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b) V·(v.)= v·(V.) + :Vy (where T denotes transpose) 1 c) Dy oy O² = -+-V(y·v)-y×(Vxv) Dt where D ə +v.V is known as the "substantial derivative" operator. Dt ôt

b) V·(v.)= v·(V.) + :Vy (where T denotes transpose) 1 c) Dy oy O² = -+-V(y·v)-y×(Vxv) Dt where D ə +v.V is known as the "substantial derivative" operator. Dt ôt

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 50E
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I need B and C please!

Prove the following identities using simplified index notation: (Vu) at b) T V·(y•t)= y·(V• 7² ) + :Vy (where 7 denotes transpose) Dv ὃν Dt where = + = V(v • v) — v × (V×v) Ət D Dt Ə -+v. V is known as the "substantial derivative" operator. Ət Hint: for part (c), it will be easier to work from the right side toward the left.
Transcribed Image Text:Prove the following identities using simplified index notation: (Vu) at b) T V·(y•t)= y·(V• 7² ) + :Vy (where 7 denotes transpose) Dv ὃν Dt where = + = V(v • v) — v × (V×v) Ət D Dt Ə -+v. V is known as the "substantial derivative" operator. Ət Hint: for part (c), it will be easier to work from the right side toward the left.
Expert Solution
Introduction

In this solution, we will derive two important vector identities.

First, we will derive an expression for the divergence of a tensor product of a vector and a second-order tensor.

Second, we will derive an expression for the substantial derivative of a vector, which is a key concept in the study of fluid motion.

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