Leak noise propagation and attenuation in submerged plastic water pipes

Detection of water leaks in buried distribution pipes using acoustic methods is common practice in many countries. Correlation techniques are widely used in leak detection, and these have been extremely effective when attempting to locate leaks in metal pipes. However, a number of difficulties have been highlighted when trying to determine the position of leaks in plastic pipes. Of particular interest here is what happens to the leak noise when the pipe passes through an expanse of water, such as across a river or lake.In this paper, the low-frequency acoustic propagation and attenuation characteristics of a submerged plastic water pipe are investigated experimentally in the laboratory, supported by predictions from a theoretical model. It is found that, whilst the signal attenuation for a submerged pipe is increased relative to that for a similar in-vacuo pipe, energy does not, in fact, radiate into the water; furthermore, the attenuation is small compared with that for a pipe buried in soil.     

WAVENUMBER PREDICTION OF WAVES IN BURIED PIPES FOR WATER LEAK DETECTION

Water leaks are a topic of great concern in Britain and many other countries, because of decreasing water supplies and the deterioration of old pipework. Correlation techniques are widely used in leak detection, but for these to be effective, the propagation wavespeeds and wave attenuation must be known. Relatively predictable for metal pipes, these are largely unknown for the newer plastic pipes, being highly dependent on the pipe wall properties and the surrounding medium. In this paper, pipe equations for n=0 axisymmetric wave motion are derived for a fluid-filled pipe, surrounded by an infinite elastic medium which can support both longitudinal and shear waves. These equations are solved for two wave types,s =1,2, which correspond to a fluid dominated wave and an axial shell wave, and expressions for a complex wavenumber for each wave are given.     

Phonon- and impurity-limited dc mobility calculation from frequency derivatives of time correlation functions. I. General formulae derivation

Starting from the first principles expression for the dc electric conductivity, as derived in 1982 by the authors, new expressions for mobility in semiconductors are derived, for the case when the carriers spectrum is parabolic and the scatterers are phonons and point impurities.     

Particle transport in space-periodic potentials in underdamped systems

We consider the motion of an underdamped Brownian particle in a tilted periodic potentialin a wide temperature range. Based on the previous data and the new simulation results weshow that the underdamped motion of particles in space-periodic potentials can beconsidered as overdamped motion in the velocity space in the effective double-wellpotential. Simple analytic expressions for the particle mobility and diffusion coefficientare derived with the use of the presented model. These accurately match numericalsimulation results.     

Elastic fields of a screw superdislocation with a hollow core (pipe) perpendicular to the free crystal surface

Screw superdislocations with hollow cores (pipes) which arise during growth of semiconductor crystals such as silicon carbide and gallium nitride are considered. Exact analytical expressions are first derived for the displacements, strains, and stresses associated with a pipe oriented perpendicular to the free planar surface of an elastically isotropic half-space. It is shown that the stress field of the dislocation present in the pipe is heavily affected when the exact boundary conditions at the free cylindrical surface of the pipe are taken into account. The influence is the strongest in the region around the pipe at distances of the order of the pipe radius from the surface of the pipe. In this region, the elastic strains can be as large as a few tenths of one percent. The results obtained can be useful in analyzing the interaction of pipes with one another and with other defects, as well as in simulating the behavior of pipes during crystal growth.     

SIMPLIFIED DISPERSION RELATIONSHIPS FOR IN-VACUO PIPES

The dispersion characteristics of a pipe offer a way to gain physical insight into its dynamic behaviour. Whilst these can be found in the literature they are generally calculated by numerically solving the characteristic equation. In this paper, a simplified characteristic equation of an in vacuo pipe is presented and from this analytical expressions for the wavenumbers for the circumferential modes below the ring frequency are derived. It is shown that before waves cut on and propagate, they change from being decaying standing waves at low frequencies to being nearfield waves. A simplified expression is also determined for the cut on frequencies of the n?2 circumferential modes. Simulations are presented to validate the results against some established theories of pipe vibration.     

The mobility of the amorphous phase in polyethylene as a determining factor for slow crack growth

Polyethylene (PE) pipes generally exhibit a limited lifetime, which is considerably shorter than their chemical degradation period. Slow crack growth failure occurs when pipes are used in long-distance water or gas distribution though being exposed to a pressure lower than the corresponding yield stress. This slow crack growth failure is characterized by localized craze growth and craze fibril rupture. In the literature, the lifetime of PE pipes is often considered as being determined by the density of tie chains connecting adjacent crystalline lamellae. But this consideration cannot explain the excellent durability of the recent bimodal grade PE for pipe application. We show in this paper the importance of the craze fibril length as the determining factor for the pipe lifetime. The conclusions are drawn from stress analysis. It is found that longer craze fibrils sustain lower stress and are deformed to a lesser degree. The mobility of the amorphous phase is found to control the amount of material that can be sucked in by the craze fibrils and thus the length of the craze fibrils. The mobility of the amorphous phase can be monitored by dynamic mechanical analysis measurements. Excellent agreement between the mobility thus derived and lifetimes of PE materials as derived from FNCT (full notch creep test) is given, thus providing an effective means to estimate the lifetime of PE pipes by considering well-defined physical properties.     

