Bernoulli’s Equation (Mechanics of Ideal Fluids)

2016 ◽  
pp. 89-97
Author(s):  
Hajime Akimoto ◽  
Yoshinari Anoda ◽  
Kazuyuki Takase ◽  
Hiroyuki Yoshida ◽  
Hidesada Tamai
Keyword(s):  
Bernoulli’S Equation ◽  
Ideal Fluids

scholarly journals Hamiltonian Aspects of Three-Layer Stratified Fluids

2021 ◽  
Vol 31 (4) ◽  
Author(s):  
R. Camassa ◽  
G. Falqui ◽  
G. Ortenzi ◽  
M. Pedroni ◽  
T. T. Vu Ho
Keyword(s):  
Hamiltonian Structure ◽  
Linear Equations ◽  
Hamiltonian Formalism ◽  
Reduction Process ◽  
Ideal Fluids ◽  
Upper Lid ◽  
Stratification Structure ◽  
Special Solutions ◽  
Dispersionless Limit ◽  
Unbounded Fluid

AbstractThe theory of three-layer density-stratified ideal fluids is examined with a view toward its generalization to the n-layer case. The focus is on structural properties, especially for the case of a rigid upper lid constraint. We show that the long-wave dispersionless limit is a system of quasi-linear equations that do not admit Riemann invariants. We equip the layer-averaged one-dimensional model with a natural Hamiltonian structure, obtained with a suitable reduction process from the continuous density stratification structure of the full two-dimensional equations proposed by Benjamin. For a laterally unbounded fluid between horizontal rigid boundaries, the paradox about the non-conservation of horizontal total momentum is revisited, and it is shown that the pressure imbalances causing it can be intensified by three-layer setups with respect to their two-layer counterparts. The generator of the x-translational symmetry in the n-layer setup is also identified by the appropriate Hamiltonian formalism. The Boussinesq limit and a family of special solutions recently introduced by de Melo Viríssimo and Milewski are also discussed.

scholarly journals Euler equations for incompressible ideal fluids

2007 ◽  
Vol 62 (3) ◽  
pp. 409-451 ◽  
Author(s):  
Claude Bardos ◽  
Edriss Titi
Keyword(s):  
Euler Equations ◽  
Ideal Fluids

Theoretical and experimental study of motion and sinking time of Saxon Bowls

2022 ◽  
Author(s):  
Jaikumar Sankar ◽  
Liu Yang
Keyword(s):  
Motion Tracking ◽  
Volumetric Flow Rate ◽  
Free Form ◽  
Motion Path ◽  
Time Interval ◽  
Flow Profile ◽  
Bernoulli’S Equation ◽  
Hole Radius ◽  
Coefficient Of Discharge ◽  
High Degree

Abstract This work focuses on investigating the time of sinking of a Saxon bowl proposed by ‘International Young Physicists’ Tournament in 2020. A quasi-static model is built to simulate the motion path of the bowl and predict the sinking time subsequently. The model assumes an open axisymmetric bowl with a hole in its base. The hole is modelled as a pipe for which the flow profile is governed by a modified Bernoulli’s equation which has a Coefficient of Discharge (C_d) added to account for energy losses. The motion of the entire bowl is assumed to be in quasi-static equilibrium for an infinitesimal time interval to calculate the volumetric flow rate through the hole. The model is used to predict the sinking times of various bowls against independent variables - hole radius, bowl dimensions, mass of bowl, mass distribution of bowl, and Coefficient of Discharge - and predict the motion path of bowls of different, axisymmetric geometries. Characterisation of C_d was done by draining a bowl filled with water and measuring the time taken to do so. Experimental verification was completed through measuring sinking times of 3D printed hemispherical bowls of the different variables in water. Motion tracking of bowls with different geometries was done using computational pixel tracking software to verify the model’s predictive power. Data from experiments for sinking time against the variables corroborate with the model to a great degree. The motion path tracked, matched the modelled motion path to a high degree for bowls of different shapes, namely a hemisphere, cylinder, frustum, and a free-form axisymmetric shape. The work is poised for an undergraduate level of readership.

scholarly journals Communicating vessels: a non-linear dynamical system

2017 ◽  
Vol 39 (3) ◽  
Author(s):  
Roberto De Luca ◽  
Orazio Faella
Keyword(s):  
Dynamical System ◽  
Fluid Flow ◽  
Ideal Fluid ◽  
Oscillatory Motion ◽  
Linear Dynamical System ◽  
Static Properties ◽  
Bernoulli’S Equation ◽  
Non Linear ◽  
Dynamical Properties

The dynamics of an ideal fluid contained in two communicating vessels is studied. Despite the fact that the static properties of this system have been known since antiquity, the knowledge of the dynamical properties of an ideal fluid flowing in two communicating vessels is not similarly widespread. By means of Bernoulli's equation for non-stationary fluid flow, we study the oscillatory motion of the fluid when dissipation can be neglected.

scholarly journals Simplified measurement of intra-access pressure.

