scholarly journals Ekman-Hartmann Boundary Layers and the Length of Day Variations

1993 ◽  
Vol 157 ◽  
pp. 453-455
Author(s):  
N. Kleeorin ◽  
I. Rogachevskii ◽  
A. Ruzmaikin
Keyword(s):  
Angular Velocity ◽  
Cylindrical Surface ◽  
Outer Sphere ◽  
Solid Core ◽  
Length Of Day ◽  
Slip Boundary ◽  
Velocity Gradients ◽  
Earth Core ◽  
Liquid Part ◽  
Angular Velocities

In the first issue of Journal of Fluid Mechanics Ian Proudman published a paper on the dynamical properties of a fluid between two concentric rotating spheres (Proudman, 1956). The angular velocities of the spheres were assumed only slightly different and the Reynolds number of the flow was large. It was found under non-slip boundary conditions that the cylindrical surface that touches the inner sphere and parallel to the axis of rotation is a singular surface in which velocity gradients are very large. Outside the cylinder the fluid rotates as a rigid body with the same angular velocity as the outer sphere. Inside the cylinder the fluid rotates with an angular velocity intermediate to the angular velocities of the spheres and there is also a meridional circulation. Later Stewartson (1966) presented a detailed investigation of structure of the shear layer near the cylindrical surface. One of the present authors (Ruzmaikin, 1989) pointed out a possible geophysical importance of these solutions. The liquid part of the Earth core occupying a shell between the inner solid core and the rock mantle can be considered as the fluid between two rotating spheres.

Finite difference code for velocity and surface traction of a Fluid between Two Eccentric Spheres

2015 ◽  
Vol 11 (1) ◽  
pp. 2960-2971
Author(s):  
M.Abdel Wahab
Keyword(s):  
Velocity Field ◽  
Angular Velocity ◽  
Finite Difference ◽  
Numerical Study ◽  
Outer Sphere ◽  
Equation Of Motion ◽  
Annular Region ◽  
Surface Traction ◽  
Angular Velocities ◽  
Axis Passing

The Numerical study of the flow of a fluid in the annular region between two eccentric sphere susing PHP Code isinvestigated. This flow is created by considering the inner sphere to rotate with angular velocity 1  and the outer sphererotate with angular velocity 2  about the axis passing through their centers, the z-axis, using the three dimensionalBispherical coordinates (, ,) .The velocity field of fluid is determined by solving equation of motion using PHP Codeat different cases of angular velocities of inner and outer sphere. Also Finite difference code is used to calculate surfacetractions at outer sphere.

Stokes Flow Around Slowly Rotating Concentric Pervious Spheres

2013 ◽  
Vol 60 (2) ◽  
pp. 165-219 ◽  
Author(s):  
Deepak Kumar Srivastava ◽  
Raja Ram Yadav ◽  
Supriya Yadav
Keyword(s):  
Angular Velocity ◽  
Stokes Flow ◽  
Outer Sphere ◽  
Present Situation ◽  
Subject Classification ◽  
Dissipated Energy ◽  
Azimuthal Component ◽  
Special Cases ◽  
Inner Sphere ◽  
Angular Velocities

In this paper, the problem of concentric pervious spheres carrying a fluid sink at their centre and rotating slowly with different uniform angular velocities 1, 2 about a diameter has been studied. The analysis reveals that only azimuthal component of velocity exists and the torque, rate of dissipated energy is found analytically in the present situation. The expression of torque on inner sphere rotating slowly with uniform angular velocity 1, while outer sphere also rotates slowly with uniform angular velocity Ω2, is evaluated. The special cases like, (i) inner sphere is fixed (i.e. Ω1 = 0), while outer sphere rotates with uniform angular velocity Ω2, (ii) outer sphere is fixed (i.e. Ω2 = 0), while inner sphere rotates with uniform angular velocity Ω1, (iii.) inner sphere rotates with uniform angular velocity 1, while outer rotates at infinity with angular velocity 2; have been deduced. The corresponding variation of torque with respect to sink parameter has been shown via figures. AMS subject classification - 76 D07

scholarly journals Slow Rotation of Concentric Spheres with Source at Their Centre in a Viscous Fluid

