Rigid Water-Column Theory in Water-Hammer Problems

1964 ◽  
Vol 86 (3) ◽  
pp. 583-588 ◽  
Author(s):  
Ignacy Swiecicki
Keyword(s):  
Water Column ◽  
Pressure Rise ◽  
Water Hammer

Equations and charts for solving pressure-rise problems by the rigid water-column theory are presented with an example of their application. These are compared with the elastic water-column theory and the merits of both are discussed.

scholarly journals Pressure generated at the instant of impact between a liquid droplet and solid surface

2018 ◽  
Vol 5 (12) ◽  
pp. 181101 ◽  
Author(s):  
Y. Tatekura ◽  
M. Watanabe ◽  
K. Kobayashi ◽  
T. Sanada
Keyword(s):  
Solid Surface ◽  
Shape Factor ◽  
Liquid Droplet ◽  
Pressure Rise ◽  
Propagation Speed ◽  
Spherical Shape ◽  
Water Hammer ◽  
Droplet Impact ◽  
Maximum Pressure ◽  
The Impact

The prime objective of this study is to answer the question: How large is the pressure developed at the instant of a spherical liquid droplet impact on a solid surface? Engel first proposed that the maximum pressure rise generated by a spherical liquid droplet impact on a solid surface is different from the one-dimensional water-hammer pressure by a spherical shape factor (Engel 1955 J. Res. Natl Bur. Stand. 55 (5), 281–298). Many researchers have since proposed various factors to accurately predict the maximum pressure rise. We numerically found that the maximum pressure rise can be predicted by the combination of water-hammer theory and the shock relation; then, we analytically extended Engel’s elastic impact model, by realizing that the progression speed of the contact between the gas–liquid interface and the solid surface is much faster than the compression wavefront propagation speed at the instant of the impact. We successfully correct Engel’s theory so that it can accurately provide the maximum pressure rise at the instant of impact between a spherical liquid droplet and solid surface, that is, no shape factor appears in the theory.

scholarly journals Impact pressure on an orifice plate by a rising water column driven by an air pocket in a vertical riser

2020 ◽  
Vol 81 (5) ◽  
pp. 1029-1038 ◽  
Author(s):  
Yu Qian ◽  
David Z. Zhu
Keyword(s):  
Water Column ◽  
Peak Pressure ◽  
Current Model ◽  
Strong Relationship ◽  
Water Hammer ◽  
Orifice Plate ◽  
Minor Effect ◽  
Initial Water ◽  
Air Pocket ◽  
Riser Height

Abstract Occurrences of storm geyser events have attracted significant attention in recent years. Previous studies suggest that using an orifice plate can reduce the intensity of a geyser event but may induce a water-hammer type of pressure on the orifice plate. This study was conducted to explore the factors that influence the pressure transients when an orifice plate was installed in a vertical riser. A novel model was developed to simulated the movement of a rising water column driven by an air pocket in a vertical riser with an orifice plate on the top. Water-hammer type of pressure occurs when the water column reaches the orifice plate. The current model accurately simulates the dynamics of the water column considering its mass loss due to the flow along the wall of the riser (film flow) and the existence of the orifice plate. It was found that the initial water column length and the driving pressure, as well as the riser material, have a strong relationship with the peak pressure. The riser diameter and riser height have minor effect on the peak pressure. The water-hammer induced peak pressure reaches the maximum when the orifice opening is around 0.2 times the diameter of the vertical riser.

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.

Analysis of Passive Water Hammer

1999 ◽  
Author(s):  
Syed M. Husaini ◽  
Asif H. Arastu ◽  
Riyad Qashu
Keyword(s):  
Flow Velocity ◽  
Water Column ◽  
Power Plants ◽  
Cold Water ◽  
Water Hammer ◽  
Saturated Water ◽  
Pipe Segment ◽  
Pressure Surge ◽  
Active Flow

Abstract This paper presents a methodology for the calculation of the severity a type of water hammer called “passive water hammer”. The passage of a cold water column followed by hot saturated water through a restricting orifice causes a reduction in flow velocity and a corresponding increase in pressure. The term passive water hammer was given to this mechanism because there is no active flow intervention required for its initiation. This type of water hammer has been observed in heater drain systems of power plants. An example is given for the calculation of pressure surge and pipe segment forces due to this mechanism.

