scholarly journals IX. On the surface-tension of liquids investigated by the method of jet vibration

Among the large number of methods available for the determinations of the surface-tension of liquids that proposed by Lord Rayleigh stands out with great fundamental advantages. The principle is as follows:—A jet of liquid issuing from a not circular aperture is executing transverse vibrations depends upon the time elapsed, it is always the same at the same point in space, and thus the motion is steady and the boundary of the jet a fixed surface showing stationary waves. Measurements of the corresponding wave-length (λ), the velocity (V), and cross-section (A) of the jet, together with density ( ρ ) of the liquid afford the necessary constants for the calculation of the capillary-tension (T) according to Lord Rayleigh's theory of jet-vibration.

1. According to Lord Rayleigh’s theory of jet-vibrations, measurement of the length of the standing waves and the velocity and cross-section of a jet, together with the density of the liquid, affords the necessary constants for the calculation of the surface-tension. Notwithstanding the great fundamental advantages of this method, it has only been used in very few cases, and only for relative measurements of the surface-tension. The explanation hereof is to be found in the great difficulties connected with the adequate exact determination of the wave-length, and cross-section or velocity of the jet. As none of the methods in use for the measurement of these quantities could be taken as satisfactory, the main object of this investigation has been to work out really good methods for them.


1940 ◽  
Vol 30 (2) ◽  
pp. 139-178
Author(s):  
J. Emilio Ramirez

Summary Over a period of six months, from July to December, 1938, an investigation on microseismic waves has been carried out in the Department of Geophysics of St. Louis University. Four electromagnetic seismographs, specially designed for recording microseisms, were installed in the city of St. Louis in the form of a triangular network. Two of these were E-W components, one at the St. Louis University Gymnasium and the other 6.4 km. due west at Washington University. The other two were arranged as N-S components, one at the St. Louis University Gymnasium and one 6.3 km. due south at Maryville College. The speed of the photographic paper was 60 mm/min., and time signals were recorded automatically and simultaneously on each paper from the same clock every minute and at shorter intervals from a special pendulum and “tickler” combination by means of telephone wires. The results have demonstrated beyond doubt that microseismic waves are traveling and not stationary waves. The same waves have been identified at each one of the stations of the network, and also at Florissant, 21.8 km. away from St. Louis University. The speed of microseismic waves at St. Louis was determined from several storms of microseisms and it was found to be 2.67±0.03 km/sec. The direction of microseisms was also established for most of the storms and it was found that about 80 per cent of incoming microseisms at St. Louis were from the northeast quadrant during the interval from July to December, 1938. No microseisms were recorded from the south, west, or southwest. The period of the waves varied between 3.5 and 7.5 sec. The average period was about 5.4 sec. The microseismic wave length was therefore of the order of 14¼ km. A study of the nature of microseismic waves from the three Galitzin-Wilip components of the Florissant station reveals in the waves many of the characteristics of the Rayleigh waves; that is, the particles in the passage of microseismic waves move in elliptical orbits of somewhat larger vertical axis and with retrograde motion. A comparison carried over a period of more than a year between microseisms and microbarometric oscillations recorded by specially designed microbarographs showed no direct relationship between the two phenomena in wave form, group form, period, or duration of storms. The source of microseisms is to be found not over the land, but rather out over the surface of the ocean. The amplitudes of microseisms depend only on the intensity and widespread character of barometric lows traveling over the ocean. Several correlations between the two phenomena seem to make this conclusion rather evident. Special emphasis is laid on the fact that all the determined directions of incoming microseisms at St. Louis point to a deep barometric low over the ocean. The period of microseisms seems to be a function of the distance between the station and the source of microseisms. The exact mechanism by which barometric lows over the ocean water result in the production of microseisms needs further investigation. Large microseisms have been produced without any indication of surf near the coasts, or with winds blowing from the land toward the ocean.


