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Part 1 – Waterhammer in Liquid Lines

This is the first in a series of articles on fluid transients in piping systems.

Four Broad Categories. From a practical point of view, fluid transients in piping systems can be divided into four categories:

  • Liquid-filled systems
  • Liquid-vapor systems
  • Liquid-gas systems
  • Gas systems

In this first article we look at transients in liquid-filled systems. This classic case will also be of importance when investigating two-phase flow transients in future articles.

By liquid-filled system we mean a case where the line does not contain vapor or gas, only liquid. A change in velocity causes a change of pressure along the line. Classic cases include valve opening or closing, and pump start or stop.

Bulk Flow

The severity of the transient depends on the duration of the flow disturbance td compared to the propagation time tp. If the disturbance time (for example the valve closure time) is much longer (slower) than the propagation time, the transient will be a bulk flow. The condition for bulk flow can be written as

 td >> tp
td = disturbance time, sec
tp = acoustic propagation time, sec

The propagation time is the time it takes the sonic pressure wave to travel down the line, or


L = length of pipeline, in
c = velocity of sound in the liquid-filled line, in/sec

In the case of bulk flow, the momentum force exerted on a gradually and linearly closing valve is


F = force on closing valve in bulk flow, lb
r = mass density of liquid, lbm/in3
A = flow area, in2
L = length of pipe, in
v = change in liquid velocity, in/sec
td = closure time, sec

Note that in the case of a long pipeline, for example in the order of 10 miles (52800 ft), common in water or oil transmission systems, the condition for bulk flow is


In other words, an isolation valve on a 10 mile pipeline would have to be closed slowly, well over 11 seconds, for the line to remain in a bulk flow condition and prevent waterhammer.

Propagative (Waterhammer) Flow

If the disturbance time td is short compared to the acoustic propagation time tp then the transient is a waterhammer. In this case the pressure rise is


DP = pressure rise, psi
r = mass density of liquid, lbm/in3
c = velocity of sound in the liquid-filled line, in/sec
Dv = change in liquid velocity, in/sec

For water at room temperature in a rigid pipe, the waterhammer pressure rise DP (psi) due to a very rapid (td < tp) flow stoppage Dv (ft/sec) can be approximated by


The stoppage of a 10 ft/sec flow of water that would yield DP < 1 psi with bulk flow (slow valve closure), will now cause a pressure rise of 650 psi in case of waterhammer (fast valve closure). Note that downstream of the closing element the pressure will drop.

Effects of Waterhammer in Liquid Lines

A waterhammer in a liquid line may cause failure in one of several ways: (1) Burst of the pipe, (2) Leakage at mechanical joints, gaskets and packing, (3) Failure or malfunction of in-line instruments and components, and (4) Movement of the line.

Figure 1 is a case in point, where a pipeline burst under the effect of an oil hammer. In this case, the burst occurred in a corroded region of the line. Note that because the breathing mode of the pipe is very stiff there will be dynamic amplification of the pressure pulse.


Figure 1 - Oil Hammer in Corroded Section of Pipeline

Deformation may be caused by the pressure imbalance in the line as the waterhammer pressure wave travels upstream. This force imbalance causes the system to move, more often jump; possibly failing braces and supports, Figure 2.


Figure 2 – Axial Thrust Block Fails from Waterhammer

Transition to Two-Phase Transient. As we have seen, the pressure at the closing valve, at the onset of the waterhammer, increases to


After the pressure wave travels upstream a distance L at the speed of sound c, reflects at the opposite end and comes back to the now closed valve (a travel which takes 2L/c seconds to accomplish), the reflected pressure at the closed valve will drop as shown in Figure 3, to become


Figure 3 - Waterhammer Pressure at the Closed Valve

And if this reduced pressure is below the vapor pressure, a steam bubble will form (a large cavitation). What started as a liquid waterhammer has now evolved into a liquid-vapor condition, itself causing its own bubble collapse waterhammer, which will be the subject of the next article.

Becht Nuclear Projects

  • CFD Analysis
  • Analysis of Buried Tanks
  • Pump Trips/Chk Valve Closure

Computational Fluid Dynamic (CFD) Analysis Resolves Deaerator Cracking

Becht Engineering recently reviewed a utility company's deaerators which experienced a through-wall, circumferential crack at the toe of the fillet weld attaching the saddle to the shell and a through-wall crack was found at the head-to-shell junction at the steam inlet end of the drum.

The saddle to shell cracking was attributed to restrained axial thermal expansion of the shell at a tightly bolted sliding saddle support. The crack was ground out, welded and the support modified to permit sliding.

The head to shell crack cause was attributed to corrosion fatigue, a common occurrence in deaerators. The crack was most likely initiated at a weld surface defect on the I.D. of the drum and grew with time. The daily operating cycles of the drum during periods of reduced steam demand and thermal stresses which we attributed to a poorly designed steam inlet nozzle were the main contributors to the crack growth.

A large diameter superheated steam inlet nozzle extended through the head of the drum terminating 18” into the vessel. The steam exited through a rectangular shaped slot opening on the underside of the pipe which directed the flow of superheated steam directly into the condensate on the bottom of the drum near the shell-to-head weld.

