Explanation Given Information: Bernoulli equation for the region of inviscid flow, The steady incompressible Euler equation equal to the product of velocity vector and vorticity vector. ∇ → ( p ρ + v 2 2 + g z ) = v → × ζ → Concept used: Bernoulli equation for the region of inviscid flow As we have ∇ → ( p ρ + v 2 2 + g z ) = v → × ζ → Where, p = p r e s s u r e o f f l u i d ρ = d e n s i t y o f f l o w i n g f l u i d v = v e c t o r o f f l o w i n g f l u i d v → = v e l o c i t y v e c t o r ζ → = v o r t i c i t y v e c t o r Case-(1) Taking dot product of equation with the velocity vector ∇ → ( p ρ + v 2 2 + g z ) . v → = ( v → × ζ → ) v → -------------------- (1) Consider RHS of equation (1) ( v → × ζ → )

Fluid Mechanics: Fundamentals and Applications

4th Edition

ISBN: 9781259696534

Author: Yunus A. Cengel Dr., John M. Cimbala

Publisher: McGraw-Hill Education

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Fluid Kinematics

The branch of science that deals with objects which are either in motion or stationary are studied under the branch of classical mechanics. Fluid mechanics is a subcategory of classical mechanics that deals with the behavior of fluids at rest (fluid stat…

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Chapter 10, Problem 44P

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The sum of the three scalar terms are constant along a streamline.

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Chapter 10, Problem 43P

Chapter 10, Problem 45P

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Fluid Mechanics: Fundamentals and Applications

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The sum of the three scalar terms are constant along a streamline.

Solution Summary: The author describes the steady incompressible Euler equation for the region of inviscid flow.

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