A Note on the Application of the Extended Bernoulli Equation

1999 ◽  
Author(s):  
Steven B. Segletes ◽  
William P. Walters
Keyword(s):  
Bernoulli Equation

An exact solution of fractional Euler-Bernoulli equation for a beam with fixed-supported and fixed-free ends

2021 ◽  
Vol 396 ◽  
pp. 125932
Author(s):  
Tomasz Blaszczyk ◽  
Jaroslaw Siedlecki ◽  
HongGuang Sun
Keyword(s):  
Exact Solution ◽  
Bernoulli Equation

The Lumped Capacitance Model for Unsteady Heat Conduction in Regular Solid Bodies With Natural Convection to Nearby Fluids Engages the Nonlinear Bernoulli Equation

2018 ◽  
Vol 10 (3) ◽  
Author(s):  
Antonio Campo
Keyword(s):  
Heat Conduction ◽  
Natural Convection ◽  
Heat Equation ◽  
Biot Number ◽  
Bernoulli Equation ◽  
Convective Coefficient ◽  
Unsteady Heat Conduction ◽  
The Mean ◽  
Capacitance Model ◽  
Solid Bodies

For the analysis of unsteady heat conduction in solid bodies comprising heat exchange by forced convection to nearby fluids, the two feasible models are (1) the differential or distributed model and (2) the lumped capacitance model. In the latter model, the suited lumped heat equation is linear, separable, and solvable in exact, analytic form. The linear lumped heat equation is constrained by the lumped Biot number criterion Bil=h¯(V/S)/ks < 0.1, where the mean convective coefficient h¯ is affected by the imposed fluid velocity. Conversely, when the heat exchange happens by natural convection, the pertinent lumped heat equation turns nonlinear because the mean convective coefficient h¯ depends on the instantaneous mean temperature in the solid body. Undoubtedly, the nonlinear lumped heat equation must be solved with a numerical procedure, such as the classical Runge–Kutta method. Also, due to the variable mean convective coefficient h¯ (T), the lumped Biot number criterion Bil=h¯(V/S)/ks < 0.1 needs to be adjusted to Bil,max=h¯max(V/S)/ks < 0.1. Here, h¯max in natural convection cooling stands for the maximum mean convective coefficient at the initial temperature Tin and the initial time t = 0. Fortunately, by way of a temperature transformation, the nonlinear lumped heat equation can be homogenized and later channeled through a nonlinear Bernoulli equation, which admits an exact, analytic solution. This simple route paves the way to an exact, analytic mean temperature distribution T(t) applicable to a class of regular solid bodies: vertical plate, vertical cylinder, horizontal cylinder, and sphere; all solid bodies constricted by the modified lumped Biot number criterion Bil,max<0.1.

Doppler echo evaluation of pulmonary venous-left atrial pressure gradients: human and numerical model studies

2000 ◽  
Vol 279 (2) ◽  
pp. H594-H600 ◽  
Author(s):  
Michael S. Firstenberg ◽  
Neil L. Greenberg ◽  
Nicholas G. Smedira ◽  
David L. Prior ◽  
Gregory M. Scalia ◽  
...  
Keyword(s):  
Numerical Modeling ◽  
Left Atrial ◽  
Atrial Pressure ◽  
Left Atrial Pressure ◽  
High Fidelity ◽  
Pressure Gradients ◽  
Bernoulli Equation ◽  
Venous Flow ◽  
Model Studies ◽  
Pulmonary Venous Flow

