# The Water Hammer Effect Engineering Essay

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Water hammer effect is normally happening in our life and only that we not realize it. A common example of a water hammer occurs in most homes everyday: Simply turning off a shower quickly will send a loud thud through the house. This paper investigate the parameters that causes the water hammer effect .Parameter that may affect would be area of pipe, material of pipe, pressure in pipe and length of pipe. Experiment would be conduct to investigate the parameters that affect the water hammer effect. These discrepancies are based on the basic assumptions used in the derivation of the water hammer equations for the liquid unsteady pipe flow. The paper presents an analysis of the water hammer experimental test performed by the LMS DAQ system. The LMS would be analysis by FFT signal and by FFT result convert to wave speed. Such information can be used further for a more detailed system study and development of improvements or preventive actions.

Pressure surge or water hammer, as it is commonly known, is the formation of pressure waves as the result of a sudden change in liquid velocity in a piping system. Water hammer usually occurs when a fluid flow starts or stops quickly or is forced to make a rapid change in direction. Quick closing of valves and stoppage of a pump can create water hammer [1¼Œ4, 7, 9, 10, 11, 12, 13, 14, 21]. A valve closing in 1.5 s or less depending upon the valve size and system conditions causes an abrupt stoppage of the flow. Since liquid is not compressible, any energy that is applied to it is instantly transmitted. The pressure waves (acoustic wave) created at rapid valve closure can reach five times the system's working pressure. Thus, investigations of water hammer effect can be conduct by an experiment.

The earliest application of the one-dimensional wave equation to explain observed water hammer effects was made by Joukowsky in 1898 [8, 9, 10]. Joukowsky correctly predicted the maximum line pressures and disturbance propagation times in a water distribution system in which sudden valve closures occurred. Joukowsky's equation is expressed as

## ΔP = ρaΔV

where ΔP is the pressure rise due to the water hammer in N/m2, a is the velocity of impulse waves in m/s, ΔV is the velocity change of liquid in the pipeline in m/s, and ρ is the density of the liquid in kg/m3. The above relation can also be written as

where ΔH is the pressure increase due to the water hammer in terms of column of water in meters and g is the gravitational acceleration in m/s2. In deriving the above equations the following assumptions were made:

The friction losses are much smaller than the static pressure in the pipe.

Flow is single phase and there are no dissolved gases in the liquid.

The liquid velocity change occurs in a time less than the critical time.

The fast block LMS algorithm uses the fast Fourier transform (FFT) to transform the input signal x(n) to the frequency domain. This algorithm also updates the filter coefficients in the frequency domain. The FFT signal can be transform and substitute to equation

## 3. Literature Review

The first to successfully investigate the water hammer problem was the Italian engineer Lorenzo Allievi which Water hammer can be analyzed by two different approaches, rigid column theory which ignores compressibility of the fluid and elasticity of the walls of the pipe, or by a full analysis including elasticity [11].

## 3.1 General Definition of Water Hammer Effect

The earliest application of the one-dimensional wave equation to explain observed water hammer effects was made by Joukowsky in 1898 [8, 9, 10]. Joukowsky correctly predicted the maximum line pressures and disturbance propagation times in a water distribution system in which sudden valve closures occurred. Joukowsky's equation is expressed as

## ΔP = ρaΔV

where ΔP is the pressure rise due to the water hammer in N/m2, a is the velocity of impulse waves in m/s, ΔV is the velocity change of liquid in the pipeline in m/s, and ρ is the density of the liquid in kg/m3. The above relation can also be written as

where ΔH is the pressure increase due to the water hammer in terms of column of water in meters and g is the gravitational acceleration in m/s2. In deriving the above equations the following assumptions were made:

The friction losses are much smaller than the static pressure in the pipe.

Flow is single phase and there are no dissolved gases in the liquid.

