Paper 2: The Velocity of Water Hammer Waves

1965 ◽  
Vol 180 (5) ◽  
pp. 12-20 ◽  
Author(s):  
I. S. Pearsall
Keyword(s):  
High Pressures ◽  
Water Hammer ◽  
Acoustic Velocity ◽  
Gas Content ◽  
Pressure Waves ◽  
Free Gas ◽  
Pumping Stations ◽  
Flow Changes ◽  
Very High ◽  
Good Agreement

Sudden flow changes in a pipeline cause water hammer waves to be transmitted up the pipe. The magnitude of these pressure waves is directly proportioned to the acoustic velocity. The value of the acoustic velocity depends on the bulk modulus or compressibility of the liquid. It is thus affected by pressure, temperature and gas content of the liquid, as well as by the elasticity of the pipe. For water, considerable data are available on the variation of acoustic velocity with temperature and pressure. These are summarized and it is shown that, whereas temperature causes changes of the order of 1 per cent per 5 degC, the variation due to pressure is negligible except at very high pressures. The presence of free gas causes a considerable increase in compressibility, and it is shown that even as little as 1 part of air in 104 parts of water by volume causes a 50 per cent reduction in acoustic velocity. The damping of the pressure waves, which has an overall beneficial effect, is also greatly increased by the presence of free gas, and data are given on these effects. Solids in liquid have a similar but less drastic influence. Experimental results are given of some tests on two sewage pumping stations in which good agreement was obtained between theory and experiment. The elasticity of the pipe also affects the acoustic velocity and a summary is given of the data available for steel, concrete, and rock-lined tunnels, with different types of pipe fixing.

scholarly journals Numerical simulations of non-spherical bubble collapse

2009 ◽  
Vol 629 ◽  
pp. 231-262 ◽  
Author(s):  
ERIC JOHNSEN ◽  
TIM COLONIUS
Keyword(s):  
Bubble Dynamics ◽  
High Pressures ◽  
Pressure Ratio ◽  
Free Field ◽  
Water Hammer ◽  
Incident Shock ◽  
Bubble Collapse ◽  
Shock Propagation ◽  
Potential Damage ◽  
Very High

A high-order accurate shock- and interface-capturing scheme is used to simulate the collapse of a gas bubble in water. In order to better understand the damage caused by collapsing bubbles, the dynamics of the shock-induced and Rayleigh collapse of a bubble near a planar rigid surface and in a free field are analysed. Collapse times, bubble displacements, interfacial velocities and surface pressures are quantified as a function of the pressure ratio driving the collapse and of the initial bubble stand-off distance from the wall; these quantities are compared to the available theory and experiments and show good agreement with the data for both the bubble dynamics and the propagation of the shock emitted upon the collapse. Non-spherical collapse involves the formation of a re-entrant jet directed towards the wall or in the direction of propagation of the incoming shock. In shock-induced collapse, very high jet velocities can be achieved, and the finite time for shock propagation through the bubble may be non-negligible compared to the collapse time for the pressure ratios of interest. Several types of shock waves are generated during the collapse, including precursor and water-hammer shocks that arise from the re-entrant jet formation and its impact upon the distal side of the bubble, respectively. The water-hammer shock can generate very high pressures on the wall, far exceeding those from the incident shock. The potential damage to the neighbouring surface is quantified by measuring the wall pressure. The range of stand-off distances and the surface area for which amplification of the incident shock due to bubble collapse occurs is determined.

Measurements of the coefficients of friction of different lubricants during impact under high pressure and shear

2003 ◽  
Vol 217 (2) ◽  
pp. 115-124 ◽  
Author(s):  
M. F. Workel ◽  
D Dowson ◽  
P Ehret ◽  
C. M. Taylor
Keyword(s):  
High Pressure ◽  
High Pressures ◽  
Large Range ◽  
Shear Stresses ◽  
Ball Impact ◽  
Shear Rates ◽  
Impact Experiment ◽  
Decreasing Functions ◽  
Very High ◽  
Good Agreement

For a comprehensive set of lubricants the friction coefficients were determined under very high pressures and shear rates by means of a ball impact experiment. Measurements of the limiting shear stresses were obtained for a large range of pressures, from about 2 to 4 GPa, as typically encountered in elastohydrodynamic contacts. It was shown that under these conditions the limiting shear stresses increased less than proportionally with the pressure; i.e. the coefficients of friction were decreasing functions of the pressures. The results were compared with previously reported values from the literature and in general good agreement was obtained.

Dislocation structures around SiO2 Particles in aged Cu-Cr-SiO2

1978 ◽  
Vol 36 (1) ◽  
pp. 594-595
Author(s):  
N.J. Long ◽  
M.H. Loretto ◽  
C.H. Lloyd
Keyword(s):  
Flow Stress ◽  
Single Crystals ◽  
Room Temperature ◽  
Thin Foil ◽  
Age Hardening ◽  
Dispersion Strengthening ◽  
Accurate Picture ◽  
The Matrix ◽  
Very High ◽  
Good Agreement

