Laplace's Equation - Revision history

Adi Kurniawan at 03:19, 23 September 2008

2008-09-23T03:19:30Z

← Older revision		Revision as of 03:19, 23 September 2008
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	direction.		direction.

	~~More details can be found on the~~ [http://en.wikipedia.org/wiki/Laplace%27s_equation ~~Wikipedia entry~~]		==See Also==
			* [http://en.wikipedia.org/wiki/Laplace%27s_equation Laplace's equation]

2008-08-21T03:12:23Z

← Older revision		Revision as of 03:12, 21 August 2008
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	The typical solution to Laplace's equation oscillates in one direction and		The typical solution to Laplace's equation oscillates in one direction and
	decays in another. The linear water wave arises as a boundary wave which		decays in another. The linear water wave arises as a boundary wave which
	decays in the vertical ~~condition~~ and has wave properties in the horizontal		decays in the vertical direction and has wave properties in the horizontal
	direction.		direction.

	More details can be found on the [http://en.wikipedia.org/wiki/Laplace%27s_equation Wikipedia entry]		More details can be found on the [http://en.wikipedia.org/wiki/Laplace%27s_equation Wikipedia entry]

2008-08-21T03:09:32Z

← Older revision		Revision as of 03:09, 21 August 2008
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	The velocity potential satisfies Laplace equation if we can assume that the fluid is inviscid, incompressible, and irrotational.		The velocity potential <math>\Phi</math> satisfies Laplace's equation if we can assume that the fluid is inviscid, incompressible, and irrotational.

	Laplace's equation is the following in two dimensions		Laplace's equation is the following in two dimensions

2006-06-08T22:06:19Z

← Older revision		Revision as of 22:06, 8 June 2006
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	direction.		direction.

	More details can be found on the [http://en.wikipedia.org/wiki/Laplace%27s_equation : Wikipedia entry]		More details can be found on the [http://en.wikipedia.org/wiki/Laplace%27s_equation Wikipedia entry]

2006-06-08T22:05:59Z

← Older revision		Revision as of 22:05, 8 June 2006
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	direction.		direction.

	More details can be found on the [http://en.wikipedia.org/wiki/Laplace%27s_equation: Wikipedia entry]		More details can be found on the [http://en.wikipedia.org/wiki/Laplace%27s_equation : Wikipedia entry]

2006-06-08T22:05:35Z

← Older revision		Revision as of 22:05, 8 June 2006
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	decays in the vertical condition and has wave properties in the horizontal		decays in the vertical condition and has wave properties in the horizontal
	direction.		direction.

			More details can be found on the [http://en.wikipedia.org/wiki/Laplace%27s_equation: Wikipedia entry]

2006-05-24T11:13:52Z

← Older revision		Revision as of 11:13, 24 May 2006
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	Laplace's equation is the following in two dimensions		Laplace's equation is the following in two dimensions

	<math>\~~Nabla~~^2\phi = \frac{\partial^2 \phi}{\partial x^2}		<math>\nabla^2\phi = \frac{\partial^2 \phi}{\partial x^2}
	+ \frac{\partial^2 \phi}{\partial z^2} = 0</math>		+ \frac{\partial^2 \phi}{\partial z^2} = 0</math>

	and in three dimensions		and in three dimensions

	<math>\~~Nabla~~^2\phi = \frac{\partial^2 \phi}{\partial x^2}		<math>\nabla^2\phi = \frac{\partial^2 \phi}{\partial x^2}
	+ \frac{\partial^2 \phi}{\partial y^2}+ \frac{\partial^2 \phi}{\partial z^2} = 0</math>		+ \frac{\partial^2 \phi}{\partial y^2}+ \frac{\partial^2 \phi}{\partial z^2} = 0</math>

2006-05-24T11:13:26Z

← Older revision		Revision as of 11:13, 24 May 2006
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	The velocity potential satisfies ~~the~~ Laplace equation ~~because of the assumptions~~ that the fluid is inviscid, incompressible, and irrotational.		The velocity potential satisfies Laplace equation if we can assume that the fluid is inviscid, incompressible, and irrotational.

			Laplace's equation is the following in two dimensions

			<math>\Nabla^2\phi = \frac{\partial^2 \phi}{\partial x^2}
			+ \frac{\partial^2 \phi}{\partial z^2} = 0</math>

			and in three dimensions

			<math>\Nabla^2\phi = \frac{\partial^2 \phi}{\partial x^2}
			+ \frac{\partial^2 \phi}{\partial y^2}+ \frac{\partial^2 \phi}{\partial z^2} = 0</math>

			The typical solution to Laplace's equation oscillates in one direction and
			decays in another. The linear water wave arises as a boundary wave which
			decays in the vertical condition and has wave properties in the horizontal
			direction.

2006-05-24T06:20:45Z

New page

The velocity potential satisfies the Laplace equation because of the assumptions that the fluid is inviscid, incompressible, and irrotational.