scholarly journals The exact analytical solution for the gas lubricated bearing in the slip and continuum flow regime

2012 ◽  
Vol 91 (105) ◽  
pp. 83-93 ◽  
Author(s):  
Nevena Stevanovic ◽  
Vladan Djordjevic
Keyword(s):  
Analytical Solution ◽  
Flow Rate ◽  
Gas Flow ◽  
Exact Analytical Solution ◽  
The Other ◽  
Two Dimensional ◽  
Lubrication Equation ◽  
Continuum Flow ◽  
Independent Variable ◽  
The Continuum

The exact analytical solution for the compressible two-dimensional gas flow in the microbearing is presented. The general slip-corrected Reynolds lubrication equation is derived and it is shown that it possesses an exact analytical solution. It is obtained by a suitable transformation of the independent variable, and it provides the pressure distribution in the bearing as well as the mass flow rate through it. By neglecting the rarefaction effect, this solution is also applicable to the continuum gas flow in the bearing, which also does not exist in the open literature. The obtained analytical solution can be usefully applied for testing the other, experimental or numerical results.

Pressure and Flow—Chickens and Eggs

2011 ◽  
pp. 63-69
Author(s):  
James R. Munis
Keyword(s):  
Pressure Gradient ◽  
Flow Rate ◽  
The Other ◽  
Pressure Gradients ◽  
Variable Effect ◽  
Paddle Wheel ◽  
Independent Variable ◽  
Mechanical Pump

We tend to assume that when 2 things are associated with each other, one must be causing the other. Nothing could be further from the truth, though. Because we're used to seeing the independent variable (‘cause’) plotted on the x-axis and the dependent variable (‘effect’) on the y-axis, this equation and graph suggest that the pressure gradient causes the paddle wheel flow rate. That, of course, is nonsense. This type of specious thinking is intended to warn you away from assuming that relationships necessarily imply causality. As you've learned already, pressure is not the same thing as energy, and pressure by itself cannot perform work or generate flow. However, flow generated by pressure-volume work (either by the heart or a mechanical pump) certainly can create pressure gradients. In this sort of chicken (flow) or egg (pressure) question, if the only energy-containing term is flow, then I'll say that the chicken came first.

Direct molecular hydrogen sulphide scrubbing with hollow fibre membranes

2001 ◽  
Vol 44 (9) ◽  
pp. 135-142 ◽  
Author(s):  
N. Boucil ◽  
B. Jefferson ◽  
S.A. Parsons ◽  
S.J. Judd ◽  
R.M. Stuetz
Keyword(s):  
Mass Transfer ◽  
Specific Surface ◽  
Surface Area ◽  
Specific Surface Area ◽  
Flow Rate ◽  
Hydrogen Sulphide ◽  
Gas Flow ◽  
Hollow Fibre ◽  
The Other ◽  
Gas Flow Rate

The emission of hydrogen sulphide is a major problem associated with anaerobic treatment of sulphate and sulphite containing wastewaters. Conventional absorbing processes, such as packed towers, spray towers or bubble columns, are all constrained by factors such as flooding and foaming. Membrane systems, on the other hand, enable independent control of the liquid and gas flow rate and a step change order of magnitude increase in the specific surface area of the contact process. The membrane acts as a gas absorber with a design similar to a shell and tube heat exchanger. On the other hand, they are limited by facets of the membrane such as its resistance to mass transfer and permselectivity, as well as its cost. The work presented in this paper refers to an absorption process based on a non-wetted hollow fibre membrane for the scrubbing of hydrogen sulphide from air, with water as the contact solvent. Results presented describe the performance of the unit in terms of overall transfer and outlet liquid concentration as a function of circulation regime, gas flow rate, liquid flow rate and specific surface area. In particular, results are presented using traditional plots of Sherwood number (Sh) against Graetz (Gr) number for the liquid flowing in the lumens, such that experimental and available empirical descriptions of the process performance are directly compared. Results suggest that, as expected, very efficient mass transfer is obtained. However, the mass transfer was found to reach a maximum value against Gr, contrary to available empirical models.

