Transcription of Potential Flow Theory - MIT
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Potential Flow Theory - MIT
Hydrodynamics Reading #4. Hydrodynamics Prof. Techet Potential Flow Theory When a flow is both frictionless and irrotational, pleasant things happen. White, Fluid Mechanics 4th ed. We can treat external flows around bodies as invicid ( frictionless) and irrotational ( the fluid particles are not rotating). This is because the viscous effects are limited to a thin layer next to the body called the boundary layer. In graduate classes like , you'll learn how to solve for the invicid flow and then correct this within the boundary layer by considering viscosity. For now, let's just learn how to solve for the invicid flow. We can define a Potential function, ! ( x, z, t ) , as a continuous function that satisfies the basic laws of fluid mechanics: conservation of mass and momentum, assuming incompressible, inviscid and irrotational flow. There is a vector identity (prove it for yourself!) that states for any scalar, " , " # "$ = 0.
Equations (4.5) and (4.6) are known as the Cauchy-Riemann equations which appear in complex variable math (such as 18.075). Bernoulli Equation The Bernoulli equation is the most widely used equation in fluid mechanics, and assumes frictionless flow with no work or heat transfer. However, flow may or may not be irrotational.
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