mathematics and physics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace, who first studied its properties...

equation in general, as the Laplace equation also models the electrostatic potential in a vacuum. There are many reasons to study irrotational flow,...

In fluid dynamics, potential flow or irrotational flow refers to a description of a fluid flow with no vorticity in it. Such a description typically arises...

into account while the Euler equations model only inviscid flow. As a result, the Navier–Stokes are an elliptic equation and therefore have better analytic...

In fluid dynamics, the Euler equations are a set of partial differential equations governing adiabatic and inviscid flow. They are named after Leonhard...

polymers generally. The equations of motion for Stokes flow, called the Stokes equations, are a linearization of the Navier–Stokes equations, and thus can be...

Laplace's demon Laplace equation for irrotational flow Laplace force Laplace number Laplace plane Laplace's invariable plane Laplace pressure Laplace-Runge-Lenz...

Harmonic morphism Harmonic polynomial Heat equation Laplace equation for irrotational flow Poisson's equation Quadrature domains Axler, Sheldon; Bourdon...

which is both irrotational and incompressible. If the field is denoted as v, then it is described by the following differential equations: ∇ × v = 0 ,...

equipotential lines is called a flow net. The flow net is an important tool in analysing two-dimensional irrotational flow problems. Flow net technique is a graphical...

to the flow. Far from the cylinder, the flow is unidirectional and uniform. The flow has no vorticity and thus the velocity field is irrotational and can...

potential-flow theory has the advantage that the equation (Laplace's equation) to be solved for the potential is linear, which allows solutions to be constructed...

layer has a uniform mean depth, and that the fluid flow is inviscid, incompressible and irrotational. This theory was first published, in correct form...

vector. Then the second Cauchy–Riemann equation (1b) asserts that f ¯ {\displaystyle {\bar {f}}} is irrotational (its curl is 0): ∂ ( − v ) ∂ x − ∂ u ∂...

the flow is inviscid, incompressible and irrotational. This case is called potential flow and allows the differential equations that describe the flow to...

conservation of mass (see continuity equation) for an incompressible flow and the zero-curl condition for an irrotational flow are used, to replace vertical...

{\displaystyle xy} -plane thus correspond to potential flow (irrotational flow). Unlike potential flow, here the circulation Γ {\displaystyle \Gamma } around...

In fluid dynamics, the Oseen equations (or Oseen flow) describe the flow of a viscous and incompressible fluid at small Reynolds numbers, as formulated...

Navier-Stokes equations. Some of the flows reflect specific constraints such as incompressible or irrotational flows, or both, as in the case of potential flow, and...

boundary layers (for the oscillatory part of the flow). Because the flow is irrotational, the wave motion can be described using potential flow theory. Details...

at z = η {\displaystyle \scriptstyle z=\eta } is given by the Young–Laplace equation: p ( z = η ) = − σ κ , {\displaystyle p\left(z=\eta \right)=-\sigma...

flow, which is an approximation to fluid flow assuming constant density, zero viscosity, and irrotational flow. One example of a fluid dynamic application...

flow pattern for an irrotational, incompressible flow can be synthesized by adding together a number of elementary flows, which are also irrotational...

solved for, not only is u found as given above, but p is also easily found—from the (linearised) Bernoulli equation for irrotational and unsteady flow—as...

Lagrangian formulation is for non-linear surface gravity waves on an—incompressible, irrotational and inviscid—potential flow. The relevant ingredients...

flow being irrotational – the flow is then potential. These are typically also good approximations for common situations. The resulting equation for the...

satisfying both the Laplace equation ∇2Φ = 0 in the fluid interior, as well as the boundary condition ∂Φ/∂z = 0 at the bed z = −h. For a given value of the...

Taylor, G.I. (March 1, 1917). "Motion of solids in fluids when the flow is not irrotational". Proc. R. Soc. Lond. A. 93 (648): 92–113. Bibcode:1917RSPSA..93...

{\displaystyle {{\vec {u}}=\nabla \phi ,}} and the potential itself satisfies Laplace's equation: ∇ 2 ϕ = 0. {\displaystyle \nabla ^{2}\phi =0.} Assuming the domain...

={\overline {f(z)}}} is irrotational (curl-free) and incompressible (divergence-free). In fact, the Cauchy-Riemann equations for f ( z ) {\displaystyle...