An improved formula for terminal velocity of rigid spheres

1997 ◽  
Vol 50 (1-2) ◽  
pp. 53-61 ◽  
Author(s):  
A.V. Nguyen ◽  
H. Stechemesser ◽  
G. Zobel ◽  
H.J. Schulze
2005 ◽  
Vol 62 (5) ◽  
pp. 1637-1644 ◽  
Author(s):  
David L. Mitchell ◽  
Andrew J. Heymsfield

Abstract Recent work on the terminal velocity of ice crystal aggregates suggests that their “Re–X” relationship may not be well predicted by current theory. This study examines possible reasons for this departure from theory, and develops a new Re–X relationship appropriate for ice crystal aggregates. The methodology of Khvorostyanov and Curry was applied to this new relationship to formulate power-law expressions for all ice particle types. Fall speed differences between the Khvorostyanov and Curry approach and the approach described here were as large as 50% for aggregates and 30% for single crystals. This was primarily due to the following: 1) surface roughness coefficients used in the former were appropriate for rigid spheres and liquid drops but not for ice crystals and 2) the relationship between Reynolds number Re and Best number X at high Re is better described for aggregates by adding a second term to the Re–X governing equation, as done in this work. The corrections and improvements described here may be critical to the calculation of snowfall rates, to the modeling of the aggregation process, and for interpreting Doppler radar measurements during snowfall events. Since most of the size distribution mass is generally associated with aggregates below cloud base, an accurate treatment of aggregate fall speeds is needed for determining snowfall rates.


2012 ◽  
Vol 8 (1) ◽  
pp. 1-15
Author(s):  
Gy. Sitkei

Motion of particles with air resistance (e.g. horizontal and inclined throwing) plays an important role in many technological processes in agriculture, wood industry and several other fields. Although, the basic equation of motion of this problem is well known, however, the solutions for practical applications are not sufficient. In this article working diagrams were developed for quick estimation of the throwing distance and the terminal velocity. Approximate solution procedures are presented in closed form with acceptable error. The working diagrams provide with arbitrary initial conditions in dimensionless form of general validity.


1998 ◽  
Vol 11 (1) ◽  
pp. 358-358
Author(s):  
M. Parthasarathy

SAO 244567 (Henl357) (IRAS 17119-5926) is a high galactic latitude (1 = 331°, b = −12°) early type star, originally classified as a B or A type H-alpha emission line star by Henize (1976). It is an IRAS source with far infrared colours similar to planetary nebulae. The IUE ultraviolet spectra obtained during the last eight years show that the central star is rapidly evolving. It is found that the central star of this young PN has faded by a factor of 3 within the last seven eight years. The terminal velocity of the stellar wind has decreased from −3500 km/sec in 1988 to almost zero in 1994. In 1988 the C IV (1550A) line which was a P-Cygni profile with strong absorption component had almost vanished by 1994. The CIII] 1909A emission strength increased markedly within 4 years from 1988 to 1992. The optical spectra obtained since 1990 shows very clearly only the nebular spectrum which is very similar to that of low excitation planetary nebula. The optical spectrum of SAO 244567 obtained in 1971 shows that it was a post-AGB B 1 or B2 supergiant at that time. This result shows that SAO 244567 has turned into a planetary nebula within the last 20 years. Recently Bobrowsky (1994) obtained narrowband optically resolved images in both H-beta and [OIII] 5007A with the HST planetary camera which revealed a well resolved nebula of size 2 seconds of arc. In this paper we discuss the recent new results.