Attenuation and scattering of axisymmetrical modes in a fluid-filled round pipe with internally rough walls

The attenuation of axisymmetric eigenmodes in a cylindrical, elastic, fluid-filled waveguide with a statistically rough elastic wall is studied. It is shown that small perturbation theory can be used to relate explicitly the statistical characteristics of the internal wall surface roughness of an elastic pipe to the attenuation and scattering coefficients of the acoustic modes in the filling fluid. Analytical expressions for modal attenuation coefficients are obtained. The analysis of the frequency dependent attenuation coefficients and the ratio between the roughness correlation length and the inner radius of the pipe is made for different correlation functions of the roughness. It is shown that two scale parameters control the overall behavior of the modal attenuation coefficients. These are the ratios of the roughness correlation length and the inner pipe radius to the acoustic wavelength. The numerical results for sound propagation in a pipe and in a borehole with statistically rough, elastic walls are obtained and discussed.     

Two-sphere hydrodynamic interactions and mobilities in a porous medium

The translational mobility tensor of an arbitrary number of spheres immersed in a viscous fluid enclosed in a porous medium is formally calculated in a power serie expansion in R⁻¹, where R is the inter-particle distance. This calculation is realized by solving the screened Navier-Stokes oquation with the recent formalism of Mazur and van Saarloos. Explicit expressions are derived for the pair mobility tensor up to order R₋₇.     

An approximation for the point mobility at the intersection of two perpendicular plates

The problem of point excitation at a T-intersection of two perpendicular plates is studied in order to establish expressions for the point mobility. It is found that the theory for point excitation of the free surface of a semi-infinite elastic solid is applicable in the frequency range associated with structure-borne sound transmission. From this theory the mobility for an infinite system is derived. Based on this model and on an experimental investigation an estimation procedure for the point mobility in the finite dimension case is developed. The agreement with measurements performed in situ is quite acceptable. Both the theoretical and the experimental investigations reveal that the real part of this mobility is small, although it is larger in the experimental results. This indicates that other components of excitation are difficult to eliminate and may contribute to the power input in practice. Because of the small real part of the mobility it is advantageous with respect to the reduction of structure-borne sound power transmission to locate the contact points between a source and the receiver at such intersections. Corrections are deduced for the measured magnitude of the mobility for the case when separate force and motion transducers are used.     

Nonaxisymmetric oscillations of a charged jet of a finite-conductivity viscous liquid

A dispersion relation for nonaxisymmetric oscillations of a charged jet of a viscous incompressible finite-conductivity liquid is derived. In the low-viscosity limit, when the dispersion relation can be reduced to a power algebraic equation, analytical expressions for its roots are found and their dependences on the conductivity of the liquid and carrier mobility are analyzed. Taking into account a finite rate of electric charge transfer introduces an additional damping and somewhat decreases the instability growth rates.     

General analytical expressions for the bit error rate of atmospheric optical communication systems

General analytical expressions are derived for the average bit error rate of an intensity modulation and direct detection link using unbounded optical wavefront with on-off keying signalling technique propagating under all possible irradiance fluctuation conditions. These expressions include in a single equation the link performance of most of the proposed statistical models derived until now.     

Quantum mechanical activation energy of vacancy diffusion in crystals

This report examines the quantum mechanical mobility of vacancies in cubic crystals using the Morse potential. Nonadiahatic effects in vacancy diffusion are considered. Analytic expressions for the probability of a diffusive jump and for the activation energy are derived.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 29–32, April, 1988.     

Surface displacements accompanying the propagation of acoustic waves within an underground pipe

Theoretical expressions for surface displacements accompanying the propagation of acoustic waves in a buried gas-filled pipe are derived. It is shown that the radiated field consists of both shear and compressional components of comparable amplitude which interfere with one another because of the large difference in the respective propagation velocites. This is manifested at the surface by a series of maxima and minima in the vertical and horizontal displacements. Comparing the theoretical calculation to experimental data on vertical surface displacements generated by plane progressive waves at frequencies ranging from 200 to 2000 Hz within an underground pipe shows that only axisymmetric radial and longitudinal vibration of the pipe wall is important. This stands in marked constant to experiments carried out by others in an air medium in which the contribution of bending mode excitation was shown to be significant, particularly at lower frequencies. The theory can be fitted to the experimental data only if the compressional and shear velocities α and β, respectively, are narrowly specified, leading to α = 259 m/s and β = 164 m/s, the latter being in reasonable agreement with the results of other investigators for clay soil.     

