# Water hammer equation pdf

Water hammer is a transient flow in pipes that was created by sudden changes of velocity in pipe lines. The equations of unsteady flow in pipelines and the method of characteristics solution to these equations are described. Normal water pressure runs between 30 and 55 psi pounds per square inch, and above this, the high pressure could be the source of water hammer. Dec 17, 2018 water hammer can also occur when the overall pressure of the main water pipe entering the building is too high. Preventing water hammer from damaging pumps and pipes. Water hammer calculator solving for valve closing time given pressure increase, flow velocity, inlet pressure and upstream pipe length. Wave speed for water, without presence of free air or gas, the more general equation to calculate the water hammer wave speed magnitude in onedimensional flows is watters, 1984. A water hammer is a pressure wave that occurs, accidentally or intentionally, in a filled liquid pipeline when a tap is suddenly closed, or a pump starts or stops, or when a valve closes or opens.

Water hammer is part of the larger subject of transient flow or surge analysis. Expressions for the wave speed in both an infinite fluid and in a thinwalled pipeline is presented. These equations are called the water hammer equations and they are the result of applying the conservation of mass and momentum to the wave. Surge calculation indicates hwhadvgc where a is the velocity of wave propagation, d is the inside pipe diameter, v is the change in velocity of the fluid, and gc. Jan 03, 2017 in this video the process of water hammer is explained and you are shown how to calculate the pressure rise using the joukowsky equation. Marshall long, in architectural acoustics second edition, 2014. The joukowsky equation for fluids and solids eindhoven university. Manual collection of surge tank volume and timing data. The normal sound of water moving through pipes is a steady, even sound. The latter occurs when condensate is allowed to accumulate in a. The water hammer equation assumes that liquid compression and pipe friction are negligible. Water hammer also known as hydraulic shock occurs in two distinct ways.

Water hammer analysis of pumping systems for control of water. Water hammer is a shock wave, usually generated by the rapid closure of a valve, but occasionally caused by a pressure. Water hammer is usually recognized by a banging or thumping in water lines. Though the joukowski equation s primary applicability is for a liquid velocity that drops to zero upon contacting a closed valve causing water hammer, the equation is valid for any instantaneous drop in velocity, not necessarily a drop to zero velocity.

Water hammer calculator washington state university. Calculates the total surge pressure due to a sudden shutting of a valve, or water hitting the end of a pipe learn more about the units used on this page. If severe enough, the fluctuating pressures can cause damage to the pipeline and other system components. Lets take our example and plug it into the equation. The basic mechanisms causing water hammer events in pipe systems are introduced. Water hammer also can occur in a multiphase fluid, which is a liquid media that also has entrained solids. In this section, the fundamental equations for 1d water hammer are derived. Note that research in recent years showed that researchers prior to joukowsky discovered this same equation, but joukowskys name is most often associated with this equation.

The water hammer generated by water column separation and closure is a two phase process. It is the special case when there is a sudden change in flow velocity. Although it might seem to be a smooth flow, the water inside the pipe actually churns and tumbles as it moves through. Although the equation at the top of the following page does not take into account the effect of pipe size and elasticity on waterhammer, it will provide some insight as to the additional pressure that is created by a waterhammer pressure wave. In unidirectional waves there is a simple linear relationship between p and u. In this video the process of water hammer is explained and you are shown how to calculate the pressure rise using the joukowsky equation. Pezzinga presented both quasi 2d and 1d unsteady flow analysis. Water hammer, fluid transient, line pack, reflected pressure waves, cavitation, vapor collapse, liquid column separation. Water hammer hydraulic pressure transient calculation. Sensitivity analysis for water hammer problem in pipelines.

Joukowskys fundamental equation of water hammer is as fol lows. In his derivation, he i ignored the axial longitudinal stresses in the. The most basic explanation is that water hammer occurs when a fluid in motion is suddenly forced to stop moving. When a flow is stopped backwater effect is produced in which a wave of water moves against the flowing water. Pdf a water hammer is a pressure wave that occurs, accidentally or intentionally, in a filled liquid pipeline when a tap is suddenly closed, or a. Transient water hammer analysis is essential to verify design and operation of piping. Water and most fluids are comparatively incompressible and heavy. Since the water flow is restricted inside a pipe, a shock wave. Water hammer definition, causes, factors affecting water. Very high pressure above 100 psi can also damage appliances. In the attached pdf for some reason they felt the need to convert the joukousky equation to a wave equation, cant the joukousky equation. Our water hammer calculation computes the maximum and minimum piezometric pressures relative to atmospheric in each pipe in a pipeline as well as the time and location at which they occur. During the accident, the rotor was seen flying through the air, still. They show that the pressure and velocity waveforms in the arteries are not independent of each other as is often thought.

