# Exact transient flow analyses can prevent immense damage

Pipelines from as little as a hundred metres in length and conveying only a few litres per second may be subject to immense damage due to surge pressures. This makes precise calculations and safety measures so important. Especially for piping systems made of several different materials, plant designers should definitely pay attention to the problem of possible pressure surges. Let us explain this problem by looking at an example.

Pipelines from as little as a hundred metres in length and conveying only a few litres per second may be subject to immense damage due to surge pressures. This makes precise calculations and safety measures so important. Especially for piping systems made of several different materials, plant designers should definitely pay attention to the problem of possible pressure surges. Let us explain this problem by looking at an example.

### When water pipes are banging: What water hammer is all about

Surge pressure has been known since antiquity: The Romans already knew about water hammer occurring in their lead and stone pipes. However, it wasn't until the late 19th century that the first detailed experiments and calculations were conducted by the Russian mathematician Nikolai Joukowsky, coining the term "Joukowsky surge" for this physical phenomenon.

Today, this term and its implications are known by everyone working with pipelines transporting liquids. Designers of piping and hydraulic systems, in particular, have to frequently deal with the question as to whether a transient flow analysis is necessary. In principle, surge pressure is hardly a problem in a domestic environment, i.e. in heating, water supply and waste water pipes of short lengths and small cross-sections. However, in unfavourable conditions, it does not take more than a pipe length of about 100 metres and a flow rate of only a few litres per second to cause major damage in the piping. The damage caused by water hammer quickly exceeds the cost of preventive analysis and surge control measures.

### What causes water hammer?

Water hammer can generally occur in all pipes filled with a liquid. Unlike gases, liquids are only minimally compressible, which means that compression hardly reduces their volume. A pressure surge occurs whenever the flow velocity of such a liquid in a pipe changes, i.e. when the flow is accelerated or decelerated. Generally speaking, every change in operating condition and every disturbance cause pressure and flow variations or, put differently, cause the flow conditions to change with time.

If a shut-off valve is closed rapidly, for example, the water volume builds up upstream of the valve. The pressure rises and the so-called pressure wave front expands in the opposite direction of the original flow – reaching a velocity as high as about 1100 m/s in a steel pipe. At the same time the pressure on the output side of the rapidly closed valve is reduced. This pressure reduction also expands, this time in the direction of flow. The developing pressure wave in the pipe opposes the original direction of flow until it meets another reflection point, e.g. a sudden change in cross-section, a tee or a swing check valve. The surge is then reflected again, moving to and fro in the system until the pressure wave dies out due to friction.

The main causes of such transient flow conditions can be:

• A pump suddenly cutting out as a result of the power being switched off or a power failure
• One or more pumps starting up or stopping whilst other pumps are in operation
• Shut-off elements closing or opening in the piping
• Changing inlet water levels
• Swing check valves slamming shut

The following figures illustrate the immense forces that can act in pipes in the event of surge pressure:

Let's look at a pipe of DN 200 (inside diameter approximately 190 mm) with a length of 900 metres and a water flow velocity of 3 m/s (equivalent to 11 km/h). The mass of water in the pipe therefore equals mwater = ((0.192 × π) / 4) × 900 × 1000 = 25,500 kg. This is more or less the same mass as that of a large truck. In other words, if the flow is suddenly stopped, our truck – referring to our illustration – runs into a wall (the closed valve) at 11 km/h. Imagine the enormous pressure this causes!

### What to expect: A brief introduction to transient flow analysis

A surge analysis to industry standards should generally be performed by the plant designer for every hydraulic piping system at risk of surge pressure. A multitude of parameters is to be considered. To name but a few examples:

• Piping elevation profile
• Lengths and diameters
• Wall thickness
• Material
• Lining
• Pipe connections
• Surface roughness coefficient
• Provision of air valves at the highest points of the piping
• Branch connections
• Zeta or flow factors as well as valve closing patterns
• Characteristic curves or performance charts and characteristic data of all hydraulic equipment
• Moments of inertia of the machine train systems
• Settings of control equipment
• Water levels in tanks and reservoirs
• Rates of flow in the individual piping branches
• Degrees of opening of all shut-off and throttling valves
• Operating pressures

This large range of data influences the transient flow analysis to different extents. Special software is available that is employed by experts in this field. Nobody would conduct a transient flow analysis by hand these days. Nevertheless we need to keep in mind that changing just one parameter can have a major impact on the entire calculation.

### Damping the power of surge pressure: How to prevent water hammer?

A number of measures can be taken to protect the piping against the power of water hammer. The slower the pressure changes in a pipe, the smaller the surge pressure. Frequency inverters and soft starters for pumps as well as hydraulically actuated butterfly valves prevent sudden changes in flow velocity during normal operation. In addition, accumulators and valves can protect the piping.

• Accumulators or surge dampeners are vessels containing compressible air cushions. Similar to a balloon the air cushion absorbs the energy generated by a pressure increase. Any excess water simply compresses the air contained in the accumulator.
• Air valves like KSB's BOAVENT-AVF provide protection against air bubbles, negative pressure and surge pressure in the system. They enable the entry and discharge of large volumes of air (e.g. for priming the pipe) and release of air pockets in working conditions. Vacuum safety valves or vacuum breaker valves installed on the discharge side of pumps, for example, allow air to enter the system if necessary to prevent a vacuum.