2009 ◽  
Vol 2009 ◽  
pp. 1-13 ◽  
Author(s):  
Deepak Kumar Srivastava
Keyword(s):  
Angular Velocity ◽  
Outer Sphere ◽  
Present Situation ◽  
Dissipated Energy ◽  
Slow Rotation ◽  
Azimuthal Component ◽  
Concentric Spheres ◽  
Special Cases ◽  
Inner Sphere ◽  
Angular Velocities

The problem of concentric pervious spheres carrying a fluid source at their centre and rotating slowly with different uniform angular velocities , about a diameter has been studied. The analysis reveals that only azimuthal component of velocity exists, and the couple, rate of dissipated energy is found analytically in the present situation. The expression of couple on inner sphere rotating slowly with uniform angular velocity , while outer sphere also rotates slowly with uniform angular velocity , is evaluated. The special cases, like (i) inner sphere is fixed (i.e., ), while outer sphere rotates with uniform angular velocity , (ii) outer sphere is fixed (i.e., ), while inner sphere rotates with uniform angular velocity , and (iii) inner sphere rotates with uniform angular velocity , while outer sphere rotates at infinity with angular velocity , have been deduced.

The almost-rigid rotation of viscous fluid between concentric spheres

1956 ◽  
Vol 1 (5) ◽  
pp. 505-516 ◽  
Author(s):  
Ian Proudman
Keyword(s):  
Reynolds Number ◽  
Angular Velocity ◽  
Rigid Body ◽  
Velocity Distribution ◽  
Outer Sphere ◽  
Reynolds Numbers ◽  
Rotating Systems ◽  
Velocity Gradients ◽  
Concentric Spheres ◽  
Viscous Stresses

Two concentric spheres are supposed to rotate about the same axis with almost the same angular velocity, so that the viscous stresses over the surfaces of the spheres induce a flow which may be represented by a small perturbation superimposed upon a rigid body rotation of the fluid as a whole. The governing equations are therefore linearized in the magnitude of the perturbation, and it appears that the validity of this linearization is independent of the Reynolds number of the primary rotation. Attention is then restricted to the case in which the Reynolds number is large, the principal object of the note being to exemplify some of the properties of rotating systems at large Reynolds numbers in terms of a particularly simple mathematical model.It is found that the cylindrical surface that touches the inner sphere (the axis being the axis of rotation) is a singular surface in which velocity gradients are very large. Everywhere outside this cylinder, the fluid rotates as a rigid body with the same angular velocity as the outer sphere. Inside the cylinder, the velocity distribution in the central (inviscid) core of the motion is shown to be determined by the velocity distribution in the boundary layers over the spheres, and explicit solutions are obtained for all these velocity distributions. The mechanics of the cylindrical shear layer itself is also discussed, though no explicit solution is obtained in this case.

The Analysis of Proprioception Alteration during First Five Months after Anterior Cruciate Ligament Reconstruction

2018 ◽  
Vol 1 (84) ◽  
Author(s):  
Vilma Jurevičienė ◽  
Albertas Skurvydas ◽  
Juozas Belickas ◽  
Giedra Bušmanienė ◽  
Dovilė Kielė ◽  
...  
Keyword(s):  
Anterior Cruciate Ligament ◽  
Angular Velocity ◽  
Knee Joint ◽  
Cruciate Ligament ◽  
Position Sense ◽  
Joint Position Sense ◽  
Joint Position ◽  
Starting Position ◽  
Angular Velocities ◽  
Anterior Cruciate

Research  background  and  hypothesis.  Proprioception  is  important  in  the  prevention  of  injuries  as  reduced proprioception  is  one  of  the  factors  contributing  to  injury  in  the  knee  joint,  particularly  the  ACL.  Therefore, proprioception appears not only important for the prevention of ACL injuries, but also for regaining full function after ACL reconstruction.Research aim. The aim of this study was to understand how proprioception is recovered four and five months after anterior cruciate ligament (ACL) reconstruction.Research methods. The study included 15 male subjects (age – 33.7 ± 2.49 years) who had undergone unilateral ACL reconstruction with a semitendinosus/gracilis (STG) graft in Kaunas Clinical Hospital. For proprioceptive assessment, joint position sense (JPS) was measured on both legs using an isokinetic dynamometer (Biodex), at knee flexion of 60° and 70°, and at different knee angular velocities of 2°/s and 10°/s. The patients were assessed preoperatively and after 4 and 5 months, postoperatively.Research results. Our study has shown that the JPS’s (joint position sense) error scores  to a controlled active movement is significantly higher in injured ACL-deficient knee than in the contralateral knee (normal knee) before surgery and after four and five months of rehabilitation.  After 4 and 5 months of rehabilitation we found significantly lower values in injured knees compared to the preoperative data. Our study has shown that in injured knee active angle reproduction errors after 4 and 5 months of rehabilitation were higher compared with the ones of the uninjured knee. Proprioceptive ability on the both legs was  independent of all differences angles for target and starting position for movement. The knee joint position sense on both legs depends upon the rate of two different angular velocities and the mean active angle reproduction errors at the test of angular velocity slow speed was the highest compared with the fast angular velocity. Discussion and conclusions. In conclusion, our study shows that there was improvement in mean JPS 4 and 5 months after ACL reconstruction, but it did not return to normal indices.Keywords: knee joint, joint position sense, angular velocity, starting position for movement.

