I. Introduction Water pipelines refer to the system that transports water from the source to the treatment plant or from the treatment plant to the distribution network. Due to the wide coverage and high-pressure nature of the water supply system, ensuring their safe operation has always been a priority for the water industry and design departments. Common accidents include pipe bursts and explosions, which are typically caused by factors such as temperature stress, pipe quality, construction defects, geological conditions, and water hammer. While air pockets themselves do not directly cause water hammer, they can lead to damage through its effects. This article explores how to properly install air vents on water pipelines to prevent gas accumulation that could form dangerous air pockets. II. Examples and Analysis In hilly areas, it is standard practice to install air vents at the highest points of the pipeline. However, in actual operations, many pipe bursts occur not at the high points but after bends or even in low-pressure sections. A notable example is the city of Hegang in Heilongjiang Province. The city is located in a hilly region, with a water purification plant and pumping station situated 5 km apart. Water flows from the plant to the pumping station via gravity, with the purification plant at an elevation of 210 meters and the pumping station's clear pool at 185 meters. A DN800 cast iron pipe carries water at an average flow rate of 1.0 m/s. Despite the installation of an air vent at the highest point (50 meters from the pumping station), multiple pipe bursts occurred. Later, additional vents were installed near the burst locations, and since then, no further bursts occurred between the two sets of valves. Only one burst was reported within 10 meters of the new vent. This clearly shows that the presence of air pockets is closely related to the occurrence of pipe bursts, as the problem disappeared after proper venting. III. Formation Process of Air Pockets and Stress Conditions Under normal operating conditions, water flow in a pipeline can be considered steady (with constant pressure, flow rate, and temperature). In this state, any air present in the water gradually rises due to buoyancy, forming bubbles of varying sizes. These bubbles move along the pipeline with the water flow. In uphill sections, the buoyant force may cause the bubbles to rise faster than the water flow. Due to the roughness of the pipe wall, small bubbles tend to remain dispersed rather than merging into larger ones. As the bubbles reach the highest point, some are discharged through the vent, while others continue downstream. Turbulence and flow characteristics allow some small bubbles to pass through the vent and move further along the pipeline. The movement direction of these bubbles is opposite to the vertical component of the buoyancy force. This resistance slows the bubble’s movement, causing subsequent bubbles to collide and merge into larger ones. Larger bubbles generate greater buoyancy, increasing the risk of forming dangerous air pockets. The buoyancy force acting on a bubble is given by: P₁ = P sin α Where: P = Buoyancy force of the bubble (P = 1/6 π d³ · ρ) ρ = Density of water d = Diameter of the bubble α = Angle of inclination The pressure exerted by the water flow is calculated as: P' = V² / (2gS) Where: V = Flow velocity (m/s) g = Acceleration due to gravity S = Cross-sectional area of the bubble When P₁ = P', the bubble remains in equilibrium within the pipeline. From the relationship between the bubble diameter and the slope angle, we find that under steady flow conditions, the bubble size is inversely proportional to the sine of the slope angle. If d·sinα > C, the bubble will rise. IV. Shape of Air Pockets in the Pipeline While the previous analysis assumes spherical bubbles, in reality, when bubbles grow large enough to accumulate against the pipe wall, they take on a semi-elliptical shape due to surface tension. As they grow, their shape becomes influenced by the water flow, gravity, and pipe geometry, often elongating along the length and arching across the width. Simulations suggest that the length L of the air pocket is approximately 15 times its height h. V. Analysis of Air Pocket Forces and Critical Positions According to hydraulic principles, the thrust experienced by an air pocket in the pipeline is equal to the pressure acting on the cross-section perpendicular to the flow. This creates a "bow" shape with a certain height, leading to potential stress concentrations. Rapid valve switching or pump start-stop events can cause sudden pressure surges, compressing the air pocket and creating high stress that may lead to pipe bursts. Research indicates that when the height of the air pocket reaches one-quarter of the pipe diameter, it becomes a critical risk point. For a DN800 pipe with a flow rate of 1.0 m/s, the thrust can be calculated using the formula: P’ = V² / (2gS) Using this, the pressure exerted on the air pocket is found to be around 5.124 kg. Comparing this with the buoyancy force, we find that the angle α is approximately 2.92 degrees, which aligns with observed burst locations. VI. Conclusion 1. Additional air vents must be installed on descending slopes, with positions determined based on the equation P’ = P sin α and appropriate flow rates. 2. If the actual slope angle is less than calculated, the vent should be placed at the intersection of the curved line and the straight slope. 3. To ensure early gas discharge and prevent air pocket formation, vents should be installed at the junctions of bends and straight sections. 4. This study confirms that air vents cannot replace the main vent at the highest point of the pipeline.

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