FLOW INTO A BLACK HOLE

1996 ◽  
Vol 11 (01) ◽  
pp. 161-170
Author(s):  
DANIELA TORDELLA ◽  
ROBERT E. BREIDENTHAL
Keyword(s):  
Black Hole ◽  
Kinetic Energy ◽  
Potential Energy ◽  
Dissipation Rate ◽  
Rotation Period ◽  
Gravitational Potential Energy ◽  
Circular Orbits ◽  
Turbulent Eddy ◽  
Orbital Radius ◽  
Flow Speeds

A simple model is proposed to describe the flow into a black hole from the turbulent flow of matter in initially circular orbits about the black hole. Magnetic effects are not considered. The shear between fluid elements at slightly different orbital radii causes turbulent eddies to be formed. These eddies determine the dissipation rate of kinetic energy into thermal energy. For approximately circular orbits, the magnitude of the gravitational potential energy is always equal to twice the kinetic energy; the destruction of the latter resulting in a reduction in the orbital radius and hence the potential energy. In this model, the turbulent eddy rotation period is presumed to be determined by the gradient in the gravity acceleration, leading to an eddy period proportional to the orbital period. If the flow speeds are supersonic but not relativistic, then the turbulent eddy size is set by the product of the eddy rotation period and the speed of sound. At a certain smaller radius, the orbital speeds and hence the dissipation rate are so great that the speeds become relativistic and the molecular speed tends toward its limit [Formula: see text]. Then the effective eddy size is controlled by the product of the eddy rotation period and the speed of light. Using these estimates for the important eddy size, the dissipation rate, temperature, density and sinking speed as a function of the orbital radius and the rate of mass flow into the black hole are derived. Subject headings: accretion, accretion disks, stars evolution, turbulence, eddy, sonic eddy.

Tracker-assisted modelling: simultaneous validation of the conservation law of energy and the work-energy theorem

2021 ◽  
Vol 57 (1) ◽  
pp. 015012
Author(s):  
Unofre B Pili ◽  
Renante R Violanda
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Gravitational Potential ◽  
Conservation Law ◽  
Gravitational Potential Energy ◽  
Time Data ◽  
Home Based ◽  
Basic Physics ◽  
Free Falling ◽  
Work Done

Abstract The video of a free-falling object was analysed in Tracker in order to extract the position and time data. On the basis of these data, the velocity, gravitational potential energy, kinetic energy, and the work done by gravity were obtained. These led to a rather simultaneous validation of the conservation law of energy and the work–energy theorem. The superimposed plots of the kinetic energy, gravitational potential energy, and the total energy as respective functions of time and position demonstrate energy conservation quite well. The same results were observed from the plots of the potential energy against the kinetic energy. On the other hand, the work–energy theorem has emerged from the plot of the total work-done against the change in kinetic energy. Because of the accessibility of the setup, the current work is seen as suitable for a home-based activity, during these times of the pandemic in particular in which online learning has remained to be the format in some countries. With the guidance of a teacher, online or face-to-face, students in their junior or senior high school—as well as for those who are enrolled in basic physics in college—will be able to benefit from this work.

scholarly journals Walking in simulated reduced gravity: mechanical energy fluctuations and exchange

1999 ◽  
Vol 86 (1) ◽  
pp. 383-390 ◽  
Author(s):  
Timothy M. Griffin ◽  
Neil A. Tolani ◽  
Rodger Kram
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Gravitational Potential ◽  
Inverted Pendulum ◽  
Mechanical Energy ◽  
Center Of Mass ◽  
Metabolic Cost ◽  
Metabolic Energy ◽  
Gravitational Potential Energy ◽  
Reduced Gravity

Walking humans conserve mechanical and, presumably, metabolic energy with an inverted pendulum-like exchange of gravitational potential energy and horizontal kinetic energy. Walking in simulated reduced gravity involves a relatively high metabolic cost, suggesting that the inverted-pendulum mechanism is disrupted because of a mismatch of potential and kinetic energy. We tested this hypothesis by measuring the fluctuations and exchange of mechanical energy of the center of mass at different combinations of velocity and simulated reduced gravity. Subjects walked with smaller fluctuations in horizontal velocity in lower gravity, such that the ratio of horizontal kinetic to gravitational potential energy fluctuations remained constant over a fourfold change in gravity. The amount of exchange, or percent recovery, at 1.00 m/s was not significantly different at 1.00, 0.75, and 0.50 G (average 64.4%), although it decreased to 48% at 0.25 G. As a result, the amount of work performed on the center of mass does not explain the relatively high metabolic cost of walking in simulated reduced gravity.