Scission and Healing in a Spinning Elastomeric Cylinder at Elevated Temperature

2002 ◽  
Vol 69 (5) ◽  
pp. 602-609 ◽  
Author(s):  
A. S. Wineman ◽  
J. A. Shaw
Keyword(s):  
Elevated Temperature ◽  
Angular Velocity ◽  
Critical Value ◽  
Anomalous Behavior ◽  
Molecular Networks ◽  
Material System ◽  
Elastomeric Material ◽  
Angular Velocities ◽  
Macromolecular Network ◽  
Temperature Responses

When an elastomeric material is subject to sufficiently high temperature, macromolecular network junctions can undergo time-dependent scission and re-crosslinking (healing). The material system then consists of molecular networks with different reference states. A constitutive framework, based on the experimental work of Tobolsky, is used to determine the evolution of deformation of a solid rubber cylinder spinning at constant angular velocity at an elevated temperature. Responses based on underlying neo-Hookean, Mooney-Rivlin, and Arruda-Boyce models, were solved numerically and compared. Different amounts of healing were studied for each case. For neo-Hookean molecular networks, there may be a critical finite time when the radius grows infinitely fast and the cylinder “blows up.” This time depends on the angular velocity and the rate of re-cross linking. In addition, no solution was possible for angular velocities above a critical value, even without the effects of scission. Such anomalous behavior does not occur for Mooney-Rivlin or Arruda-Boyce network response.

The Relationship between Consistency of Propulsive Cycles and Maximum Angular Velocity during Wheelchair Racing

2008 ◽  
Vol 24 (3) ◽  
pp. 280-287 ◽  
Author(s):  
Yong “Tai” Wang ◽  
Konstantinos Dino Vrongistinos ◽  
Dali Xu
Keyword(s):  
Angular Velocity ◽  
Upper Limb ◽  
Wheelchair Propulsion ◽  
Upper Arm ◽  
Wheelchair Athletes ◽  
Angular Velocities ◽  
Limb Kinematics ◽  
Analysis System ◽  
The Right ◽  
The Relationship

The purposes of this study were to examine the consistency of wheelchair athletes’ upper-limb kinematics in consecutive propulsive cycles and to investigate the relationship between the maximum angular velocities of the upper arm and forearm and the consistency of the upper-limb kinematical pattern. Eleven elite international wheelchair racers propelled their own chairs on a roller while performing maximum speeds during wheelchair propulsion. A Qualisys motion analysis system was used to film the wheelchair propulsive cycles. Six reflective markers placed on the right shoulder, elbow, wrist joints, metacarpal, wheel axis, and wheel were automatically digitized. The deviations in cycle time, upper-arm and forearm angles, and angular velocities among these propulsive cycles were analyzed. The results demonstrated that in the consecutive cycles of wheelchair propulsion the increased maximum angular velocity may lead to increased variability in the upper-limb angular kinematics. It is speculated that this increased variability may be important for the distribution of load on different upper-extremity muscles to avoid the fatigue during wheelchair racing.

scholarly journals Profil izokinetickej sily extenzorov a flexorov kolena u mladých futbalových hráčov

2012 ◽  
Vol 6 (1) ◽  
pp. 53-60
Author(s):  
Tomáš Malý ◽  
František Zahálka ◽  
Lucia Malá ◽  
Jaroslav Teplan
Keyword(s):  
Angular Velocity ◽  
Research Group ◽  
Eccentric Contraction ◽  
Baseline Data ◽  
Soccer Players ◽  
Knee Extensors ◽  
Isokinetic Strength ◽  
Concentric Contraction ◽  
Angular Velocities

