Download PDF by Dennis Garvie: Higher Chemistry

By Dennis Garvie

ISBN-10: 0199140529

ISBN-13: 9780199140527

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The absence of vortex tubes. Such motion is called irrotational and is characterized by the equation rot V = 0 in the whole region of flow. § 9. Rate of Strain Tensor Let us turn now to the second component of the motion of an infinitesimal volume of fluid — its distorting motion. zy Sr SyZ\ £, (32) where the values of the separate quantities composing the table are given by the system of equations (18). The physical quantities, whose coordinate representation in three-dimensional space requires nine values, are known as the components of a tensor of the second rank.

The position of the particles of fluid at time t is given by expressing their Cartesian coordinates as functions of the quantities t, a, b, c, which are called the Lagrange variables: % = fi (*; #o> y*> so) = Ψι (*; a> & > c ) > \ y = h (*; #o> y<» ^o) =

Substituting these expressions in ( 11) and collecting like terms, we get . 1 (du dw\ , . 1 (dv . \ (dv 1 (du . dw\ . . du\ . v , du Λ , 1 f9w> 9tA , >, } ( 13 ) . , 1 /-9w 1 (dw + τΐ9ΐ + % ν 3 - ^ · , 9ή 9/Λ . / v \ i Vdz)o + [%\ 1 (du , , dw\ , 1 (Qu> 1 Q»\ 1 x , (z- The first lines of the right-hand sides of these equations can be regarded as velocity components in a motion of the fluid as a sohd body V = u0 + co y (Z — Zo) — <*>z{y — Vo)> ) ω (χ^qs = v0 + 2 Wtqs = w0 + ox{y- - * o ) - - ω χ (z -- 2 o ) .

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Higher Chemistry by Dennis Garvie

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