries multiplied by local flow areas to determine boundary component forces. The overall reaction force is calculated as the sum of these boundary component forces. While well-intentioned, using endpoint pressures only is effectively a steady-state approach taken at every step because it neglects terms such as the acceleration of fluid within the control volume or behavior of the fluid through devices.

**1.3 Assumptions**

The approach outlined here is not without assumptions of its own. Most importantly, deformation of piping is not considered – the entire assembly is assumed to be completely rigid.

Results can therefore be regarded as the reaction forces required to keep a piping assembly in place. Specific reactions at supports can be determined for statically determinant systems. The presented method serves only to determine the overall reaction – effects of determinacy or deformation are out of scope.

External elements such as heavy valve stems, pump skids, or wind are not considered. Forces due to thermal expansion, multi-phase flows, or other complex fluid dynamics are also neglected.

Flow and all related parameters within the piping are considered in a one-dimensional context. That is, pressure, velocity, or any other parameter, are considered averaged values throughout the cross-section of flow.

**1.4 Numerical Examples**

The examples discussed in Part 1 are intentionally simple in nature and serve only to enhance discussion on the theory and method behind the force calculation. For more in depth examples and results, see Part 2 [7].

**1.5 Reactions vs. Forces on a Piping Assembly**

This paper is focused on the determination of reaction forces on a piping assembly. These are forces required to keep a system from moving, which must be provided by external supports – for example, a reaction due to a mass on a surface is the normal force acting upward to counteract weight. Piping stress analysts may be concerned with the net force acting on a piping assembly – which is equal in magnitude but opposite in sign to the reaction.

*Use the links above to view the full papers. *

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