scholarly journals Particle deposition characteristics in entrained flow coal gasifier

2012 ◽  
Vol 16 (5) ◽  
pp. 1544-1548
Author(s):  
Sheng Liu ◽  
Ying-Li Hao
Keyword(s):  
Numerical Simulation ◽  
Flow Rate ◽  
Particle Deposition ◽  
Gas Flow ◽  
Water Flow Rate ◽  
Deposition Process ◽  
The Other ◽  
Central Channel ◽  
Gas Flow Rate ◽  
Coal Gasifier

Cold state experiment and numerical simulation are carried out to study particle deposition process. The deposit mass can be divided into two parts, one directly collides with the wall and the other is brought by the backflow. The deposit flux increases with the increase of gas flow rate or water flow rate or both, and decreases with the increase of the central channel gas flow rate.

scholarly journals Recovery of transit times and frequencies of multiple pulses via the Short-Time Fourier Transform

2018 ◽  
Vol 64 (3) ◽  
pp. 296
Author(s):  
Jesus Manzanares-Martinez ◽  
Carlos Ivan Ham-Rodriguez ◽  
Betsabe Manzanares-Martinez
Keyword(s):  
Fourier Transform ◽  
Analytical Solution ◽  
Transit Time ◽  
Acoustic Signal ◽  
Exact Analytical Solution ◽  
The Other ◽  
Short Time Fourier Transform ◽  
Transit Times ◽  
Multiple Pulses ◽  
Short Time

In this work, we present a study to determine the transit times and frequencies of pulses by usingthe Short-Time Fourier Transform (STFT). We consider the case of an acoustic signal composed offive Gaussian pulses which have a high overlapping in time but oscillate at different frequencies. Weproceeded in three steps. First, we illustrate how the STFT calculated through a sliding windowproduces a spectrogram where transit time is on one axis and frequency on the other. Second, wederive an exact analytical solution of the STFT to develop an intuitive vision of the mathematicaltechnique. Finally, in a third step, we present an experiment to demonstrate that the STFT is auseful technique to characterize a complex acoustical signal.

Longitudinal Impact of Semi-Infinite Elastic Bars: Plane Any Time Solution

2013 ◽  
Vol 81 (5) ◽  
Author(s):  
M. A. Malkov
Keyword(s):  
Analytical Solution ◽  
Exact Analytical Solution ◽  
The Other ◽  
Longitudinal Impact ◽  
Infinite Plane ◽  
One Dimensional ◽  
Dimensional Approximation ◽  
Contact Surfaces ◽  
The One ◽  
The Impact

Using the Sobolev–Smirnov method, we have found the exact analytical solution of a longitudinal impact of semi-infinite plane elastic bars for any time after the impact. After collision, there are loading waves from contact surfaces of bars and unloading waves from lateral surfaces. Then the unloading waves reach the opposite surface of the bars and create the reflected loading waves. These loading waves reach the other surface of the bars and generate new unloading waves. The number of waves grows exponentially. The sum of waves tends to the wave of the one-dimensional approximation.

Second-order isothermal reaction in a semi-batch reactor: modeling, exact analytical solution, and experimental verification

2019 ◽  
Vol 4 (11) ◽  
pp. 2011-2020
Author(s):  
Mana Kord ◽  
Ali Nematollahzadeh ◽  
Behruz Mirzayi
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
Flow Rate ◽  
Experimental Verification ◽  
Exact Analytical Solution ◽  
Batch Reactor ◽  
Second Order ◽  
Reaction Conditions ◽  
Reactor Modeling ◽  
Isothermal Reaction

Mathematical model of a semi-batch reactor (SBR) can be employed for tuning the concentration or flow rate of the external-feed of reactants, to control the reaction conditions and product properties.

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