Explanation Given information: The vector field, G → is G x i → + G y j → + G z k → and vector field, F → is F x i → + F y j → + F z k → . Write the expression for product of two vectors . F → G → = [ F z G x F x G y F z G z F y G x F y G y F y G z F z G x F z G y F z G z ] ........... (I) Here, the vector field is G → , components of vector field G → are G x , G y and G z , the vector field is F → and components of vector field F → are F x , F y and F z . Write the expression for given relation. ∇ → ⋅ ( F → G → ) = G → ( ∇ → ⋅ F → ) + ( F → ⋅ ∇ → ) G → ........... (II) Here, the del operator is ∇ . Write the expression for del operator. ∇ = ( ∂ ∂ x i → + ∂ ∂ y j → + ∂ ∂ z k → ) ........... (III) Here, direction vector in x-direction is i → , direction vector in y-direction is j → and direction vector in z-direction is k → . Calculation: Substitute ( ∂ ∂ x i → + ∂ ∂ y j → + ∂ ∂ z k → ) for ∇ , G x i → + G y j → + G z k → for G → , F x i → + F y j → + F z k → for F → and [ F z G x F x G y F z G z F y G x F y G y F y G z F z G x F z G y F z G z ] for F → G → in Equation (I). ..........

Fluid Mechanics: Fundamentals and Applications

4th Edition

ISBN: 9781259877827

Author: CENGEL

Publisher: MCG

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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 9, Problem 18P

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The verification of the relation ∇→⋅(F→G→)=G→(∇→⋅F→)+(F→⋅∇→)G→.

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Chapter 9, Problem 17P

Chapter 9, Problem 19P

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Fluid Mechanics: Fundamentals and Applications

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The verification of the relation ∇ → ⋅ ( F → G → ) = G → ( ∇ → ⋅ F → ) + ( F → ⋅ ∇ → ) G → .

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The verification of the relation ∇→⋅(F→G→)=G→(∇→⋅F→)+(F→⋅∇→)G→.

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