**2. Pressure transient evaluation criteria for water pipelines**

In any transient evaluation, pressure is the most important evaluation variable, but certainly not the only one. Component-specific criteria must be taken into account as well, such as a minimum fluid level in air vessels, maximum air pressure during air release from an air valve or the maximum fluid deceleration through an undamped check valve.

**3. Systematic approach to pressure transient analysis**

**3. Systematic approach to pressure transient analysis**

**Preconditions (steady)** Basic Pipeline design Pumping station design

> Criteria acceptable?

Design anti-surge devices and

Define normal operating procedures and

Emergency controls triggered? No Yes

**Figure 2.** Integrated design for pressure transients and controls.

**Figure 2.** Integrated design for pressure transients and controls.

No

Surge analysis without provisions 3.2

List possible solutions 3.3

Yes

emergency controls 3.3

control systems 3.4

The flow chart in Figure 2 integrates the design of anti-surge devices and distributed control systems. It is emphasised that a surge analysis is strongly recommended upon each modifi‐ cation to an existing system. The systematic approach also applies to existing systems.

The flow chart in Figure 2 integrates the design of anti-surge devices and distributed control systems. It is emphasised that a surge analysis is strongly recommended upon each modifi‐ cation to an existing system. The systematic approach also applies to existing systems.

3.1

Guideline for Transient Analysis in Water Transmission and Distribution Systems

Guidelines for Transient Analysis in Water Transmission and Distribution Systems

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5

5

Finish Surge Analysis

Modify Pipeline or Pumping station Design

The maximum and minimum allowable pressure is directly related to the pressure rating of the components. Thin-walled steel and plastic pipes are susceptible to buckling at a combi‐ nation of external pressure and minimum internal pressure.

The design pressure for continuous operation is normally equal to the pressure rating of the system. During transient events or emergency operation, the system pressure may exceed the design pressure up to a certain factor of the design pressure. Table 1 provides an over‐ view of maximum allowable incidental pressure (MAIP) in different national and interna‐ tional codes and standards.


**Table 1.** Overview of maximum allowable incidental pressures (MAIP) in international standards, expressed as a factor of the nominal pressure class.

The minimum allowable pressure is rarely explicitly addressed in existing standards. The commonly accepted minimum incidental pressure in drinking water distribution systems is atmospheric pressure or the maximum groundwater pressure necessary to avoid intrusion at small leaks. If the water is not for direct consumption, negative pressures down to full vacuum may be allowed if the pipe strength is sufficient to withstand this condition, al‐ though tolerance to such conditions varies with jurisdiction. Full vacuum and cavitation can be admitted under the condition that the cavity implosion is admissible. Computer codes that are validated for cavity implosion must be used to determine the implosion shock. The maximum allowable shock pressure is 50% of the design pressure. This criterion is based on the following reasoning: The pipeline (including supports) is considered a single-massspring system for which a simplified structural dynamics analysis can be carried out. The ratio of the dynamic response (i.e., pipe wall stress) to the static response is called the dy‐ namic load factor (DLF). The dynamic load factor of a mass-spring system is equal to 2. It is therefore recommended that a maximum shock pressure of no more than 50% of the design pressure be allowed. This criterion may be relaxed if a more complete Fluid-Structure-Inter‐ action (FSI) simulation is performed for critical above-ground pipe sections.

http://dx.doi.org/10.5772/53944

### **3. Systematic approach to pressure transient analysis 3. Systematic approach to pressure transient analysis**

**2. Pressure transient evaluation criteria for water pipelines**

valve or the maximum fluid deceleration through an undamped check valve.

nation of external pressure and minimum internal pressure.

tional codes and standards.

4 Water Supply System Analysis - Selected Topics

of the nominal pressure class.

In any transient evaluation, pressure is the most important evaluation variable, but certainly not the only one. Component-specific criteria must be taken into account as well, such as a minimum fluid level in air vessels, maximum air pressure during air release from an air

The maximum and minimum allowable pressure is directly related to the pressure rating of the components. Thin-walled steel and plastic pipes are susceptible to buckling at a combi‐

The design pressure for continuous operation is normally equal to the pressure rating of the system. During transient events or emergency operation, the system pressure may exceed the design pressure up to a certain factor of the design pressure. Table 1 provides an over‐ view of maximum allowable incidental pressure (MAIP) in different national and interna‐

