When the Joukowsky Equation Does Not Predict Maximum Water Hammer Pressures

2019 ◽  
Vol 141 (6) ◽  
Author(s):  
Trey W. Walters ◽  
Robert A. Leishear
Keyword(s):  
Pipe Wall ◽  
Water Hammer ◽  
Wall Material ◽  
Reflected Waves ◽  
First Approximation ◽  
Fluid Transient ◽  
Fundamental Goal ◽  
Maximum Water ◽  
Frictional Effects

Abstract The Joukowsky equation has been used as a first approximation for more than a century to estimate water hammer pressure surges. However, this practice may provide incorrect, nonconservative, pressure calculations under several conditions. These conditions are typically described throughout fluid transient text books, but a consolidation of these issues in a brief paper seems warranted to prevent calculation errors in practice and to also provide a brief understanding of the limits and complexities of water hammer equations. To this end, various issues are discussed here that result in the calculation of pressures greater than those predicted by the Joukowsky equation. These conditions include reflected waves at tees, changes in piping diameter, and changes in pipe wall material, as well as frictional effects referred to as line pack, and the effects due to the collapse of vapor pockets. In short, the fundamental goal here is to alert practicing engineers of the cautions that should be applied when using the Joukowsky equation as a first approximation of fluid transient pressures.

When the Joukowsky Equation Does Not Predict Maximum Water Hammer Pressures

2018 ◽  
Author(s):  
Trey W. Walters ◽  
Robert A. Leishear
Keyword(s):  
Pipe Wall ◽  
Water Hammer ◽  
Wall Material ◽  
Reflected Waves ◽  
First Approximation ◽  
Fluid Transient ◽  
Fundamental Goal ◽  
Maximum Water ◽  
Frictional Effects

The Joukowsky equation has been used as a first approximation for more than a century to estimate water hammer pressure surges. However, this practice may provide incorrect, non-conservative, pressure calculations under several conditions. These conditions are typically described throughout fluid transient text books, but a consolidation of these issues in a brief paper seems warranted to prevent calculation errors in practice and to also provide a brief understanding of the limits and complexities of water hammer equations. To this end, various issues are discussed here that result in the calculation of pressures greater than those predicted by the Joukowsky equation. These conditions include reflected waves at tees, changes in piping diameter, and changes in pipe wall material, as well as frictional effects referred to as line pack, and the effects due to the collapse of vapor pockets. In short, the fundamental goal here is to alert practicing engineers of the cautions that should be applied when using the Joukowsky equation as a first approximation of fluid transient pressures.

Comparison of Experimental to Theoretical Pipe Strains During Water Hammer

2006 ◽  
Author(s):  
Robert A. Leishear
Keyword(s):  
Hoop Stress ◽  
Maximum Stress ◽  
Pipe Wall ◽  
Equations Of Motion ◽  
Water Hammer ◽  
Stress And Strain ◽  
Hoop Strain ◽  
Fluid Transient ◽  
Basic Equations ◽  
Experimental Strains

Experimental strains during water hammer were compared to theoretical equations for strain. These equations were derived from the basic equations of motion, which lead to equations for the hoop stress and hoop strain. In this particular case, a sudden pressure increase traveling in a pipe was measured, and the hoop strains resulting from this fluid transient were also measured. Measuring the strains at numerous locations along the pipe permitted comparison of the strains as a function of position with respect to the fluid shock wave. This comparison of strains at different positions along the pipe permits analysis of the vibratory nature of the strain in the pipe wall. Essentially, the equations of motion provide an approximate technique to find the maximum stress and strain due to water hammer.

