Explanation Given Information: Bernoulli equation for region of inviscid flow, ( v → . ∇ → ) = ∇ → ( v 2 2 ) − v → × ( ∇ → × v → ) Also,contusion coordinate equation v → = u i → + v j → + w k → Concept used: Bernoulli equation for the regionof inviscid flow. The vector identity and also Bernoulli's equation in inviscid form is given by ( v → . ∇ → ) = ∇ → ( v 2 2 ) − v → × ( ∇ → × v → ) --------------------- (1) Also,the velocity vector in cartesian coordinate is v → = u i → + v j → + w k → v → In confession coordinate v → = ( ∂ ∂ x , ∂ ∂ y , ∂ ∂ z ) Expanding each term individually. 1 s t term is, ( v → . ∇ → ) v → = ( u ∂ u ∂ x + v ∂ u ∂ y + w ∂ u ∂ z ) i → + ( u ∂ v ∂ x + v ∂ v ∂ y + w ∂ v ∂ z ) j → + u → ( u ∂ w ∂ x + v ∂ w ∂ y + w ∂ w ∂ z ) k → Similarly,the 2 n d term is ∇ → [ v 2 2 ] = 1 2 [ ( ∂ u 2 ∂ x + ∂ v 2 ∂ x + ∂ w 2 ∂ x ) i → + ( ∂ u 2 ∂ y + ∂ v 2 ∂ y + ∂ w 2 ∂ y ) j → + u → ( ∂ u 2 ∂ z + ∂ v 2 ∂ z + ∂ w 2 ∂ z ) k → = <

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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Chapter 10, Problem 45P

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The vector identity is satisfied for the case of velocity vector in Cartesian coordinates.

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Chapter 10, Problem 44P

Chapter 10, Problem 46P

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Fluid Mechanics: Fundamentals and Applications

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