### Practical example 1:

The following rule of thumb is often used to determine whether a transient flow analysis is necessary:

K = (l × v) / √H

Where:

l = pipe length between the pump or valve and the nearest reflection point in metres

v = flow velocity in m/s

If the K value calculated exceeds 70, a transient flow analysis is recommended. (Source: Lehr- und Handbuch der Abwassertechnik 3, 3rd edition, published by Wilhelm Ernst & Sohn)

The example: A Compacta lifting unit made by KSB is to be installed. Key data:

Q = 47 m³/h

Htotal = 19.6 m (hgeo 13.3 m included)

Discharge line:

DN 100 / d i = 102.2 mm

Length: 127.3 m

Flow velocity: 1.6 m/s

PE pipe

Entering the values in the above formula results in a K value of approx. 46. Given the threshold of K = 70, this does not seem to be a critical case. Or does it? The dynamic behaviour of the swing check valve has got a dramatic impact on the issue of surge pressure: Assuming that an ideal swing check valve is used, everything is fine. The originally planned standard check valve, however, leads to "horrific" results in the calculation, see figure 1 below. This means: A special quick-closing valve has to be fitted.

Conclusion: The commonly used rule of thumb for assessing the necessity of a transient flow analysis is not always reliable. In the above formula, for example, the secondary surge pressure effect of the check valve slamming shut is not taken into account.

### Practical example 2: How KSB managed the surge pressure behaviour of a steel pipe bridge

A customer was planning a new waste water line, approximately five kilometres in length. The design was as follows: A 170-metre long pipe bridge was planned about 180 metres downstream of the pump station. The waste water line is a buried PE pipe. The bridge, however, is above the ground, located on stilts. It is made of steel pipes, which is a relatively common construction and highly relevant to the plant designer. For the initial assessment of the required air valve positions the pipe was regarded as a single-piece PE pipe.

The red line graphically illustrates the minimum pressure established during the course of simulation (minimum envelope). As you can see: When using the two air valves BEV A and B the pressure remains within the permissible range. Additional safety measures do not seem to be necessary.

The project managers consulted KSB to examine the transient flow conditions of the project in detail and to recommend suitable measures to protect the piping. Naturally, the final calculations were based on steel as the correct material for the piping system on the bridge. The KSB experts quickly understood that the piping system responded quite noticeably to any changes in operating point, e.g. to a pump failure.

Fig. 3 shows the envelope for the minimum pressure during simulation of a power failure. Without any additional safety measures the pressure in the pipe sections examined visibly drops down to the vaporisation pressure of water (cavitation) at times (green line). Even when an air valve (BEV C) is fitted at the connection point of the two pipes, the corresponding envelope (pink) shows some impermissible pressure drops. Only when another air valve (BEV D) is fitted near the connection point can the pressure be maintained within the permissible range (brown line).

Why is this the case?

The wave propagation velocity "a" equals 270 m/s in the PE pipe and 1100 m/s in the steel pipe of the bridge. The abrupt change of "a" results in a partial reflection point for the pressure waves where the two pipes connect. This entails a complex development of pressure waves. The distribution of the pipe pressure in space and time finally requires another air valve (BEV D) to be fitted in the immediately vicinity (37 m) to the air valve (BEV C) at the connection point.

### Conclusion: In what cases is a precise transient flow analysis especially worthwhile?

The German Technical and Scientific Association for Gas and Water (DVGW), Germany's recognised regulator for the gas and water industry, spells it out clearly: Their technical instruction leaflet W 303 "Dynamic Pressure Changes in Water Supply Systems" explicitly states that pressure transients have to be considered for the design and operation of water supply systems because they can cause extensive damage.

The above example is an impressive illustration of how the transition from one type of pipe material to another, like in the case of a steel pipe bridge, can lead to system response anomalies. Such scenarios are far from rare: Especially in roadworks, new property development, the construction of new suburban trains and tramways, the routing of communication cables, etc. pressure pipes often have to be laid or altered for temporary or permanent use. Steel pipe sections inside plastic pipes are not uncommon in such cases. A change in pipe cross-section also forms partial reflection points in the piping system and can lead to similar issues. These are cases in which plant designers should carry out precise transient flow analyses and, if necessary, take the corresponding measures to prevent far-reaching, expensive damages before they occur. KSB's specialists gladly support you with your calculations and offer advice on your project. Don’t hesitate to contact us.

## Suitable products

#### BOAVENT-AVF

Automatic air valve with two floats and three functions. Flanged ends, body made of nodular cast iron, double-chamber design with ABS floats. The air valve ensures proper operation of piping systems. It is specially designed to allow the entry and discharge of large volumes of air and the release of air pockets in working conditions.

#### BOAVENT-SVA

Automatic air valve with one float and three functions. With flanged ends or threaded ends, body made of nodular cast iron, single-chamber design with polypropylene float. The air valve ensures proper operation of piping systems. It is specially designed to allow the entry and discharge of large volumes of air and the release of air pockets in working conditions.

## Stay up to date with the KSB Newsletter.

Want to make sure you never miss the latest news? With the KSB Newsletter you will receive information on our products and solutions, current promotions and events as well as fascinating insights into the world of KSB.