Closure to “Analysis of PVC Pipe-Wall Viscoelasticity during Water Hammer” by A. K. Soares, D. I. C. Covas, and L. F. R. Reis

2010 ◽  
Vol 136 (8) ◽  
pp. 548-550
Author(s):  
Alexandre Kepler Soares ◽  
Dídia I. Covas ◽  
Luisa Fernanda Reis
Keyword(s):  
Pipe Wall ◽  
Water Hammer ◽  
Pvc Pipe

Finite Element Modeling of the Dynamic Response of a Steel Pipe During Water Hammer

2012 ◽  
Author(s):  
Juan C. Suárez ◽  
Paz Pinilla ◽  
Javier Alonso
Keyword(s):  
Finite Element ◽  
Wall Thickness ◽  
Pipe Wall ◽  
Element Model ◽  
Water Hammer ◽  
Steel Pipe ◽  
Dynamic Stresses ◽  
Rate Dependent ◽  
Simple Step ◽  
Von Mises

Water hammer imposes a steep rise in pipe pressure due to the rapid closure of a valve or a pump shutdown. Transversal strain waves propagate along the pipe wall at sonic velocities, and dynamic stresses are developed in the material, which can interact with discontinuities and contribute to an unexpected failure. Pressure increase has been modeled as a simple step front in a finite element model of a short section of a steel pipe. Boundary conditions have been considered to closely resemble the conditions of longer pipe behavior. The shock traveling along the length of the fluid-filled pipe causes a vibration response in the pipe wall. Dynamic strains and stresses follow the water hammer event with a certain delay, as is shown from the results of the FEA. Response of the material is strain rate dependent and dynamic peak stresses are substantially larger than the expected from the static pressure loads. Damping of the waves, neither by the material of the pipe nor by the interaction fluid-pipe, has not been considered in this simple model. Hoop, axial, radial, and Von Mises equivalent stresses have been evaluated both for the overshooting and the following phase of decompression of a pipe without discontinuities. However, dynamic stresses can be enhanced in the presence of discontinuities such as laminations, thickness losses in the pipe wall due to corrosion, changes in the wall thickness in neighboring pipe sections, dents, etc. These dynamic effects are able to explain how certain discontinuities that were reported as passing an Engineering Critical Assessment can eventually cause failure to the integrity of the structure. Deflections in the pipe wall can be altered by the welded transition from a pipe with a certain thickness to another with a smaller thickness, and wavelength changes of one order of magnitude can be expected. This can result in different approaches towards the risk assessment for discontinuities in the proximity of changes in wall thickness.

Charts for water hammer in pipelines with air chambers

1977 ◽  
Vol 4 (3) ◽  
pp. 293-313 ◽  
Author(s):  
Eugen Ruus
Keyword(s):  
Water Column ◽  
Pipe Wall ◽  
Water Hammer ◽  
Wall Friction ◽  
Low Resistance ◽  
Discharge Line ◽  
Air Chamber ◽  
Basic Parameters ◽  
Computer Studies

Upsurges and downsurges are calculated and plotted for a simple pump discharge line provided with an air chamber. Basic parameters such as pipeline constant, air chamber parameter, pipe wall friction, and orifice resistance are used. The results of this paper can be used to determine the necessary volume of the air chamber. Computer studies indicate that the assumption of the rigid water column and the concentration of pipe friction at the pump end of the pipeline yields reasonably good results at the pump end; however, because of these assumptions, large errors in estimation of both upsurges and downsurges occur at the midpoint and particularly at the quarter point of the pipeline. Pipe friction has a substantially different effect on surges than that of the orifice resistance; these two effects should therefore be considered separately. A differential orifice is recommended and considered; this orifice should have a low resistance to flow out of the chamber.

Application of a Dynamic Stress Theory to Pipe Leaks

2006 ◽  
Author(s):  
Robert A. Leishear
Keyword(s):  
Radioactive Waste ◽  
Failure Mechanism ◽  
Dynamic Stress ◽  
Water Hammer ◽  
Stress Theory ◽  
Fluid Transient ◽  
Cause Of Failure

Leaks in system piping used to transfer radioactive waste were attributed to water hammer. Ball valves leaked on several occasions and the cause of failure was not obvious. Facility records were used to determine the facility status at the time the leaks occurred. For one particular leak, valve manipulations controlling flow were shown to be coincident to the time of leak. The fluid transient pressures were calculated, and once the maximum pressures were established, the stresses on the equipment could be discerned. Water hammer was concluded to be the failure mechanism. To eliminate this failure mechanism, procedural and equipment modifications were made and further leaks have been eliminated.