This paper considers water hammer analysis of pumping systems for control of water in underground mines. Water hammer is a pressure surge or wave that occurs when there is a sudden momentum change of a fluid within an enclosed pipeline system. A very simple and important relationship between the change in pressure dp and the change in velocity du in a wavefront can be derived from the method of characteristics solution. Water hammer occurs when the flowrate of fluid in the pipe changes rapidly. Overall, water hammer creates by rapidly closing valves, shutting off or suddenly restarting pumps.

Though the joukowski equation s primary applicability is for a liquid velocity that drops to zero upon contacting a closed valve causing water hammer, the equation. Joukowskis allievi equation estimate transient pressure rise due. Water hammer causes piping, valves, pipe fixtures, sup. The latter term suitably reflects the harmful effects that the hammer like blows accompanying the pressure surges can have on pipes and system components. The joukowsky equation for fluids the fundamental equation in waterhammer theory relates pressure changes. For each water hammer, characteristics of pressure change and valve closing were recorded. There seems to be two different ways to calculate the pressure andor force exerted when flow is stopped by a quick acting valve, i.

Forces acting on pipelines as a result of water hammer. Water hammer phenomenon analysis using the method of. Experimental study of water hammer phenomena in drinking. Afterward, in mid twentieth century allievi 1 exhibited the differential equations for water hammer state after which several methods have changed for solving. We could find the pressure by considering the dynamics of a thin slice of water, but a much easier way is to equate the kinetic energy of the water when the tap was closed to the strain energy of the water at rest, compressed by the extra pressure.

Change equation select to solve for a different unknown. Joukowskys fundamental equation of water hammer is as follows. The fundamental equation in waterhammer theory relates pressure changes. Proceedings of the asme 2018 pressure vessels and piping. The below water hammer calculator helps you calculate pressure increase p, flow velocity v, upstream pipe length l, valve closing time t and inlet pressure p i alternatively with. Water hammer pressure increase equations formulas calculator. Jan 11, 2016 hello all, so i found this article on water hammer and i have since beefed up my math skills. Pdf wave speed calculation for water hammer analysis. Dp56radv or dh56 adv g 1 where a5acoustic waterhammer. The measurements were compared with the results of calculations perfomed by common methods used by engineers michauds equation. Water hammer is a specific plumbing noise, not a generic name for pipe clatter. For more on the history of water hammer, consult tijsseling and anderson 9. In the attached pdf for some reason they felt the need to convert the joukousky equation to a wave equation, cant the joukousky equation be solved analytically for pressure vs velocity and then.

The wave surge constant may be used to quickly calculate pressure rise due to water hammer as illustrated to the right. This pressure wave is commonly referred to as fluid hammer also known as water. This commonly occurs in pipelines when a valve is closed suddenly at the end of a pipeline where the velocity of the fluid is high. Change equation select to solve for a different unknown maximum. Instantaneous waterhammer equation joukowsky equation. Pwh pressure resulting from water hammer v change in velocity of the liquid in the pipe l upstream pipe length t valve closing time pi inlet pressure pressure before hammer condition. Although the equation at the top of the following page does not take into account the effect of pipe size and elasticity on waterhammer, it will provide some insight as to the additional pressure that is created. Hydraulic shock is a pressure surge or wave caused when a fluid, usually a liquid but. The hydraulic transient calculation is helpful in design to determine the maximum or minimum expected pressures due to valve closure or opening. Water hammer is a shock wave transmitted through fluid contained in a piping system.