The first section of this paper is an account of some experiments on the absorption of light in sodium vapour from the series limit at 2412 Å to about 1600 Å (an energy difference of 2·6 eV). The absorption cross-section at the limit is 11·6 ± 1·2 x 10 -20 cm 2 . The cross-section decreases giving a minimum of 1·3 ± 0·6 x 10 -20 cm 2 at 1900 Å and then increases to 1600 Å. A theoretical calculation by Seaton based on the dipole-length formula gives good agreement with the experiments at the series limit and also correctly predicts the wave-length for the minimum, but it predicts a significantly lower absorption at the minimum. The experiments described in the first section of the paper conclude a series on the absorption of light in the alkali metals. The second section consists of a general discussion of the results of these experiments and of their relation to theoretical calculations. There is good agreement between theory and experiment except in regard to the magnitude of the absorption at the minimum.


1977 ◽  
Vol 44 (4) ◽  
pp. 737-742 ◽  
Author(s):  
B. Downs

Natural frequencies of doubly symmetric cross section, isotropic cantilever beams, based on both Euler and Timoshenko theories, are presented for 36 combinations of linear depth and breadth taper. Results obtained by a new dynamic discretization technique include the first eight frequencies for all geometries and the stress distribution patterns for the first four (six) modes in the case of the wedge. Comparisons are drawn wherever possible with exact solutions and with other numerical results appearing in the literature. The results display outstanding accuracy and demonstrate that it is possible to model with high precision the dynamic behaviour of continuous systems by discretization on to a strictly limited number of degrees of freedom.


Author(s):  
Songwan Jin ◽  
Choonghyo Choi ◽  
Kenneth S. Breuer ◽  
Jung Yul Yoo

Effects of cross-section geometry of capillary on the evaporation from the meniscus have been investigated by adopting several circular and rectangular capillaries. The evaporating meniscus shape, evaporation rate and flow near the evaporating meniscus of various liquids such as water, ethanol and methanol are determined. The shapes of water and ethanol menisci in circular capillary are quite different from each other due to the difference in surface tension. But the difference in meniscus shapes is relatively small in rectangular channel. The averaged evaporation fluxes in rectangular channel are much larger than that in circular capillary. The rotating vortex motion is observed near the evaporating menisci of ethanol and methanol except for the case of methanol in 200 × 20-μm capillary. The reason for this is considered to be the existence of the corner menisci at the four corners.


The absorption of radiation of wave-length between 230 and 800 Å in neon was measured photometrically in a grazing incidence vacuum spectrograph. For wave-lengths longer than that corresponding to the first ionization limit the absorption coefficients were found to be zero except for photo-excitation of resonance transitions. Two sharp absorption edges were observed at 575 and 256 Å corresponding to the L 3 - and L 1 -edges respectively with a flat maximum between them. The photo-ionization cross-section at the first ionization limit was found to be 5⋅4 x 10 -18 cm 2 independent of the pressure between 50 and 500 μ ; this should be compared with the theoretical value of 5⋅8 x 10 -18 cm 2 obtained by Seaton using a dipole-length approximation. Between 575 and 400 Å the calculated and experimental curves agreed closely within the limits of measurement.


1977 ◽  
Vol 44 (1) ◽  
pp. 123-126 ◽  
Author(s):  
D. O. Banks ◽  
G. J. Kurowski

We analyze the transverse vibrations of a thin homogeneous beam which is symmetric with respect to the x-y and x-z planes. The cross section of the beam at x is assumed to have the form D(x)={(x,y,z)|x∈[0,1],y=xαy1,z=xβz1,(y1,z1)∈D1} where D1 is the cross section at x = 1. Expressions are obtained from which the eigenvalues and eigenfunctions can be easily found for 0 ≤ α < 2 and all combinations of clamped, hinged, guided, and free boundary conditions at both ends of the beam.


1958 ◽  
Vol 9 (4) ◽  
pp. 331-345
Author(s):  
E. H. Mansfield

SummaryThe natural transverse vibrations of a long cylindrical box of doubly symmetrical rectangular cross section are considered. Explicit stress-function solutions are obtained for the webs and the top and bottom surfaces so that the effects of shear lag and shear deflection are inherently included. The results are expressed simply in terms of an effective flexural rigidity, which may be determined with the aid of a number of graphs.


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