New line integral expressions for Fraunhofer diffraction

New expressions for Fraunhofer diffraction at an arbitrary shape aperture are presented. These are expressed in the simple form of the line integral over the rim of the aperture. Far field patterns for various shaped apertures are easily derived from these expressions which are well suited for numerical calculation. As examples, Fraunhofer diffraction fields for elliptical, polygonal, and sinusoidal apertures are shown.     

Optimization of in-vacuo template-stripped Pt surfaces via UHV STM

A recently demonstrated [1] in-vacuo template-stripping process is applied to the study of platinum films stripped from ultra-flat silicon-oxide surfaces. Template-stripped (TS) Pt surfaces, prepared with a range of post-deposition annealing times prior to being stripped from the templating surface in an ultra-high vacuum (UHV) environment, are examined by UHV scanning tunneling microscopy (STM). These studies reveal that without post-deposition annealing, TS Pt surfaces are largely made up of poorly-ordered, granular nanostructures undesirable for many applications. The post-deposition annealing treatments explored in the study result in the emergence and continuous growth of large smooth crystallites. Issues with crystallite orientation relative to the TS surface and artefacts arising as a result of the epoxy used in the template-stripping process are presented and discussed in relation to optimizing the template-stripping procedure for specific applications such as self-assembled monolayer (SAM) formation for molecular electronics. PACS 68.37.Ef; 68.47.De; 68.55.Jk; 81.05.Bx; 81.15.Ef     

Correct determination of net gain in Er-doped optical waveguide amplifier from pump-on/off measurement

Starting with evolution equation of signal optical power in an Er-doped channel waveguide, rigorous theoretical expressions used for correct determination of net gain from signal enhancement measured by using pump-on/off method are derived. These expressions allow to clarify the argument on relationships between net gain, internal gain and signal enhancement in some earlier literatures. Physical implications of net gain, internal gain and signal enhancement expressions are analyzed. Standardized definitions for the three physical quantities are proposed. The definition for net gain is proposed on the basis of practical application of an EDWA in optical fiber communication and the definitions for the latter two are suggested based on the physical implication analysis of their expressions.     

The opportunistic transmission of wireless worms between mobile devices

The ubiquity of portable wireless-enabled computing and communications devices has stimulated the emergence of malicious codes (wireless worms) that are capable of spreading between spatially proximal devices. The potential exists for worms to be opportunistically transmitted between devices as they move around, so human mobility patterns will have an impact on epidemic spread. The scenario we address in this paper is proximity attacks from fleetingly in-contact wireless devices with short-range communication range, such as Bluetooth-enabled smart phones.An individual-based model of mobile devices is introduced and the effect of population characteristics and device behaviour on the outbreak dynamics is investigated. The model uses straight-line motion to achieve population, though it is recognised that this is a highly simplified representation of human mobility patterns. We show that the contact rate can be derived from the underlying mobility model and, through extensive simulation, that mass-action epidemic models remain applicable to worm spreading in the low density regime studied here. The model gives useful analytical expressions against which more refined simulations of worm spread can be developed and tested.     

Electrostatic force between rings and discs of charge inside a grounded metallic pipe using the Green’s function technique

We derive analytic formulae for the electrostatic force between ring and disc charge distributions inside a grounded metallic pipe using the Green’s function technique. These distribution models are useful in the modeling of electron beams commonly employed in microwave tubes. We analyze the electric force between two discs, between two rings, and between a disc and a ring and we compare the results for the electric potential, field, and force to numerical ones obtained from a 3D electrostatic solver. Present expressions were developed to avoid an oscillatory noise when the field diverges by axial proximity between source and observer.     

On Synge's covariant conservation laws for general relativity

Following Synge, the covariant formulas for the total four-momentum and angular momentum of an isolated physical system in general relativity are derived. These formulas are first obtained in the weak-field approximation, for which they are shown to be expressible in surface integral form, to be unique, and to represent covariantly conserved quantities. The covariant expressions for the general case are then shown to be identical to those for the weak-field case. The uniquely determined and covariantly conserved quantities so obtained are found to agree with the corresponding canonical, noncovariant surface integral expressions.