Dynamic Pipe Stresses During Water Hammer: III — Complex Stress Relationships

2002 ◽  
Author(s):  
Robert A. Leishear
Keyword(s):  
Pressure Wave ◽  
Dynamic Stress ◽  
Pipe Wall ◽  
Three Dimensional ◽  
Complex Stress ◽  
Water Hammer ◽  
Dynamic Stresses ◽  
Vibration Theory ◽  
Pressure Spike ◽  
Fluid Transients

Complex three-dimensional dynamic stresses occur in a pipe following a water hammer event. Equations from vibration theory were adapted for use to describe the dynamic stresses at any point along the pipe wall. Hoop, radial, and axial dynamic stress equations are presented to approximate the stresses at a point on the pipe wall. Dynamic stress equations for beams and other simple shapes are also considered. The dynamic pipe stresses are affected principally by the types of water hammer waves or fluid transients, by the wave impacts at elbows or tees, and by the reflections of the waves from these elbows or tees. The three fluid transients considered are a moving step pressure wave, a ramp pressure, and a moving pressure spike. Approximate techniques are presented for evaluating the effects on piping due to the impingement of these transients on an elbow. For an equivalent pressure in a long pipe, application of the step pressure created the largest stress increases of the three transients considered. The vibration equations also prompt a solution to reduce water hammer effects. To this end, slow closing valves are frequently employed. Vibration theory may be applied to quantify the stress reductions afforded by these valves. Pipe stress equations may be manipulated to reduce pipe stresses for a linearly increasing, or ramp, pressure wave traveling along the pipe.

Deflected Stress Corrosion Cracks in the Pipeline Steel

2004 ◽  
Author(s):  
Robert Sutherby ◽  
Weixing Chen
Keyword(s):  
Stress Corrosion ◽  
Hoop Stress ◽  
Pipe Wall ◽  
Pipeline Steel ◽  
Maximum Shear Stress ◽  
Mechanical Damage ◽  
Wall Material ◽  
Corrosion Attack ◽  
Pipeline Steels ◽  
Pipe Surface

This research reports a special case of stress corrosion cracks (SCC) in the pipeline steels that had propagated in the direction deviated from the pipe radial direction. It was characterized that the cracks were intergranular in nature with relatively wide crack crevice. Most of crack being characterized consisted of two segments: a crack segment near pipe surface that is normal to the axis of hoop stress, and the subsequent segment that is inclined to the axis of the hoop stress. The segment near the surface was usually less than 1.5 mm long, and the inclined one was up to 10 mm in length. The angle of the inclined segment was dominantly in the range of 30° to 60°. To understand the mechanisms related to the deflected crack growth, the microstructure of the pipeline steels was studied. It was found that The pipeline steel is characterized with a sandwich-like microstructure, for which it is harder at the surface (∼ 1.5 mm thick) and progressively softer towards the center of the wall. This particular structure might have caused a complex loading condition to the pipe wall material such that yielding of the soft material become possible, particularly when crack has propagated into the soft region of the pipe wall. As a result, corrosion attack may take place in a direction consistent with the maximum shear stress, and cracking preceded by the concurrent interaction between corrosion attack and mechanical damage.

Charts for water hammer in pipelines resulting from valve closure

1980 ◽  
Vol 7 (2) ◽  
pp. 243-255 ◽  
Author(s):  
Eugen Ruus ◽  
Farouk A. El-Fitiany
Keyword(s):  
Pipe Wall ◽  
Pressure Head ◽  
Water Hammer ◽  
Wall Friction ◽  
Maximum Pressure ◽  
Valve Closure ◽  
Closure Time ◽  
Basic Parameters

Maximum pressure head rises, which result from valve closure according to (a) uniform, (b) equal-percentage, and (c) optimum valve closure arrangements, are calculated and plotted for the valve end and for the midpoint of a simple pipeline. Basic parameters such as the pipeline constant, relative closure time, and pipe wall friction are considered for closures both from partial as well as from full valve openings. The results of this paper can be used to draw the maximum hydraulic grade line along the pipe for these closure arrangements. It is found that the equal-percentage closure arrangement yields consistently less pressure head rise than does the uniform closure arrangement. Further, the optimum closure arrangement yields consistently less head rise than the equal-percentage one. Closures from partial valve openings increase the pressure head rise considerably and must always be considered.

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