Water Hammer in Pipes, Including Those Supplied by Centrifugal Pumps: Graphical Treatment

1937 ◽  
Vol 136 (1) ◽  
pp. 245-331 ◽  
Author(s):  
Robert W. Angus
Keyword(s):  
Integration Method ◽  
Pressure Rise ◽  
Water Hammer ◽  
The Other ◽  
Mathematical Treatment ◽  
Centrifugal Pumps ◽  
Slide Rule ◽  
Arbitrary Rule ◽  
The Subject ◽  
Fundamental Equations

The damage done to pipes as a result of water hammer is so serious that no engineer can afford to neglect it in the design of long pipes, particularly those under low heads. Unfortunately the problem has appeared to many to be very intricate, and indeed the mathematical treatment is so involved and so lengthy that few practising engineers would attempt to solve water-hammer problems mathematically. In many cases a purely arbitrary rule has been employed in finding the pressure rise, with little knowledge on the part of the engineer as to whether the formula fits his case or not, and thus much money may be wasted on too heavy a line, or, on the other hand, it may be so light as to be dangerous. In the following treatment of the subject, the rigid theory has first been explained and some problems have been solved, but most of the paper deals with the elastic (and correct) theory. A problem is first worked out by the arithmetical integration method in order to establish ideas and to make the subsequent argument clear. The fundamental equations giving rise to Allievi's equations must be clearly understood for a grasp of the true relationships that exist, and these have been treated in some detail, but it is safe to say that if the argument has been followed up to the end of the general equations, no difficulty will be experienced with the graphical treatment. In explaining the diagrams, very simple cases are first dealt with and the elegance of the method will make an appeal at once. The water-hammer pressure can be found for any simple pipe, and at any point on the pipe, and for any chosen gate movement, and results can be obtained with accuracy in less than thirty minutes in simple cases. For compound pipes, the solution is nearly as rapid. The pressures arising in the discharge lines from pumps have been fully discussed in the case of pumps with small inertia, and also in cases in which the inertia is large enough for consideration, when an existing pump has been employed to supply the data used. The accuracy of the method is beyond question; where intersections are at small angles the exact points are hard to determine, but this trouble may easily be avoided by changing the scales. If a slide rule is used in solving the problem mathematically the corresponding case will be encountered.

Charts for water hammer in low head pump discharge lines resulting from water column separation and check valve closure

1984 ◽  
Vol 11 (4) ◽  
pp. 717-742 ◽  
Author(s):  
Eugen Ruus ◽  
Bryan Karney ◽  
Farouk A. El-Fitiany
Keyword(s):  
Water Column ◽  
Pressure Rise ◽  
Check Valve ◽  
Pressure Head ◽  
Maximum Pressure ◽  
Valve Closure ◽  
High Point ◽  
Column Separation ◽  
Discharge Line ◽  
Low Head

Maximum pressure head rises resulting from water column separation and check valve closure are calculated and plotted for a simple low head pump discharge line with one well-defined high point. Basic parameters such as pipeline constant, pipe wall friction, complete pump characteristics, pump inertia constant, and the relative location of the high point are accounted for in the analyses. The results of this paper can be used to determine (a) when water column separation is expected, (b) how to avoid water column separation, and (c) the necessary wall thickness in cases where no protection against water column separation is provided. Computer studies indicate that both the vertical and horizontal location of the high point as well as the pipe friction, the pipeline constant, and the pump inertia have a major effect on pressure head rises. Water column separation does not always constitute a danger to the pipeline. Key words: waterhammer, water column separation, check valve closure, pressure rise, pump discharge line, chart.

Charts for Determining Size of Surge Suppressors for Pump-Discharge Lines

1961 ◽  
Vol 83 (1) ◽  
pp. 43-45
Author(s):  
Carl W. Lundgren
Keyword(s):  
Water Column ◽  
Water Hammer ◽  
Column Separations

Surge suppressors are often used for the control of water-hammer pressures which occur in pump-discharge lines subsequent to power interruptions. This paper includes charts for determining the size of the required suppressors when water-column separations do not occur.

Effect of multi-valve closure on superposed pressure in a tree-type long distance gravitational water supply system

2019 ◽  
Vol 68 (6) ◽  
pp. 420-430
Author(s):  
Xingtao Wang ◽  
Jian Zhang ◽  
Xiaodong Yu ◽  
Sheng Chen ◽  
Wenlong Zhao ◽  
...  
Keyword(s):  
Water Supply ◽  
Pressure Rise ◽  
Water Hammer ◽  
Supply System ◽  
Water Supply System ◽  
Maximum Pressure ◽  
Valve Closure ◽  
Long Distance ◽  
Maximum Water ◽  
Tree Type

Abstract Valves are installed at the end of each branch pipeline in a tree-type long distance gravitational water supply system to regulate flow. However, the sequential closing of all valves may cause a tremendous superposed pressure rise, even larger than the pressure rise under simultaneous valve closure. In this paper, the effects of sequential valve closure on the superposed maximum water hammer pressure rise in a pipeline were investigated. By using the wave superposition principle, a sequential valve closure formula leading to maximum water hammer was proposed and verified using numerical simulation based on a practical project. In addition, the superposed maximum pressure rises in the pipeline were compared under single, simultaneous and sequential valve closure, respectively. The results show that the sequential valve closure formula agrees well with the numerical results and the pressure rise in the pipeline under the sequential closing was the largest. Moreover, compared with the superposed maximum pressure rises at the main pipeline, the effect of sequential valve closure on superposed maximum pressure rise at the branch pipeline is more sensitive.

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