DVGW W303:1994 (German guideline) 1.00

NEN 3650-1:2012 1.15 BS 806 1.20

Italian ministerial publication 1.25 – 1.50

**Table 1.** Overview of maximum allowable incidental pressures (MAIP) in international standards, expressed as a factor

The minimum allowable pressure is rarely explicitly addressed in existing standards. The commonly accepted minimum incidental pressure in drinking water distribution systems is atmospheric pressure or the maximum groundwater pressure necessary to avoid intrusion at small leaks. If the water is not for direct consumption, negative pressures down to full vacuum may be allowed if the pipe strength is sufficient to withstand this condition, al‐ though tolerance to such conditions varies with jurisdiction. Full vacuum and cavitation can be admitted under the condition that the cavity implosion is admissible. Computer codes that are validated for cavity implosion must be used to determine the implosion shock. The maximum allowable shock pressure is 50% of the design pressure. This criterion is based on the following reasoning: The pipeline (including supports) is considered a single-massspring system for which a simplified structural dynamics analysis can be carried out. The ratio of the dynamic response (i.e., pipe wall stress) to the static response is called the dy‐ namic load factor (DLF). The dynamic load factor of a mass-spring system is equal to 2. It is therefore recommended that a maximum shock pressure of no more than 50% of the design pressure be allowed. This criterion may be relaxed if a more complete Fluid-Structure-Inter‐

ASME B31.4 (1992), IS 328, BS 8010, ISO CD 16708:2000 1.10

action (FSI) simulation is performed for critical above-ground pipe sections.

**Code Maximum Incidental Pressure Factor [-]**

The flow chart in Figure 2 integrates the design of anti-surge devices and distributed control systems. It is emphasised that a surge analysis is strongly recommended upon each modifi‐ cation to an existing system. The systematic approach also applies to existing systems. The flow chart in Figure 2 integrates the design of anti-surge devices and distributed control systems. It is emphasised that a surge analysis is strongly recommended upon each modifi‐ cation to an existing system. The systematic approach also applies to existing systems.

**Figure 2.** Integrated design for pressure transients and controls. **Figure 2.** Integrated design for pressure transients and controls.

Because system components are tightly coupled, detailed economic analysis can be a com‐ plex undertaking, However, the net present value of anti-surge equipment may rise to 25% of the total costs of a particular system. Therefore, the systematic approach to the pressure transient analysis is preferably included in a life cycle cost optimisation of the water system, because savings on investment costs may lead to operation and maintenance costs that ex‐ ceed the net present value of the investment savings.

E = Young's modulus of pipe material (N/m2

)

C1 = Constant depending on the pipe anchorage (order 1).

The acoustic wave speed in water pipelines is shown in Figure 3.

)

K = Bulk modulus of fluid (N/m2

ρ = Fluid density (kg/m<sup>3</sup>

e = Wall thickness (m) and

Steel Cast iron

Ductile iron

concrete Asbestos cement GRP (woven)

GRP (fibre) Perspex PVC PVC (ductile)

HDPE

LDPE

length L:

D = Pipe diameter (m)

)

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**Figure 3.** Graph of acoustic wave speed in water pipelines in relation to pipe material (E) and wall thickness (D/e).

The pipe period *T* [s] is defined as the time required for a pressure wave to travel from its source of origin through the system and back to its source. For a single pipeline with

*T Lc* = 2 (2)

### **3.1. Necessary information for a pressure transient analysis**

The phenomenon of pressure transients, surge or water hammer is defined as the simultane‐ ous occurrence of a pressure and velocity changes in a closed conduit. Water hammer may occur in both long and short pipes. The larger and faster the change of velocity, the larger the pressure changes will be. In this case, 'fast' is not an absolutely term, but can only be used relative to the pipe period, that is, relative to the pipe's internal communications. The most important parameters for the magnitude of transient pressures are:


The acoustic wave speed *c* is the celerity at which pressure waves travel through pressurised pipes. The wave speed accounts for both fluid compressibility and pipe stiffness: the more elastic the pipe, the lower the wave speed. In fact, all phenomena that create internal storage contribute to a reduction of wave speed. Since air is much more compressible than water, air bubbles reduce the wave speed considerably, but this is the primary positive effect of air in pipelines. The negative consequences of air in water pipelines, particularly in permitting or generating large velocity changes, can greatly exceed this positive effect in mitigating cer‐ tain transient changes; thus, as an excellent precaution, free or mobile air must generally be avoided in water systems whenever possible and cost-effective. The maximum acoustic wave speed in an excavated water tunnel through rocks is 1430 m/s and drops to approxi‐ mately 1250 m/s in steel, 1000 m/s in concrete and ductile iron, 600 m/s in GRP, 400 m/s in PVC and about 200 m/s in PE pipes.

$$c = \frac{1}{\sqrt{\rho \left(\frac{C\_1 D}{eE} + \frac{1}{K}\right)}}\tag{1}$$

where:

c = Acoustic wave speed (m/s)


