What is the P.D.E. governing this phenomemon?

  • Thread starter lavinia
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In summary, there is no specific physical law like the heat equation that describes the flow of an incompressible fluid spreading across a surface at a constant rate. However, the Navier-Stokes equations, coupled with continuity and possibly the energy equation, can be used to describe the system. It is also possible to achieve an equilibrium distribution of fluid flow on a closed surface with no boundaries by allowing sinks to appear and keep the volume of fluid constant.
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lavinia
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At a point on a surface an incompressible fluid begins to up well at a constant rate and spread across the surface.

Is there a physical law - like the heat equation - that describes the flow?

Will the fluid eventually cover the whole surface?

Once the surface is covered allow sinks to appear to keep the volume of fluid on the surface constant. Will one then get an equilibrium distribution of fluid flow on the surface?

I have in mind closed surfaces with no boundary so that the fluid can't fall of any edges or leak through any holes.
 
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  • #2
I am not visualizing your setup perfectly, but given that it is a fluids problem, the Navier-Stokes equations coupled with continuity and (depending on what you are looking for) perhaps the energy equation will be able to describe your system.
 

1. What is a P.D.E.?

A P.D.E. stands for Partial Differential Equation. It is a type of mathematical equation used to describe the relationship between multiple variables in a system that is changing over time and space.

2. How is a P.D.E. different from an ordinary differential equation (ODE)?

A P.D.E. involves multiple independent variables, such as time and space, while an ODE only involves one independent variable. P.D.E.s are also used to model systems that are changing over both time and space, while ODEs are typically used for systems that only change over time.

3. What types of phenomena can be described with a P.D.E.?

P.D.E.s are used to describe a wide range of phenomena, including heat transfer, fluid dynamics, and quantum mechanics. They are particularly useful for systems that involve continuous changes over time and space.

4. How is a P.D.E. solved?

Solving a P.D.E. involves finding a function that satisfies the equation and any given boundary conditions. This can be done analytically, using mathematical techniques, or numerically, using numerical methods and computer simulations.

5. What are some real-life applications of P.D.E.s?

P.D.E.s are used in many fields of science and engineering, including physics, chemistry, biology, and engineering. They are used to model and predict a wide range of phenomena, such as weather patterns, heat transfer in engines, and chemical reactions.

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