The liquid velocity change occurs in a time less than the critical time. Critical time can be obtained from

Where tr is the critical time which is defined as the time in which the pressure waves would reflect and L is the distance between the point at which the pressure waves are generated and the nearest point at which they would reflect.

The speed of the pressure waves, a, is a function of the following parameters:

1. Specific weight and elasticity module of the liquid.

2. Pipe diameter, wall thickness, and the distance between the support points.

3. The elasticity module of the pipe material.

The derived relation for calculating the pressure wave speed is as follows:

Where D is the pipe diameter, e is the pipe wall thickness, E is the elasticity module of the pipe material, K is the elasticity module of the liquid, and C1 is a constant that can be assumed to be equal to one.

## 3.2 Parameter that affect the Water Hammer Effect

Pressure waves in pipelines are generated due to different normal operations in the system such as opening and closing the valves, start up or shutting down the pumps, or any sudden change in the pump rotational speed [10, 12].

Generally, the sources that may affect the water hammer attenuation, shape and timing would be the pressure in pipe, velocity flow in pipe, and sudden change of velocity flow. However there is other sources that may affect the waveform predicted by classical water hammer theory include viscoelastic behavior of the pipe-wall material, blockage and leakage in addition to the previously discussed unsteady friction, cavitations and fluid-structure interaction. These discrepancies are based on the derivation of the water hammer equations for the liquid unsteady pipe flow [5].

## 3.3 Experiment Method to investigate Water Hammer

There are several methods to analysis the water hammer effect such as FAST method, mathematical modal method, validation, wave method, characteristic method, and etc.

## 3.3.1 Water hammer model sensitivity study by the FAST method

Fourier amplitude sensitivity test (FAST) method is the sensitivity study which aims to determine the most important input parameters that are major contributors to the model output uncertainty.

In this work, as an illustration, RELAP5 analysis of a water hammer test was performed.

The experiments were conducted using the dynamic behavior of closing and opening valves in a steady-state liquid flow. A centrifugal pump produces steady-state flow into the circuit from the pressurized vessel into the test pipe section [7]. During the first phase of the transient, a rarefaction wave is travelling inside the pipe towards the downstream reservoir. As a consequence, cavitation occurs downstream the valve, and a vapour bubble is formed. The generated pressure wave oscillates between the vessel and the vapour bubble until the cavitation condenses, inducing a cavitational hammer.

Figure 3.1 - Comparison of the RELAP5 basic case calculation with UMSICHT experimental data

After that, they select and qualify the most important parameters for the sensitivity analysis for FAST method. The first-order sensitivity index is calculated and the higher order sensitivity indices estimate the contribution of the interactions of various input parameters into the model output variance. After that, total up the entire sensitivity index and total effect sensitivity index indicates the degree of interaction between the parameter of interest and the rest of the parameters. This index provides important additional information and can be used to determine strong interaction effects among the input parameters or to prove absence of the interactions.

## 3.3.2 Water Hammer analysis by Characteristic method

The method of characteristics (MOC) is conceptually somewhat complex and requires numerous steps or calculations to solve a typical transient pipe flow problem. As the complexity of the pipe system increases, the number of required calculations increases and for practical applications a computer program is required. Various computer programs have been developed based on the MOC and procedures for handling pipe junctions, pumps, surge tanks, and cavitations have been included are most of these programs [3, 4, 11].

This method is based on the physically accurate concept that the transient pipe flow results from the generation and propagation of pressure waves that occur as a result of a disturbance in the pipe system ~valve closure, pump trip, etc.!. A pressure wave, which represents a rapid pressure and associated flow change, travels at sonic velocity for the liquid-pipe medium, and the wave is partially transmitted and reflected at all discontinuities in the pipe system ~pipe junctions, pumps, open or closed ends, surge tanks, etc!. A pressure wave can also be modified by pipe wall resistance. This description is one that closely represents the actual mechanism of transient pipe flow. In this paper this method is referred to as the wave characteristic method (WCM) [3, 4, 19].