scholarly journals Feedback of outflows in the Taurus Molecular Cloud

2012 ◽  
Vol 8 (S292) ◽  
pp. 47-47
Author(s):  
Huixian Li ◽  
Di Li ◽  
Rendong Nan
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Gravitational Potential ◽  
Molecular Cloud ◽  
Feedback Effect ◽  
Total Kinetic Energy ◽  
Gravitational Potential Energy ◽  
Taurus Molecular Cloud

AbstractWe collected 27 outflows from the literature and found 8 new ones in the FCRAO CO maps of the Taurus molecular cloud. The total kinetic energy of the 35 outflows is found to be about 3% of the gravitational potential energy from the whole cloud. The feedback effect due to the outflows is minor in Taurus.

Accretion onto a Black Hole

2014 ◽  
Author(s):  
Charles D. Bailyn
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Potential Energy ◽  
Gravitational Potential ◽  
Gas Flow ◽  
Gravitational Potential Energy ◽  
Spherically Symmetric ◽  
Potential Well ◽  
Accretion Flows ◽  
Flow Geometry

This chapter explores the ways that accretion onto a black hole produces energy and radiation. As material falls into a gravitational potential well, energy is transformed from gravitational potential energy into other forms of energy, so that total energy is conserved. Observing such accretion energy is one of the primary ways that astrophysicists pinpoint the locations of potential black holes. The spectrum and intensity of this radiation is governed by the geometry of the gas flow, the mass infall rate, and the mass of the accretor. The simplest flow geometry is that of a stationary object accreting mass equally from all directions. Such spherically symmetric accretion is referred to as Bondi-Hoyle accretion. However, accretion flows onto black holes are not thought to be spherically symmetric—the infall is much more frequently in the form of a flattened disk.

scholarly journals Rapidly rotating strange stars

2000 ◽  
Vol 177 ◽  
pp. 661-662 ◽  
Author(s):  
D. Gondek-Rosińska ◽  
P. Haensel ◽  
J. L. Zdunik ◽  
E. Gourgoulhon
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Quark Mass ◽  
Strange Quark ◽  
Gravitational Potential Energy ◽  
Rapid Rotation ◽  
Strange Stars ◽  
Absolute Value ◽  
Strange Quark Mass ◽  
Global Parameters

AbstractWe study effects of the strange quark mass,ms, and of the QCD interactions, calculated to lowest order inαc, on the rapid rotation of strange stars (SS). The influence of rotation on global parameters of SS is greater than in the case of the neutron stars (NS). We show that independently ofmsandαcthe ratio of the rotational kinetic energy to the absolute value of the gravitational potential energyT/Wfor a rotating SS is significantly higher than for an ordinary NS. This might indicate that rapidly rotating SS could be important sources of gravitational waves.

scholarly journals Differential Rotation and the v sin i Parameter

2004 ◽  
Vol 215 ◽  
pp. 21-22 ◽  
Author(s):  
J. Zorec ◽  
A. Domiciano de Souza ◽  
Y. Frémat
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Line Width ◽  
Differential Rotation ◽  
Rotation Velocity ◽  
Rigid Rotation ◽  
Gravitational Potential Energy ◽  
Aspect Angle ◽  
Energy Ratios

We study the effects of a differential rotation upon the determination of the v sin i parameter. The effects are studied for several values of the ratio t = kinetic energy/gravitational potential energy, which include energy ratios higher than permitted for critical rigid rotation and using an internal conservative rotation law that allows for a latitudinal differential rotation in the stellar surface. Two effects are outstanding: when differential rotation is dependent on the stellar latitude the v sin i parameter does not necessarily correspond to the equatorial rotation velocity; the line width is a double valued function of v sin i and it is dependent on t and the aspect angle i.

scholarly journals Numerical Simulation of Katabatic Flow with Changing Slope Angle

2005 ◽  
Vol 133 (11) ◽  
pp. 3065-3080 ◽  
Author(s):  
Craig M. Smith ◽  
Eric D. Skyllingstad
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Slope Angle ◽  
Gravitational Potential Energy ◽  
Flow Profile ◽  
Advanced Regional Prediction System ◽  
Regional Prediction ◽  
Les Model ◽  
Lower Slope ◽  
Upper Slope