IntroductionThere have been several t.e.m. studies (1,2,3,4) of the dislocation arrangements in the matrix and around the particles in dispersion strengthened single crystals deformed in single slip. Good agreement has been obtained in general between the observed structures and the various theories for the flow stress and work hardening of this class of alloy. There has been though some difficulty in obtaining an accurate picture of these arrangements in the case when the obstacles are large (of the order of several 1000's Å). This is due to both the physical loss of dislocations from the thin foil in its preparation and to rearrangement of the structure on unloading and standing at room temperature under the influence of the very high localised stresses in the vicinity of the particles (2,3).This contribution presents part of a study of the Cu-Cr-SiO2 system where age hardening from the Cu-Cr and dispersion strengthening from Cu-Sio2 is combined.

scholarly journals Separate Universe calibration of the dependence of halo bias on cosmic web anisotropy

2020 ◽  
Vol 499 (3) ◽  
pp. 4418-4431 ◽  
Author(s):  
Sujatha Ramakrishnan ◽  
Aseem Paranjape
Keyword(s):  
Dark Matter ◽  
High Precision ◽  
Gaussian Distribution ◽  
Initial Perturbation ◽  
Analytical Framework ◽  
Web Environment ◽  
Wide Range ◽  
Galaxy Assembly ◽  
Very High ◽  
Good Agreement

ABSTRACT We use the Separate Universe technique to calibrate the dependence of linear and quadratic halo bias b1 and b2 on the local cosmic web environment of dark matter haloes. We do this by measuring the response of halo abundances at fixed mass and cosmic web tidal anisotropy α to an infinite wavelength initial perturbation. We augment our measurements with an analytical framework developed in earlier work that exploits the near-lognormal shape of the distribution of α and results in very high precision calibrations. We present convenient fitting functions for the dependence of b1 and b2 on α over a wide range of halo mass for redshifts 0 ≤ z ≤ 1. Our calibration of b2(α) is the first demonstration to date of the dependence of non-linear bias on the local web environment. Motivated by previous results that showed that α is the primary indicator of halo assembly bias for a number of halo properties beyond halo mass, we then extend our analytical framework to accommodate the dependence of b1 and b2 on any such secondary property that has, or can be monotonically transformed to have, a Gaussian distribution. We demonstrate this technique for the specific case of halo concentration, finding good agreement with previous results. Our calibrations will be useful for a variety of halo model analyses focusing on galaxy assembly bias, as well as analytical forecasts of the potential for using α as a segregating variable in multitracer analyses.

scholarly journals Gaseous combustion at high pressures. —Part X. The co-volume corrections, maximum temperatures and dissociation of steam and carbon dioxide in explosions

1928 ◽  
Vol 119 (782) ◽  
pp. 464-480
Keyword(s):  
Carbon Dioxide ◽  
High Pressure ◽  
Internal Energy ◽  
High Temperatures ◽  
High Pressures ◽  
Internal Combustion ◽  
Systematic Survey ◽  
Explosion Method ◽  
Maximum Temperatures ◽  
Very High

During the researches upon high-pressure explosions of carbonic oxide-air, hydrogen-air, etc., mixtures, which have been described in the previous papers of this series, a mass of data has been accumulated relating to the influence of density and temperature upon the internal energy of gases and the dissociation of steam and carbon dioxide. Some time ago, at Prof. Bone’s request, the author undertook a systematic survey of the data in question, and the present paper summarises some of the principal results thereof, which it is hoped will throw light upon problems interesting alike to chemists, physicists and internal-combustion engineers. The explosion method affords the only means known at present of determining the internal energies of gases at very high temperatures, and it has been used for this purpose for upwards of 50 years. Although by no means without difficulties, arising from uncertainties of some of the assumptions upon which it is based, yet, for want of a better, its results have been generally accepted as being at least provisionally valuable. Amongst the more recent investigations which have attracted attention in this connection should be mentioned those of Pier, Bjerrum, Siegel and Fenning, all of whom worked at low or medium pressures.

Responses of cerebral arteries and arterioles to acute hypotension and hypertension

1978 ◽  
Vol 234 (4) ◽  
pp. H371-H383 ◽  
Author(s):  
H. A. Kontos ◽  
E. P. Wei ◽  
R. M. Navari ◽  
J. E. Levasseur ◽  
W. I. Rosenblum ◽  
...  
Keyword(s):  
Pressure Range ◽  
High Pressures ◽  
Cerebral Arteries ◽  
Pial Arteries ◽  
Small Vessels ◽  
Size Dependent ◽  
Arterial Blood ◽  
Vascular Bed ◽  
Acute Hypotension ◽  
Very High

The responses of cerebral precapillary vessels to changes in arterial blood pressure were studied in anesthetized cats equipped with cranial windows for the direct observation of the pial microcirculation of the parietal cortex. Vessel responses were found to be size dependent. Between mean arterial pressures of 110 and 160 mmHg autoregulatory adjustments in caliber, e.g., constriction when the pressure rose and dilation when the pressure decreased, occurred only in vessels larger than 200 micron in diameter. Small arterioles, less than 100 micron in diameter, dilated only at pressures equal to or less than 90 mmHg; below 70 mmHg their dilation exceeded that of the larger vessels. When pressure rose to 170- 200 mmHg, small vessels dilated while the larger vessels remained constricted. At very high pressures (greater than 200 mmHg) forced dilation was frequently irreversible and was accompanied by loss of responsiveness to hypocapnia. Measurement of the pressure differences across various segments of the cerebral vascular bed showed that the larger surface cerebral vessels, extending from the circle of Willis to pial arteries 200 micron in diameter, were primarily responsible for the adjustments in flow over most of the pressure range.

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