Because system components are tightly coupled, detailed economic analysis can be a com‐ plex undertaking, However, the net present value of anti-surge equipment may rise to 25% of the total costs of a particular system. Therefore, the systematic approach to the pressure transient analysis is preferably included in a life cycle cost optimisation of the water system, because savings on investment costs may lead to operation and maintenance costs that ex‐

The phenomenon of pressure transients, surge or water hammer is defined as the simultane‐ ous occurrence of a pressure and velocity changes in a closed conduit. Water hammer may occur in both long and short pipes. The larger and faster the change of velocity, the larger the pressure changes will be. In this case, 'fast' is not an absolutely term, but can only be used relative to the pipe period, that is, relative to the pipe's internal communications. The

The acoustic wave speed *c* is the celerity at which pressure waves travel through pressurised pipes. The wave speed accounts for both fluid compressibility and pipe stiffness: the more elastic the pipe, the lower the wave speed. In fact, all phenomena that create internal storage contribute to a reduction of wave speed. Since air is much more compressible than water, air bubbles reduce the wave speed considerably, but this is the primary positive effect of air in pipelines. The negative consequences of air in water pipelines, particularly in permitting or generating large velocity changes, can greatly exceed this positive effect in mitigating cer‐ tain transient changes; thus, as an excellent precaution, free or mobile air must generally be avoided in water systems whenever possible and cost-effective. The maximum acoustic wave speed in an excavated water tunnel through rocks is 1430 m/s and drops to approxi‐ mately 1250 m/s in steel, 1000 m/s in concrete and ductile iron, 600 m/s in GRP, 400 m/s in

1

r

*C D eE K*

æ ö ç ÷ + è ø

*c*

=

1

1

(1)

ceed the net present value of the investment savings.

**•** Acoustic wave speed, *c* (m/s)

6 Water Supply System Analysis - Selected Topics

**•** Joukowsky pressure, *Δp* (Pa)

PVC and about 200 m/s in PE pipes.

c = Acoustic wave speed (m/s)

**•** Pipe period, *T* (s)

**•** Elevation profile

where:

**3.1. Necessary information for a pressure transient analysis**

most important parameters for the magnitude of transient pressures are: **•** Velocity change in time, *Δv* (m/s) (or possibly the pressure equivalent)


The acoustic wave speed in water pipelines is shown in Figure 3.

**Figure 3.** Graph of acoustic wave speed in water pipelines in relation to pipe material (E) and wall thickness (D/e).

The pipe period *T* [s] is defined as the time required for a pressure wave to travel from its source of origin through the system and back to its source. For a single pipeline with length L:

$$\mathbf{T} = \mathbf{2L}/\mathbf{c} \tag{2}$$

This parameter defines the natural time scale for velocity and pressure adjustments in the system.

Only after the pipe period the pressure wave will start to interact with other pressure waves from the boundary condition, such as a tripping pump or a valve closure. Any velocity change *Δv* within the pipe period will result in a certain "practical maximum" pressure, the so-called Joukowsky pressure, *Δp*.

$$
\Delta p = \pm \rho \cdot \mathbf{c} \cdot \Delta \mathbf{v} \tag{3}
$$

positive pressure wave (Figure 4). In this way, the maximum allowable pressure may be ex‐

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9

Hydraulic grade line

Hydraulic grade line

Check valves will generally close after pump trip. The transient closure of a check valve is driven by the fluid deceleration through the check valve. If the fluid decelerates quickly, an undamped check valve will slam in reverse flow. Fast-closing undamped check valves, like a nozzle- or piston-type check valve, are designed to close at a very small return velocity in order to minimize the shock pressure. Ball check valves are relatively slow, so that their ap‐

Hydraulic grade line

ceeded during a pump trip scenario.

**Figure 4.** Pressure wave propagation following a pump trip

plication is limited to situations with small fluid decelerations.

A slightly more conservative assessment of the maximum transient pressure includes the steady friction head loss *Δp<sup>s</sup> = ρgΔHs.*

$$
\Delta p = \pm \left( \rho \cdot c \cdot \Delta v + \rho \, \text{g} \, \text{A} \, H\_s \right) \tag{4}
$$

All these parameters follow directly from the basic design. The maximum rate of change in velocity is determined by the run-down time of a pump or a valve closure speed. The pump run-down time is influenced by the polar moment of inertia of the pump impeller, the gear box and motor. The full stroke closure time of valves may be increased in order to reduce the rate of velocity change.

Pressure waves reflect on variations of cross-sectional area (T-junctions, diameter changes, etc.) and variation of pipe material. All these parameters must be included in a hydraulic model.

Finally, the elevation profile is an important input, because extreme pressures typically oc‐ cur at its minimum and maximum positions.
