hw2 - 16.100 Homework Assignment#2 Due:Wednesday September...

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Unformatted text preview: 16.100 Homework Assignment #2 Due:Wednesday, September 21 th , 9am Reading Assignment Anderson, 3 rd edition: Chapter 2, Sections 2.4-2.6, 2.10 Chapter 3, Sections 3.1-3.2, 3.5-3.16 Problem 1 (30%) Useful reading: Sections 2.10, 3.6 of Anderson The incompressible, inviscid flow equations (called the incompressible Euler equations) are: 2) (Eq. 1) (Eq. p Dt V D V −∇ = = ⋅ ∇ r r ρ a) Starting from the incompressible Euler equations, derive the following ‘Bernoulli-like’ equation: ω ρ ρ ρ r r r r × = + ∇ + ∂ ∂ V V p t V 2 2 1 where is the vorticity. The following vector calculus identity might be helpful: V r r × ∇ = ω ( ) ω r r r r r × − ∇ = ∇ ⋅ V V V V 2 2 1 b) Show that the total pressure, 2 2 1 V p r ρ + , is constant along a streamline in a steady, inviscid flow. c) Show that the total pressure is constant everywhere in a steady, inviscid, and irrotational flow....
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hw2 - 16.100 Homework Assignment#2 Due:Wednesday September...

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