(Editor's Note: The figures referenced here could not be reproduced electronically. Please see the print edition to view them.)
Anniversaries come in a wide range of guises, from the personal to the professional, from the state sponsored to the genuinely historic. By the time this column is read, we will be close to the centenary of the Wright brothers first flight at Kittyhawk, an anniversary that perhaps proves more than most that engineering really can change the world. Other anniversaries are only remembered by those with an intimate knowledge of the circumstances or a professional or personal cause to remember the event.
One such anniversary falls this year. In 1903, Joukowsky completed his assignment to investigate the water hammer problems encountered at the Imperial Water Works in St. Petersburg, Russia. In doing so, Joukowsky initiated the analysis and simulation of pressure transients, a subject that now has implications across a whole range of fluid system design. Affected systems include large scale hydroelectric schemes, oil and gas production, water and pumped sewage systems, and building utility services, including the safety of water closets and cross-contamination via building drainage and vent systems.
Joukowsky, who in the 1920s was to make considerable contributions to the understanding of lift and aerofoil shape within the USSR as an aeronautical engineer, approached his investigation at the Imperial Water Works by both a detailed experimental study of transient propagation and a theoretical study of the mechanisms of wave transmission. He showed for the first time that the pressure excursion, delta p, following a change in flow conditions, represented by a velocity change, delta V, could be expressed as:
delta p = Pc delta V
Where P is the fluid density and c is the local wave speed. Joukowsky's measurements of wave speed over several kilometers of pipe remain close to the values we would expect to record today. More importantly, he realized that the wave speed, central to the pressure prediction, depended upon both fluid properties and the elasticity and thickness/diameter ratio of the pipeline.
The nature of the water distribution system within which Joukowsky undertook his experimental work made it essential that he understood the complex pressure time traces he recorded. He was therefore the first to define the likely reflection and transmission coefficients applicable to a pressure wave arriving at any physical pipeline feature, such as a change in diameter, wall thickness or material, or a pipe junction. His explanations remain those we use today.
Joukowsky recognized the importance of the rate of change of flow conditions relative to the reflection time for pressure waves within a system. If a reduction in flow velocity takes longer than the time taken for a reflection to return from an upstream junction, reservoir or pump (the pipe period defined as tp = 2L/c, where L is the distance to the reflector), then the simplistic pressure rise calculation does not apply. Joukowsky understood that the full pressure rise predicted only occurs for "rapid" changes in flow, i.e., changes completed in less than a pipe period. As the pipe period depends on wave speed, changes in flow conditions must be defined in elapsed pipe periods and not time.
Joukowsky's work might have remained unrecognized if not for its translation by Simin on behalf of the American Water Works Association. In this form, it received worldwide attention and formed the basis for surge analysis.
The Kuhn model for the advancement of knowledge suggests that new paradigms arise to move subjects forward. While Joukowsky certainly did that in 1903, the next shift to the computer-based transient analysis may undoubtedly be traced to Streeter and Lai's 1963 paper demonstrating for the first time the application of the method of characteristics to the simulation of pressure transient propagation. Streeter's work drew on the mathematical basis laid by Mary Lister and suggested internationally by Gray in Australia, Fox in the U.K. and Paynter in the U.S.; however, it was the first paper to demonstrate the elegance of the methodology. There followed an explosion of applications to such diverse system problems as sodium-cooled reactors, fire fighting systems, and in-flight refueling--an exciting time to have been involved in an emerging discipline.
While the method of characteristics has become the industry standard for surge analysis, recently it has been used to simulate the low-amplitude air pressure transients set up in building drainage and vent systems. Any appliance discharge to a vertical stack, regardless of the venting system, will entrain an airflow that passes through the network to the sewer connection. Normally, in the U.K., venting is provided by an open upper termination to atmosphere, plus air admittance valves where necessary, and in some cases, a secondary vent stack cross-connected into the main waste water carrying stack. Increases in appliance discharge rate increase the entrained airflow, which is communicated to the system by the propagation of low-amplitude air pressure transients that lower the system pressure. Any interruption to the airflow due to stack surcharge will generate positive air pressure transients that reduce or destroy the entrained airflow. This generates the air pressure excursion indicated by the Joukowsky expression. Any externally imposed air pressure fluctuations, such as wind shear over the roof termination, pressure waves from remote surcharges, or pump selection in the sewer network, also propagate through the network. This leads to trap seal oscillation and possible depletion. The transient analysis based on Joukowsky and the modeling demonstrated by Streeter simulate these effects, and may be used forensically to determine the cause of system failure.
Figures 1 and 2 simulate a fatal system failure on the Fishguard to Rosslare ferry that involved trap seal loss in an en-suite cabin bathroom. This failure was attributed to appliance discharge to the stack while the stack upper termination was inadvertently blocked. Noxious fumes from the bilge tanks rose up the stack, causing the asphyxiation of two sleeping passengers. Figure 2 also illustrates the effect of replacing one of the system traps with a waterless trap capable of acting as an air admittance valve when the system pressure falls below atmosphere. In the U.K., the Hepworths HepV0(TM) Hygenic self-sealing waste valve unit would be suitable. The unit consists of a flexible self-sealing sheath that opens to allow water and air flows from habitable space to the drain branch when the differential pressure across the unit from appliance to drain is positive (Figure 3). Clearly, trap depletion and system failure would have been prevented.
Thus the centenary of Joukowsky's work should be remembered as laying the foundation for the simulation and analysis of pressure surge across a whole spectrum of fluid systems. In particular, these methods provide potential forensic tools to allow the understanding and prevention of system failure. They also demonstrate that system design within the built environment may benefit from the introduction of methodologies developed in the wider arena of fluid system design.
