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partial vx w/ respect to x + partial vy w/ respect to y + partial vz w/ respect to z = 0

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Q: What is laplace equation of continuity?
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What was Pierre Simon Laplace known for?

Work in Celestial Mechanics Laplace's equation Laplacian Laplace transform Laplace distribution Laplace's demon Laplace expansion Young-Laplace equation Laplace number Laplace limit Laplace invariant Laplace principle -wikipedia


Application of Laplace equation?

The Laplace equation is used commonly in two situations. It is used to find fluid flow and in calculating electrostatics.


Why Laplace transform not Laplace equation?

Laplace equation: in 3D U_xx+U_yy+U_zz=0 Or in 2D U_xx+U_yy=0 where U is a function of the spatial variables x,y,z in 3D and x,y in 2D.Also, U_xx is the second order partial derivative of u with respect to x, same for y and z. Laplace transform: L(f(t))=integral of (e^(-s*t))*f(t) dt as t goes from 0 to infinity. Laplace transform is more like an operator rather than an equation.


How are the continuity equation and bernoulli's equation related?

The continuity equation states that the mass flow rate is constant in an incompressible fluid, while Bernoulli's equation relates the pressure, velocity, and elevation of a fluid in steady flow. Together, they help describe the relationship between fluid velocity, pressure, and flow rate in a system. The continuity equation can be used to derive Bernoulli's equation for incompressible fluids.


Application of Laplace transform to partial differential equations. Am in need of how to use Laplace transforms to solve a Transient convection diffusion equation So any help is appreciated.?

yes


What did Pierre Simon Laplace Invent?

He formulated Laplace's equation, and invented the Laplace transform which appears in many branches of mathematical physics, a field that he took a leading role in forming. The Laplacian differential operator, widely used in applied mathematics, is also named after him.


Applications of laplace transform in engineering?

Laplace transforms to reduce a differential equation to an algebra problem. Engineers often must solve difficult differential equations and this is one nice way of doing it.


What is Laplace transform?

A Laplace transform is a mathematical operator that is used to solve differential equations. This operator is also used to transform waveform functions from the time domain to the frequency domain and can simplify the study of such functions. For continuous functions, f(t), the Laplace transform, F(s), is defined as the Integral from 0 to infinity of f(t)*e-stdt. When this definition is used it can be shown that the Laplace transform, Fn(s) of the nth derivative of a function, fn(t), is given by the following generic formula:Fn(s)=snF(s) - sn-1f0(0) - sn-2f1(0) - sn-3f2(0) - sn-4f3(0) - sn-5f4(0). . . . . - sn-nfn-1(0)Thus, by taking the Laplace transform of an entire differential equation you can eliminate the derivatives of functions with respect to t in the equation replacing them with a Laplace transform operator, and simple initial condition constants, fn(0), times a new variable s raised to some power. In this manner the differential equation is transformed into an algebraic equation with an F(s) term. After solving this new algebraic equation for F(s) you can take the inverse Laplace transform of the entire equation. Since the inverse Laplace transform of F(s) is f(t) you are left with the solution to the original differential equation.


What is continuity equation in fluid mechanics?

Area*Velocity=Constant


Difference between poisson's equation and Laplace equation?

Poisson's equation includes a source term representing the charge distribution in the region, while Laplace's equation does not have any source term and describes the behavior in the absence of charges. Poisson's equation is a generalization of Laplace's equation, which makes it more suitable for situations involving charge distributions and electric fields.


When is the speed of a fluid maximum in a venturi meter?

from the continuity equation A1v1 = A2v2 according to the continuity equation as the area decreases the velocity of the flow of the liquid increases and hence maximum velocity can be obtained at its throat


What is continuity equation for compressible fluids?

The continuity equation for compressible fluids states that the rate of change of density (ρ) in a fluid is equal to -∇⋅(ρu), where ρ is density, u is velocity, and ∇⋅ is the divergence operator. This equation is derived from the conservation of mass principle in fluid dynamics.