Figure 3.2 - Comparison of results of wave characteristic and method of characteristics comparison.

Transient (water hammer) analysis is essential to good design and operation of piping systems. This important analysis can be done using the mathematically based MOC or the WCM based on the action of pressure waves. The MOC and WCM methods are both capable of accurately solving for transient pressures and flows in water distribution networks including the effects of pipe friction. The MOC requires calculations at interior points to handle the wave propagation and the effects of pipe friction. The WCM handles these effects using pressure waves [3,19].

## 3.3.3 Pressure Transducer Method

An experiment is set up as figure below [16].

Figure 3.3 - Experiment set up

The experiment is done with the initially open with a fully developed flow; the valve was then closed for the remainder of the trial. When the valve is closed a positive pressure wave propagates from the valve. This wave bounces between the reservoir and the valve until the pressure everywhere in the tube is equal to the pressure in the reservoir [14]. The result would be mostly like the Flownet simulation result graph [6].

The result of pressure sensor and force sensor is collected and the graph is plotted as figure below:

Figure 3.4 - Pressure and force plots for valve closing [17].

## 3.3.4 Mathematical model and numerical solution

Mathematical model and numerical solution is the method where by using the numerical solution method to calculate the theoretical analysis of water hammer in pipe. The calculations of pipe as shown equations below and until it get the answer of H(t) meter [2, 5, 8, 9, 18].

By using numerical solution, a first order finite difference method is applied. If the Courant number (aDt/ Ds) is 1, this method is exact. Otherwise, interpolation along time or space is needed. After the calculation, the Head meter (by calculation) is plot. All calculations have been performed always assuming a Courant number equal to 1 and a single time step Dt for the whole system [2].

Figure 3.5 - Plot H(t) with interpolation

## 3.4 Water Hammer controlling method (Prevention)

To prevent the severe pressure rise during a water hammer occurrence, the following methods can be used [10, 12, 13 15]:

Design the Discharge Pipe Based on Lower Liquid Velocities.

- By decreasing the flow velocity, the effect of the water hammer will be minimized.

Increasing the Moment of Inertia of the Pump.

- Adding a flywheel on the rotating axis of the driving motor would prevent the rotational speed to reduce sharply and therefore restrain the excess pressure decrease or increase. This method is usually economical for small pump stations and the discharge pipes for up to 3 km.

By-Pass Pipes.

- One of the simpler methods to prevent the damaging effects of the water hammer is to install a by-pass pipe with a non-return valve. Under normal conditions, the pressure supplied by the pump would keep the non-return valve closed. However, after the shutdown of the pump, pressure will be decreased in the discharge pipe and once it becomes less than the suction pressure, the non-return valve will open and the liquid would enter from the suction pipe to the discharge pipe thereby preventing more pressure reduction. This method may be used in systems in which the supplied head of the pump is not very high.

Surge Tanks.

- These tanks act as a reservoir to suppress the pressure waves and are installed on the discharge pipe. When the pressure in the pipe increases, liquid enters the tank and is stored there. During periods of subnormal pressure in the pipe, then, the liquid would flow back to the pipe, preventing rapid velocity changes [1].

Air Chambers.

- Air chambers are basically a type of high pressure surge tanks which can be built in smaller sizes. In these tanks, the pressurized air locates on the top of liquid. The size of the chamber must be large enough to compensate the liquid in the subnormal pressure periods without allowing air to enter into the system. The volume of the air must be chosen such that during filling period of the pipes, its pressure does not change significantly.

Non-return Valves.

- The discharge pipes of the pumps are normally equipped with non-return valves. The main application of these valves is to prevent the flow running toward the pump when it stops, thereby reducing the adverse effects. During normal working conditions of the pump, the supply flow would keep the non-return valve open. Upon sudden stop of the pump, the flow rate would reduce rapidly until it reaches zero and would then flow back to the pump. Once the liquid flow is reversed, the disk of the valve is sharply closed, causing an intense impact on the valve seat. This would create more pressure waves. Neglecting the pressure losses, this pressure rise is the same as the subnormal pressure produced when the flow returns back to the pump.

