The effect of weak inertia on the emptying of a tube (vol 14, pg 2102, 2002)

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The effect of weak inertia on the emptying of a tube (vol

14, pg 2102, 2002)

Alain de Ryck

To cite this version:

Alain de Ryck. The effect of weak inertia on the emptying of a tube (vol 14, pg 2102, 2002): Erratum. Physics of Fluids, American Institute of Physics, 2002, 14 (7), p. 2102-2108. �10.1063/1.1511732�. �hal-01652386�

Erratum: ‘‘The effect of weak inertia on the emptying of a tube’’

†

Phys. Fluids 14, 2102

„

2002

…‡

Alain de Rycka)

Ecole des Mines d’Albi, Campus Jarlard, route de Teillet, F-81000 Albi Cedex 09, France

The original manuscript contained errors requiring the following changes to six of the equations. There is a term lacking in Eq.共26兲, and the coefficients in Eq. 共27兲 and 共28兲 have to be corrected. In Eqs.共1兲, 共13兲 and 共22兲, there is a mix with previous coordinates.

共1兲 In Eq. 共1兲 r should be replaced by y and the second ⫹ in the left member replaced by⫺ to give

␩

再

⳵ 2_u ⳵x2⫹ ⳵2_u ⳵y2⫺ 1 r⫺y ⳵u ⳵y

冎

⫽ ⳵p ⳵x⫹␳

冉

␯ ⳵u ⳵y⫹u ⳵u ⳵x

冊

. 共2兲 Equation 共13兲 should be Q⫽

冕

0 h 2␲共r⫺y兲udy⫽

冕

0 e 2␲共r⫺y兲Vdy.

共3兲 In Eq. 共22兲, h should be replaced by (r⫺h) to give

ps⫽⫺␥c⫺2␩ ⳵u0

⳵x

冏

_s⫺2␩ uos

r⫺hhx.

共4兲 In Eq. 共26兲, w should be replaced by u and it lacks a term in the left member. Eq.共26兲 now writes

␩

再

⳵ 2_u 0 ⳵x2 ⫹ ⳵2_u ⳵y2⫺ 1 r⫺y ⳵u ⳵y

冎

⫽ ⳵p ⳵x⫹␳

冉

␯0 ⳵uo ⳵y ⫹uo ⳵uo ⳵x

冊

.

共5兲 In Eq. 共27兲, some numerical coefficients in the second term of the right hand side are wrong. It should be

Cx⫽3 1⫺Y Y3

冉

1⫹E Y⫺1 2

冊

⫹3 Ca2/3 Y3 ⫻

再

YXXY

冋

33⫺7Y 20 ⫹E ⫺99⫹150Y⫺31Y2 120

册

⫹YX 2

冋

⫺31⫺2Y 10 ⫹E 31⫺19Y⫺2Y2 20

册冎

⫹ 1 35FECa 4/3YX Y3

冋

6共⫺9⫹Y⫹Y 2_兲 ⫹E1728⫺1131Y⫺171Y 2_⫹134Y3 32

册

.

共6兲 In Eq. 共28兲, two coefficients are wrong. It should be

s3⫹ E 2 Ca2/3 s 共1⫺E兲2⫹3⫺Ca2/3s2

冉

39 10⫹ E 2

冊

⫹FECa4/3_s

冉

6 5⫺ E 2

冊

⫽0.

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