Abstract A large eddy simulation (LES) model and the Advanced Regional Prediction System (ARPS) model, which does not resolve turbulent eddies, are used to study the effect of a slope angle decrease on the structure of katabatic slope flows. For a simple, uniform angle slope, simulations from both models produce turbulence kinetic energy and momentum budgets that are in good overall agreement. Simulations of a compound angle slope are compared to a uniform angle slope to demonstrate how a changing slope angle can strongly affect the strength of katabatic flows. Both ARPS and the LES model show that slopes with a steep upper slope followed by a shallower lower slope (concave shape) generate a rapid acceleration on the upper slope followed by a transition to a slower evolving structure characterized by an elevated jet over the lower slope. In contrast, the case with uniform slope (having the same total height change) yields a more uniform flow profile with stronger winds at the slope bottom. Higher average slope in the uniform slope angle case generates greater gravitational potential energy, which is converted to kinetic energy at the bottom of the slope. Analysis of the total energy budget of slope flows indicates a consistent structure where potential energy generated at the top of the slope is transported downslope and converted into kinetic energy near the slope base.

A Friction-Bearing Calorimeter Experiment Yielding Joule's Constant

1996 ◽  
Vol 24 (4) ◽  
pp. 235-242 ◽  
Author(s):  
R. S. Mullisen
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Laboratory Experiment ◽  
Heat Loss ◽  
Gravitational Potential ◽  
Data Reduction ◽  
Gravitational Potential Energy ◽  
Experimental Procedure ◽  
Friction Bearing ◽  
Elastic Potential Energy

A simple, friction-bearing calorimeter that yields Joule's constant is described in this paper. The apparatus is easily constructed at minimal expense and may be used as a laboratory experiment. Although the design is very simple, the experimental procedure and data reduction analysis account for gravitational potential energy, elastic potential energy, translational and rotational kinetic energy, and heat loss. The result is a Joule's constant value accurate within 3%.

Mechanics of locomotion in lizards.

1997 ◽  
Vol 200 (16) ◽  
pp. 2177-2188 ◽  
Author(s):  
C T Farley ◽  
T C Ko
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Gravitational Potential ◽  
Inverted Pendulum ◽  
Mechanical Energy ◽  
Center Of Mass ◽  
Gravitational Potential Energy ◽  
Lateral Bending ◽  
Walking Gait ◽  
Bending Force

Lizards bend their trunks laterally with each step of locomotion and, as a result, their locomotion appears to be fundamentally different from mammalian locomotion. The goal of the present study was to determine whether lizards use the same two basic gaits as other legged animals or whether they use a mechanically unique gait due to lateral trunk bending. Force platform and kinematic measurements revealed that two species of lizards, Coleonyx variegatus and Eumeces skiltonianus, used two basic gaits similar to mammalian walking and trotting gaits. In both gaits, the kinetic energy fluctuations due to lateral movements of the center of mass were less than 5% of the total external mechanical energy fluctuations. In the walking gait, both species vaulted over their stance limbs like inverted pendulums. The fluctuations in kinetic energy and gravitational potential energy of the center of mass were approximately 180 degrees out of phase. The lizards conserved as much as 51% of the external mechanical energy required for locomotion by the inverted pendulum mechanism. Both species also used a bouncing gait, similar to mammalian trotting, in which the fluctuations in kinetic energy and gravitational potential energy of the center of mass were nearly exactly in phase. The mass-specific external mechanical work required to travel 1 m (1.5 J kg-1) was similar to that for other legged animals. Thus, in spite of marked lateral bending of the trunk, the mechanics of lizard locomotion is similar to the mechanics of locomotion in other legged animals.

scholarly journals Observations of Small-Scale Secondary Instabilities during the Shoaling of Internal Bores on a Deep-Ocean Slope

2016 ◽  
Vol 46 (1) ◽  
pp. 219-231 ◽  
Author(s):  
Frédéric Cyr ◽  
Hans van Haren
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Dissipation Rate ◽  
Deep Ocean ◽  
Temperature Sensors ◽  
Small Scale ◽  
Cooling Phase ◽  
Northeast Atlantic Ocean ◽  
Internal Bores ◽  
Secondary Instabilities

AbstractThe Rockall Bank area, located in the northeast Atlantic Ocean, is a region dominated by topographically trapped diurnal tides. These tides generate up- and downslope displacements that can be locally described as swashing motions on the bank. Using high spatial and time resolution of moored temperature sensors, the transition toward the upslope flow (cooling phase) is described as a rapid upslope-propagating bore, likely generated by breaking trapped internal waves. Buoyant anomalies are found during the bore propagation, likely resulting from small-scale instabilities. The imbalance between the rate of disappearance of available potential energy and the dissipation rate of turbulent kinetic energy suggests that these instabilities are growing (i.e., young) and have high mixing potential.

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