Becht’s computational fluid dynamics model (CFD) indicated that there was little dispersion of the steam exiting the nozzle and that the velocity of the steam mixing with the condensate was relatively high. The superheated steam contact with the cooler condensate resulted in a violent reaction with localized heating and cooling of the vessel shell. This cycling can cause thermal stresses which can result fatigue cracking. Generally, fatigue cracking occurs at welds and heat affected zones adjacent to the weld. Notably no such weld cracking occurred at

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Soil-Structure Interaction Analysis of Buried Tanks

Becht Engineering is performing a seismic analysis to assess the structural integrity of the tanks subjected to a postulated earthquake. The motivation for performing the soil-structure interaction (SSI) analysis in the time domain is to capture the behavior of several contact interfaces present in the tanks including the interface between the tank concrete and the surrounding soil. The presence of this contact interface helps to establish a realistic initial geostatic stress state under gravity loading.

Before the SSI analysis was conducted, a site-response analysis was performed to determine the strain-compatible soil properties. Boundary conditions on the model were prescribed to enforce shear beam behavior of the soil column surrounding and supporting the tank. The seismic input was applied at the base of the SSI model as a force time series corresponding to the known acceleration record.

The model includes the tank waste and the effects of concrete degradation as illustrated below. The soil and concrete are modeled using linear elastic material properties with concrete degradation simulated through the use of equivalent degraded elastic properties. When linear elastic material properties are used to model soils, there is potential for developing artificial soil arching. Excessive arching behavior will result in underestimating the vertical loads on the concrete dome and tank sidewalls. To mitigate the potential for soil arching above the dome, vertical contact surfaces are inserted into the soil above the dome to create annular rings of soil that are free to displace vertically consistent with the tank dome, but allow the load to be transferred laterally during horizontal motion. This effectively creates a nonlinear yield mechanism that acts in the vertical direction only and allows for horizontal load transfer from one ring to the other ring. A low coefficient of friction is used, thereby ensuring

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Pump Trips/Check Valve Closure

pump tripSystems running multiple pumps in parallel can undergo serious equipment and piping damage during a pump trip caused by a power outage or pump mechanical failure. Uncontrolled reverse flow in the system can occur and if improperly selected check valves are used it can result in pumps running backwards or transient pressure spikes in the system, i.e., water hammer.

Water hammer will occur if reverse flow occurs prior closure of the check valve and the effect increases with higher reverse flow velocity. Becht has worked with clients on analysis of the design of their systems, e.g., a water treating facility running multiple 52,000 gpm pumps in parallel, a seawater pump station pumping cooling water through a several mile pipeline to an inland facility and a boiler feed water circulation system for a 3000 psig forced circulation boiler.

In a three pump system (two operating and one spare), one and two pump trips were analyzed to determine the response of the system, i.e., fluid deceleration, time at the occurrence of reverse flow vs. time of check valve closure, pressure transients and unbalanced forces that are imposed on the piping and pumps. The figure shows the forward fluid velocity vs. time as the speed of the pump(s) slows, the point of reverse flow, the time at check valve closure and pressure spikes in the system.

Based on the analysis, the required performance of the check valve to minimize reverse flow can be determined and a valve selected. No valve will close precisely at "zero" fluid velocity; however, certain type valves perform significantly better than others.

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Becht Nuclear - Articles

  • Fluid Transients in Piping Systems 1 +

    Part 1 – Waterhammer in Liquid Lines This is the first in a series of articles on fluid transients in piping systems. Four Broad Categories. From a practical point of view, fluid transients in piping systems can be divided into four Read More
  • Fluid Transients in Piping Systems 2 +

    Pressure Transients in Liquid-Gas Lines - Part 2 This is the second in a series of articles on fluid transients in piping systems. A trapped gas pocket in a liquid system can occur in several configurations, as illustrated in Figure 1. Read More
  • Fluid Transients in Piping Systems 3 +

    Fluid Transients in Piping Systems - Part 3 Liquid-Gas Transients Modeling water hammer due to trapped gas can involve complicated equations while requiring potentially overly conservative assumptions.  In an effort to better show the effects of different modeling methods, this paper will Read More
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Becht Nuclear Lunch & Learn

becht nuclear training

Becht Nuclear Services offers free, 1-hour overview sessions on a variety of topics such as:

  • Wall Thinning Corrosion or Erosion in Piping Systems using ASME XI CC N-513 and N-597
  • Operability of Piping Systems using ASME III Div.1 Appendix F
  • Crack-Like Flaws using ASME XI Failure Assessment Diagram
  • Wall Thinning Corrosion or Erosion in Buried Piping Systems using ASME XI CC N-806
  • Plus much, much more...

Each seminar is followed by a question period for participants.

47 georgeablogInstructor:  George Antaki, PE, fellow ASME, is chairman of ASME III Working Group Piping Design, chairman of ASME B31 Mechanical design Committee, and member of ASME O&M Subgroup Piping.  George is the Division Manager for Becht Nuclear and has over 40 years of hands-on experience.

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