Processes ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 711
Author(s):  
Zdzisław Kaliniewicz ◽  
Dariusz J. Choszcz

Viburnum is a genus of colorful and ornamental plants popular in landscape design on account of their high esthetic appeal. The physical properties of viburnum seeds have not been investigated in the literature to date. Therefore, the aim of this study was to characterize the seeds of selected Viburnum species and to search for potential relationships between their physical attributes for the needs of seed sorting operations. The basic physical parameters of the seeds of six Viburnum species were measured, and the relationships between these attributes were determined in correlation and regression analyses. The average values of the evaluated parameters were determined in the following range: terminal velocity—from 5.6 to 7.9 m s−1, thickness—from 1.39 to 1.87 mm, width—from 3.59 to 6.33 mm, length—from 5.58 to 7.44 mm, angle of external friction—from 36.7 to 43.8°, mass—from 16.7 to 35.0 mg. The seeds of V. dasyanthum, V. lentago and V. sargentii should be sorted in air separators, and the seeds of V. lantana and V. opulus should be processed with the use of mesh screens with round apertures to obtain uniform size fractions. The seeds of V. rhytodophyllum cannot be effectively sorted into batches with uniform seed mass, but they can be separated into groups with similar dimensions.


1959 ◽  
Vol 3 (1) ◽  
pp. 137-152 ◽  
Author(s):  
Irvin M. Krieger ◽  
Thomas J. Dougherty
Keyword(s):  

2021 ◽  
pp. 014459872110204
Author(s):  
Wan Cheng ◽  
Chunhua Lu ◽  
Guanxiong Feng ◽  
Bo Xiao

Multistaged temporary plugging fracturing in horizontal wells is an emerging technology to promote uniform fracture propagation in tight reservoirs by injecting ball sealers to plug higher-flux perforations. The seating mechanism and transportation of ball sealers remain poorly understood. In this paper, the sensitivities of the ball sealer density, casing injection rate and perforation angle to the seating behaviors are studied. In a vertical wellbore section, a ball sealer accelerates very fast at the beginning of the dropping and reaches a stable state within a few seconds. The terminal velocity of a non-buoyant ball is greater than the fluid velocity, while the terminal velocity of a buoyant ball is less than the fluid velocity. In the horizontal wellbore section, the terminal velocity of a non-buoyant or buoyant ball is less than the fracturing fluid flowing velocity. The ball sealer density is a more critical parameter than the casing injection rate when a ball sealer diverts to a perforation hole. The casing injection rate is a more critical parameter than the ball sealer density when a ball sealer seats on a perforation hole. A buoyant ball sealer associated with a high injection rate of fracturing fluid is highly recommended to improve the seating efficiency.


1983 ◽  
Vol 100 ◽  
pp. 133-134
Author(s):  
Frank N. Bash

Bash and Peters (1976) suggested that giant molecular clouds (GMC's) can be viewed as ballistic particles launched from the two-armed spiral-shock (TASS) wave with orbits influenced only by the overall galactic gravitational potential perturbed by the spiral gravitational potential in the arms. For GMC's in the Milky Way, the model predicts that the radial velocity observed from the Sun increases with age (time since launch). We showed that the terminal velocity of CO observed from l ≃ 30° to l ≃ 60° can be understood if all GMC's are born in the spiral pattern given by Yuan (1969) and live 30 × 106 yrs. Older GMC's were predicted to have radial velocities which exceed observed terminal velocities.


1998 ◽  
Vol 539 ◽  
Author(s):  
T. Cramer ◽  
A. Wanner ◽  
P. Gumbsch

AbstractTensile tests on notched plates of single-crystalline silicon were carried out at high overloads. Cracks were forced to propagate on {110} planes in a <110> direction. The dynamics of the fracture process was measured using the potential drop technique and correlated with the fracture surface morphology. Crack propagation velocity did not exceed a terminal velocity of v = 3800 m/s, which corresponds to 83%7 of the Rayleigh wave velocity vR. Specimens fractured at low stresses exhibited crystallographic cleavage whereas a transition from mirror-like smooth regions to rougher hackle zones was observed in case of the specimens fractured at high stresses. Inspection of the mirror zone at high magnification revealed a deviation of the {110} plane onto {111} crystallographic facets.


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