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Elliptic Equations: Equilibrium in Two Dimensions
Published in Saad A. Ragab, Hassan E. Fayed, Introduction to Finite Element Analysis for Engineers, 2018
Saad A. Ragab, Hassan E. Fayed
which is Laplace’s equation. Therefore, the major step in finding the velocity field V→ $ \vec{V} $ of an irrotational flow is to solve Laplace’s equation subjected to proper boundary conditions. The pressure is found by integrating the momentum Equation (4.278). Assuming incompressible inviscid flow and conservative body force, the integrated momentum equation is Bernoulli’s equation which we write here for steady or unsteady potential flow, ∂ϕ∂t+12V2+pρ+G=C $$ \frac{{\partial \phi }}{{\partial t}} + \frac{1}{2}V^{2} + \frac{p}{\rho } + G = C $$
Units and Significant Figures
Published in Patrick F. Dunn, Fundamentals of Sensors for Engineering and Science, 2019
An engineering student measures an ambient lab pressure and temperature of 405.35 in. H2O and 70.5 °F, respectively, and a wind tunnel dynamic pressure (using a pitot-static tube) of 1.056 kN/m2. Assume that Rair = 287.04 J/(kg · K). Determine with the correct number of significant figures (a) the room density using the perfect gas law in SI units (state the units with the answer) and (b) the wind tunnel velocity using Bernoulli’s equation in units of ft/s. Bernoulli’s equation states that for irrotational, incompressible flow the dynamic pressure equals one-half the product of the density times the square of the velocity.
Ideal fluid flow
Published in Amithirigala Widhanelage Jayawardena, Fluid Mechanics, Hydraulics, Hydrology and Water Resources for Civil Engineers, 2021
Amithirigala Widhanelage Jayawardena
Fluid flows can also be considered as rotational flows and irrotational flows. Rotational flows are flows where the fluid particles rotate about their own axes while flowing along streamlines. The solar system is rotational. Irrotational flows are flows where the fluid particles do not rotate about their own axes while flowing along streamlines. It is a simplified assumption since no real fluid is really irrotational. A fluid inside a rotating tank is irrotational once it has reached steady-state conditions since the flow is in rigid body motion. However, at the centre of rotation, the angular velocity is so high resulting in the flow to be rotational.
Weakly nonlinear ship motion calculation and parametric rolling simulation based on the 3DTGF-HOBEM method
Published in Ships and Offshore Structures, 2021
Wen-jun Zhou, Ren-chuan Zhu, Xi Chen, Liang Hong
Assuming the fluid is inviscid and impressible and the flow is irrotational, the velocity of fluid particle is expressed by the gradient of velocity potential. Supposing both the steepness of incident waves and the motions of the ship are small enough, the total velocity potential can be linearised aswhere the first terms correspond to the steady-state potential due to the ship speed and is the incident potential, while and represent the diffraction potential scattered by the ship hull and the radiation potential resulting from the motion in the j-th mode, respectively.
The influence of flexible bottom on wave generation by an oscillatory disturbance in the presence of surface tension
Published in Geophysical & Astrophysical Fluid Dynamics, 2023
Selina Hossain, Arijit Das, Soumen De
Since the motion of the fluid is irrotational, there exists a velocity potential that satisfies the Laplace equation with the bottom boundary condition (cf. Mohapatra and Sahoo 2011) where , EI is the flexural rigidity of the flexible bottom, and . E, ν and , respectively, denote the Young's modulus, Poisson's ratio and density of the elastic plate and ρ is the density of the fluid.
A reduced-order hydroelastic analysis of 2D hydrofoil considering supercavitation effects
Published in Ships and Offshore Structures, 2018
S. M. Alavi, H. Haddadpour, R. D. Firouz-Abadi
The assumption of inviscid, irrotational and incompressible flow is named as potential flow which leads to the Laplace equation as the governing differential equation. This equation can be obtained by simplifying the Navier–Stockes equations and is expressed as follows (Katz and Plotkin 2001): The total potential at any point can be specified as the summation of the undisturbed, φ0, and disturbed, , potentials as follows: In order to employ the Laplace equation for the hydrodynamic simulation, boundary conditions must be imposed on any of the boundaries, which are introduced in the following section.