1998 ◽  
Vol 9 (2) ◽  
pp. 284-289
Author(s):  
A Besarab ◽  
S Frinak ◽  
R A Sherman ◽  
J Goldman ◽  
F Dumler ◽  
...  
Keyword(s):  
Blood Flow ◽  
Delivery Systems ◽  
Chamber Pressure ◽  
Hemodialysis Access ◽  
Fluid Density ◽  
Special Equipment ◽  
Venous Outflow ◽  
Bernoulli’S Equation ◽  
The Difference ◽  
Zero Flow

The measurement of intra-access pressure (P[IA]) normalized by mean arterial BP (MAP) helps detect venous outlet stenosis and correlates with access blood flow. However, general use of P(IA)/MAP is limited by time and special equipment costs. Bernoulli's equation relates differences between P(IA) (recorded by an external transducer as PT) and the venous drip chamber pressure, PDC; at zero flow, the difference in height (deltaH) between the measuring sites and fluid density determines the pressure deltaPH = P(IA) - P(DC) Therefore, P(DC) and PT measurements were correlated at six different dialysis units, each using one of three different dialysis delivery systems machines. Both dynamic (i.e., with blood flow) and static pressures were measured. Changes in mean BP, zero calibration errors, and hydrostatic height between the transducer and drip chamber accounted for 90% of the variance in P(DC), with deltaPH = -1.6 + 0.74 deltaH (r = 0.88, P < 0.001). The major determinants of static P(IA)/MAP were access type and venous outflow abnormalities. In grafts, flow averaged 555 +/- 45 ml/min for P(IA)/MAP > 0.5 and 1229 +/- 112 ml/min for P(IA)/MAP < 0.5. DeltaPH varied from 9.4 to 17.4 mmHg among the six centers and was related to deltaH between the drip chamber and the armrest of the dialysis chair. Concordance between values of P(IA)/MAP calculated from PT and from P(DC) + deltaPH was excellent. It is concluded that static P(DC) measurements corrected by an appropriate deltaPH can be used to prospectively monitor hemodialysis access grafts for stenosis.

scholarly journals q-Bernoulli’s Equation

2020 ◽  
Vol 17 (1) ◽  
pp. 214-217
Author(s):  
Salih Y. Arbab ◽  
Sami H. Altoum
Keyword(s):  
Bernoulli’S Equation

scholarly journals Nonlinear higher-order spectral solution for a two-dimensional moving load on ice

2009 ◽  
Vol 621 ◽  
pp. 215-242 ◽  
Author(s):  
FÉLICIEN BONNEFOY ◽  
MICHAEL H. MEYLAN ◽  
PIERRE FERRANT
Keyword(s):  
Critical Speed ◽  
Moving Boundary ◽  
Moving Load ◽  
Phase Speed ◽  
Nonlinear Effects ◽  
Higher Order ◽  
Two Dimensions ◽  
Linear Solution ◽  
Nonlinear Solution ◽  
Bernoulli’S Equation

We calculate the nonlinear response of an infinite ice sheet to a moving load in the time domain in two dimensions, using a higher-order spectral method. The nonlinearity is due to the moving boundary, as well as the nonlinear term in Bernoulli's equation and the elastic plate equation. We compare the nonlinear solution with the linear solution and with the nonlinear solution found by Parau & Dias (J. Fluid Mech., vol. 460, 2002, pp. 281–305). We find good agreement with both solutions (with the correction of an error in the Parau & Dias 2002 results) in the appropriate regimes. We also derive a solitary wavelike expression for the linear solution – close to but below the critical speed at which the phase speed has a minimum. Our model is carefully validated and used to investigate nonlinear effects. We focus in detail on the solution at a critical speed at which the linear response is infinite, and we show that the nonlinear solution remains bounded. We also establish that the inclusion of nonlinearities leads to significant new behaviour, which is not observed in the linear solution.

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