The simplified Bernoulli equation relates fluid convective energy derived from flow velocities to a pressure gradient and is commonly used in clinical echocardiography to determine pressure differences across stenotic orifices. Its application to pulmonary venous flow has not been described in humans. Twelve patients undergoing cardiac surgery had simultaneous high-fidelity pulmonary venous and left atrial pressure measurements and pulmonary venous pulsed Doppler echocardiography performed. Convective gradients for the systolic (S), diastolic (D), and atrial reversal (AR) phases of pulmonary venous flow were determined using the simplified Bernoulli equation and correlated with measured actual pressure differences. A linear relationship was observed between the convective ( y) and actual ( x) pressure differences for the S ( y = 0.23 x + 0.0074, r = 0.82) and D ( y = 0.22 x + 0.092, r = 0.81) waves, but not for the AR wave ( y = 0.030 x + 0.13, r = 0.10). Numerical modeling resulted in similar slopes for the S ( y = 0.200 x − 0.127, r = 0.97), D ( y = 0.247 x − 0.354, r= 0.99), and AR ( y = 0.087 x − 0.083, r = 0.96) waves. Consistent with numerical modeling, the convective term strongly correlates with but significantly underestimates actual gradient because of large inertial forces.

scholarly journals Is the use of modified Bernoulli equation valid in estimating pulmonary artery pressures in patients with severely dilated tricuspid annulus?

2002 ◽  
Vol 39 ◽  
pp. 425 ◽  
Author(s):  
H.Mehrdad Sadeghi ◽  
Alborz Hassankhani ◽  
Rod Serry ◽  
Ajit Raisinghani ◽  
Anthony N. DeMaria
Keyword(s):  
Pulmonary Artery ◽  
Bernoulli Equation ◽  
Tricuspid Annulus

The Analysis of Automotive Door Seal Energy Consumption

2011 ◽  
Vol 80-81 ◽  
pp. 714-718
Author(s):  
Yun Kai Gao ◽  
Da Wei Gao
Keyword(s):  
Energy Consumption ◽  
Elastic Force ◽  
Bernoulli Equation ◽  
Analysis Model ◽  
Damping Force ◽  
Total Energy Consumption ◽  
Linear Elastic ◽  
Non Linear ◽  
Linear Damping ◽  
Simplified Analysis

The seal deformation of automotive door is caused by the door compression forces, including non-linear elastic force and non-linear damping force. The working principles of them are analyzed and a new simplified analysis model is built. Based on the Bernoulli equation and the law of conservation of mass, the mathematical models are established to calculate energy consumption of the seal system. According to the analysis results, the energy consumption of non-linear elastic force and non-linear damping force are respectively 84% and 16% of the total energy consumption of the seal system. At last, the calculation data is compared with the test data and the error is less than 5%, so the calculation method proposed in this paper is observed to be accurate.

Bernoulli Equation

2015 ◽  
pp. 151-176
Keyword(s):  
Bernoulli Equation

scholarly journals Akdeniz İklim Koşullarında Seralarda Havalandırma Açıklık Oranlarının Belirlenmesi

2017 ◽  
Vol 5 (4) ◽  
pp. 409
Author(s):  
Abdullah Nafi Baytorun ◽  
Sait Üstün ◽  
Adil Akyüz ◽  
Derya Önder
Keyword(s):  
Energy Balance ◽  
Environmental Factors ◽  
Temperature Difference ◽  
Mediterranean Region ◽  
Bernoulli Equation ◽  
Outdoor Temperature ◽  
Optimal Point ◽  
Air Ventilation ◽  
Roof Area ◽  
The Mediterranean

Ventilation is one of the methods used to obtain the biological optimal point of environmental factors needed for the plants in greenhouses. In the greenhouses, air change coefficient must be more than 50 h-1 in order to supply effective air ventilation. Temperature differences like air change coefficient can be regarded as a criterion to determine efficiency of ventilation in the greenhouses. In this study, the temperature values were calculated by using energy balance and Bernoulli equation at different ventilation opening ratios (AV/AG) depending on climatic properties in the Mediterranean region (Antalya). If was found that, based on temperature and radiation values of Antalya province, 20% ventilation opening rate is sufficient in the roof area. A temperature difference (∆T) of 1K can be achieved with a 50% shading of radiation and a 20% ventilation opening in June in the Mediterranean region. However, additional cooling is necessary in the greenhouses around noon hours because outdoor temperature is greater than 30°C.

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