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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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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 do jet engines provide a forward thrust for an airplane by using the continuity Equation?
they move
The Laplace transform of sin3t?
find Laplace transform? f(t)=sin3t
When did Pierre Simon Laplace die?
Pierre Simon Laplace died on March 5, 1827.
What is the difference between Fourier transform and Laplace transform and z transform?
Fourier transform and Laplace transform are similar. Laplace transforms map a function to a new function on the complex plane, while Fourier maps a function to a new function on the real line. You can view Fourier as the Laplace transform on the circle, that is |z|=1. z transform is the discrete version of Laplace transform.
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.
How are the continuity equation and bernoulli's equation related?
Continuity equations describe the movement of constant. Bernoulli's equation also relates to movement, the flow of liquids. For some situations, where the liquid flowing is a constant, both a continuity equation and Bernoulli's equation can be applied.
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.
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.
What is continuity equation tell us?
fluid flow.
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
What is the equation of continuity?
The Equation of Continuity is the four dimensional derivative of a four dimensional variable set to zero. This is also called the limit equation and the Boundary equation, and the Homeostasis Equation. The Continuity Equation is also called the Invariant Equation or Condition. The most famous equation that is in fact a continuity Equation is Maxwell's Electromagnetic equations. (d/dR + Del)(Br + Bv) = (dBr/dR -Del.Bv) + (dBv/dR + DelxBv + Del Br) = 0 This gives two equations the real Continuity Equation: 0=(dBr/dR - Del.Bv) and the vector Continuity Equation: 0=(dBv/dR + Del Br) This Equation will be more familiar when R=ct and dR=cdt and cB = E then 0=(dBr/dt - Del.Ev) and 0=(dBv/dt + Del Er) The Continuity Equation says the sum of the derivatives is zero. The four dimensional variable has two parts a real part Br and a vector part Bv. The Continuity Equation is the sum of the real derivatives is zero and the sum of the vector derivatives is zero. The term DelxBv is zero at Continuity because this term is perpendicular to both the other two terms and makes it impossible geometrically for the vectors to sum to zero unless it is zero. Only if the DelxBv=0 can the vectors sum to zero. This situation occurs when the other two terms are parallel or anti-parallel. If anti-parallel then dBv/Dr is equal and opposite to Del Br and the vectors sum to zero. This is Newton's Equal and Opposite statement in his 3rd Law and is a geometrical necessity for the vectors to sum to zero.. Many Equations of Physics have misrepresented the Continuity Equation and others have not recognized the continuity Equation as in Maxwell's Equations. The Continuity Equation is probably the most important equation in science! The Four dimensional space of science is a quaternion non-commutative (non-parallel) space defined by William Rowan Hamilton in 1843, (i,j,k and 1), with rules i^2=j^2=k^2=-1.
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