Th e aim of the study was to present isokinetic strength profi le of knee fl exors and extensors during concentric contraction in young soccer players. Particularly in knee fl exors was evaluated also strength during eccentric contraction. Research group was state from young soccer players U17 category (n=19, age=16,4±0,3 years). All of them are the participant of highest junior soccer league. Isokinetic strength was evaluated by isokinetic dynamometr Cybex Humac Norm in following angular velocities: 30, 60 and 120°/s in eccentric contraction and 60, 180, 240 and 300 °/s in concentric contraction. Th e results did not revealed signifi cant diff erences at three diff erent speed levels of knee fl exors’ strength during eccentric contraction (p>0,05). Regarding the concentric contraction we found signifi cant diff erences for strength production depending on angular velocity for both knee extensors and fl exors (p<0,01). Knee fl exors generated more strength during eccentric contraction compared to concentric contraction. Th e strength profi les developed in the present study can assist in the establishment of baseline data in young soccer players or for comparison values with other researchers.

scholarly journals Fertilizer deposition as a function of angular velocity and inclination of the helical dosing mechanism

2022 ◽  
Vol 26 (3) ◽  
pp. 226-235
Author(s):  
Gabriel G. Zimmermann ◽  
Samir P. Jasper ◽  
Daniel Savi ◽  
Leonardo L. Kmiecik ◽  
Lauro Strapasson Neto ◽  
...  
Keyword(s):  
Angular Velocity ◽  
Process Control ◽  
Statistical Process Control ◽  
Industrial Process ◽  
Descriptive Statistics ◽  
Flow Data ◽  
Statistical Process ◽  
Flow Rates ◽  
Angular Velocities

ABSTRACT The establishment of grain crops in Brazil is an important industrial process in the agricultural chain, requiring the correct deposition of granular fertilizer over the sowing furrow and more efficient, precise, and sustainable assessments in the operation, which can be achieved with the statistical process control. This study aimed to assess the effect of the angular velocity on different inclinations of the helical metering mechanism on the granular fertilizer deposition. An automated electronic bench was used to assess the deposition quality of granular fertilizers considering different angular velocities (1.11, 1.94, and 2.77 m s-1) and longitudinal and transverse inclinations (+15, +7.5, 0, −7.5, and −15°), with the helical doser by overflow. Flow data were collected and submitted to descriptive statistics and statistical process control. The metering mechanism showed expected variations, with acceptable performance under process control. The values of the flow rates of the granular fertilizer increased as velocity increased, standing out longitudinal inclinations of +7.5 and +15°, providing higher fertilizer depositions.

Gyroscope-Free Link Parameter Measurement Using Accelerometers and Magnetometer

2014 ◽  
Author(s):  
Vishesh Vikas ◽  
Carl D. Crane
Keyword(s):  
Angular Velocity ◽  
Joint Angle ◽  
Inertial Sensors ◽  
Angular Acceleration ◽  
Parameter Measurement ◽  
Joint Angles ◽  
Symmetry Constraint ◽  
Estimation Techniques ◽  
Angular Velocities ◽  
Joint Parameters

Knowledge of joint angles, angular velocities is essential for control of link mechanisms and robots. The estimation of joint angles and angular velocity is performed using combination of inertial sensors (accelerometers and gyroscopes) which are contactless and flexible at point of application. Different estimation techniques are used to fuse data from different inertial sensors. Bio-inspired sensors using symmetrically placed multiple inertial sensors are capable of instantaneously measuring joint parameters (joint angle, angular velocities and angular acceleration) without use of any estimation techniques. Calibration of inertial sensors is easier and more reliable for accelerometers as compared to gyroscopes. The research presents gyroscope-less, multiple accelerometer and magnetometer based sensors capable of measuring (not estimating) joint parameters. The contribution of the improved sensor are four-fold. Firstly, the inertial sensors are devoid of symmetry constraint unlike the previously researched bio-inspired sensors. However, the accelerometer are non-coplanarly placed. Secondly, the accelerometer-magnetometer combination sensor allows for calculation of a unique rotation matrix between two link joined by any kind of joint. Thirdly, the sensors are easier to calibrate as they consist only of accelerometers. Finally, the sensors allow for calculation of angular velocity and angular acceleration without use of gyroscopes.

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