Application of newtons second law of motion to the case of unsteady flow of a compressible liquid in an elastic. Water hammer calculations pipelines, piping and fluid. Pwh pressure resulting from water hammer v change in velocity of the liquid in the pipe l upstream pipe length t valve closing time pi inlet pressure pressure before hammer. Hello all, so i found this article on water hammer and i have since beefed up my math skills. A surge or water hammer in pipe or tube is a pressure spike caused by sudden variation of flow rate. Infrastructure deterioration sewer assessment the first to successfully investigate the water hammer problem was the italian engineer lorenzo allievi which water hammer can be analysed by two different approaches, rigid column theory which ignores compressibility of the fluid and elasticity of the walls of the pipe, of by full analysis including elasticity. Water hammer can be a big thump that shakes the house, or a series of banging noises starting with a loud bang followed by several echoes.

Water hammer fluid hammer is a pressure surge or wave that occurs when the fluid flowing in a particular direction is forced to stop or change direction. This commonly occurs in pipelines when a valve is closed. An analysis of the impact of valve closure time on the. In a two phase system, water changes state and can exist both as a liquid and a vapor within the same confined volume. When a fluid in motion is forced to either stop or change direction suddenly a pressure wave will be generated and propagated through the fluid. Advantages of rules of thumb and manual calculations. Examples of water hammer there is a simple equation used to calculate the pressure created inside a pipe due to water hammer. The regular arrivals are like the blows of a hammer, and the phenomenon is called water hammer. Pdf in order to accurately solve the water hammer problem using the method of the characteristics moc is necessary to fulfil with the socalled. If water is flowing through a channel and it is stopped abruptly i. Water hammer is the dynamic slam, bang, or shudder that occurs in pipes when a sudden change in fluid velocity creates a significant change in fluid pressure. The key factor is that water is the main transport medium in the piping system, and water can transmit shock waves very effectively.

If a valve at the end of the pipe is suddenly closed, the momentum of the fluid is changed and this will give rise to forces on the valve and within the pipe. The video also proves the joukowsky equation from first. An example would be sand slurry or liquid pulp which is basically water transporting the pulp fibers. We could find the pressure by considering the dynamics of a thin slice of water, but a much easier way is to equate the kinetic energy of the water when the tap was closed to the strain energy of the water. V velocity reduction causing water hammer ftsec for convenience, table 2 lists wave surge constants for common sizes of pipe carrying water at 73f. Water hammer analysis of pumping systems for control of. Wave speed for water, without presence of free air or gas, the more general equation to calculate the water hammer wave speed. This phenomenon can cause strong positive and negative pressures in water conveyance pipes and usually it poses pipeline to danger.

Nov 06, 2014 the joukowsky equation is a method of determining the surge pressures that will be experienced in a fluid piping system. The pressure profile of the water hammer pulse can be calculated from the joukowsky equation. Additional water hammer calculators can be found in a previous post, 3 calculators for water hammer and pressure drop. Water hammer calculator solving for pressure increase given flow velocity, upstream pipe length, valve closing time and inlet pressure. Water hammer events rarely lead to pipe rupture in nuclear power plants but due to conservative calculations together with limited models many calculations are being made which costs time and money in the end. More rigorous derivation of the classical water hammer equations than the one presented here can be found in 8, 9 and 10. Instantaneous waterhammer equation joukowsky equation when a transient event is introduced into a hydraulic system, there is a pressure and flow response to the event. Before water hammer occurred, speed of wave propagation can be written as an initial form in ghidaoi 3. Equation 1 is the continuity equation and takes into account the compressibility of water and the flexibility of pipe material. A very simple and important relationship between the change in pressure dp and the change in velocity du in a wavefront can be derived from the method of. This phase change can take place whenever the pressure in a pipeline is reduced to that of the vapor pressure of the water. When the joukowsky equation does not predict maximum water. When they flow down a pipe, depending on the diameter and length, there is a weight of fluid in motion. Pdf dynamics of the solutions of the water hammer equations.

In the 2009 sayanoshushenskaya power station accident, the lid to a 640 mw turbine was ejected upwards, hitting the ceiling above. This sudden rise in pressure in a pipe due to stoppage of the flow is known as water hammer or hammer blow water hammer. Muhammad akbar 2005ce12 defination whenever, the velocity in pipe line is reduced instantaneously or in a very short time, a sudden increase in pressure takes place. The same equation had earlier been derived and validated, through experiments in water.

165 144 1440 169 895 175 70 1212 1475 1422 1000 307 1037 5 32 1082 408 1021 400 996 1503 1410 238 11 1328 1231 296 1152 1356 1080 1230 80 607 251