Pressure Control Valves.

- These valves are designed to open at very high pressures and are installed at the critical points of the piping system. During the pressure rise period, the valve would release liquid to the outside. This would reduce the pressure in the line and prevents any possible damages.

Vacuum Valves.

- These valves are installed on those points of the piping system in which there is a possibility of liquid evaporation due to subnormal pressures. When the pressure reduces beyond certain level in the pipe, these valves close and let the atmospheric air to enter the system.

## 4. Methodology

Fifure4.1 - Flow chart of the Project

Figure above shown the flow of the project, which the project will start from the Literature review and than the experiment set up. After the experiment analysis is done, the prevention of water hammer is proposed. The experiment will be analysis base on prevention method.

## 4.1 Experimental Set up

In this project, an experiment would be conduct to analysis the parameter that affects the water hammer effect.

Apparatus that include: ¾' PVC pipe, ¾' steel pipe, 1' PVC pipe, surge tank, pump with inverter, fitting, connector, pressure gauge, and LMS DAQ system.

Figure 4.2 - Experiment set up

An experiment is set up as figure 1 to analysis the parameter that affects the water hammer effect. The parameter tested would be the area of pipe, material of pipe and the length of the pipe. The pipe with difference parameter would be installing at the tested area.

Sensor of the LMS would put at the tested area and data would be collect by DAQ system. The FFT signal would be taking and the signal is calculated in the wave speed. The graph would be plot by the LMS DAQ system and by calculation of wave speed, the graph of wave speed versus the frequency also would be plot.

The data of the FFT signal will be taken after the sudden shut off valve. The wave speed of pipe will be calculated as table 3.1.

Table 4.1 - Example of data collecting

Frequency

FFT

Wave speed

## 4.2 Expected Result

The expected result of the graph shape by LMS FFT signal would be shown as figure 3.2 below [20].

Figure 4.2 - Expected FFT transformed signal in pipe

After get the FFT signal, the measured pressure signals were FFT transformed and substituted to

to obtain frequency series wave speed data.

After obtain the frequency wave speed data, the graph of wave speed versus the frequency is ploted [20].

Figure 3.3 - Expected wave speed graph

By the wave speed data, we can compare the wave speed by theoretical calculation as below:

Where D is the pipe diameter, e is the pipe wall thickness, E is the elasticity module of the pipe material, K is the elasticity module of the liquid, and C1 is a constant that can be assumed to be equal to one.

After the analysis of parameter that affects the water hammer, prevention or reducing of water hammer method would be proposed. Another experiment will be conduct to prove the prevention of water hammer can be used.

## 5. Project Progress

The Gantt chart that had planed as below:

Expected

Actual

Figure 5.1 - Gantt chart of project planning

From the Gantt chart, the experiment should setup in at September. However, the experiment is setup in October. This is due to some delay of the item finding. The progress report and the thesis is also start writing since September. Experiment will be start after the experiment done set up. If possible, the experiment may start at earlier than planning.

As summary, the progress of the project is still in the time planning schedule.

## 6. Conclusion

The scientific study of water hammer fluid flow has been undertaken since the middle of the nineteenth century. As is true of every other area of engineering research, a great many advances have been made in the accuracy of analysis and the range of applications since then. Although only a few simple problems were approachable by earlier analytical methods and numerical techniques, a much broader spectrum of water hammer problems could be solved once graphical methods were developed.

Although there are a lot of water hammer prevention methods, the water hammer seen still happen in our real life. Therefore, the scientists or engineers today still keep hand on the project of investigation of water hammer effect.

A water hammer investigation should be an integral part during the design phase for a new project, and if potential water hammer problems are identified, then the most effective selection of protection devices should be installed for that system.

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