Journal of the Franklin Institute, Volume 80; Volume 110Franklin Institute, 1880 Vols. 1-69 include more or less complete patent reports of the U. S. Patent Office for years 1825-1859. cf. Index to v. 1-120 of the Journal, p. [415] |
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Results 1-5 of 9
Page 218
... dy dz = ( 2 ) expressing the continuity of the fluid . On account of the viscosity of the fluid the motion will be ... ( dy - de ) , dz du δι η 12 dz dv dx ¿ = } ( d 4 ( dedu ) dy ( 3 ) The following relations , which are readily ...
... dy dz = ( 2 ) expressing the continuity of the fluid . On account of the viscosity of the fluid the motion will be ... ( dy - de ) , dz du δι η 12 dz dv dx ¿ = } ( d 4 ( dedu ) dy ( 3 ) The following relations , which are readily ...
Page 220
... dy p dy ρ dw d ( V + q ) 1 dp + + + 2 ( 15 — un ) = Pw . dt dz ρ dz p ( 12 ) In the case of steady motion the first term in the left hand member of each of these equations vanishes , and for this case we have as the differential ...
... dy p dy ρ dw d ( V + q ) 1 dp + + + 2 ( 15 — un ) = Pw . dt dz ρ dz p ( 12 ) In the case of steady motion the first term in the left hand member of each of these equations vanishes , and for this case we have as the differential ...
Page 221
... dy + 42 w . dz shall be an exact differential are obviously ξ 42 = 0 , 42 n = 0 , 12 C = 0 . ( 17 ) These conditions may also be arrived in a different way from equa- tions ( 14 ) ; the quantity ( wŋ — v¿ ) dx + ( u ? —wɔ̃ ) dy + ( v3 — uŋ ) ...
... dy + 42 w . dz shall be an exact differential are obviously ξ 42 = 0 , 42 n = 0 , 12 C = 0 . ( 17 ) These conditions may also be arrived in a different way from equa- tions ( 14 ) ; the quantity ( wŋ — v¿ ) dx + ( u ? —wɔ̃ ) dy + ( v3 — uŋ ) ...
Page 222
... dy + 42 w . dz ) = 0 . - ( 20 ) In this general case the quantities in parentheses in the left hand members of equations ( 13 ) are not the first differential coefficients of a function x , y , z , but in equations ( 14 ) we may write ...
... dy + 42 w . dz ) = 0 . - ( 20 ) In this general case the quantities in parentheses in the left hand members of equations ( 13 ) are not the first differential coefficients of a function x , y , z , but in equations ( 14 ) we may write ...
Page 223
... dy dP ― 2A = k42u 2Bk4v 2C = k42w — dz And from these we have 42P = 2 dx dA dB dC + + dy dz ( 27 ) ( 28 ) It is easy to see that an equation of precisely the same form will hold in the case where the motion is not supposed to be steady ...
... dy dP ― 2A = k42u 2Bk4v 2C = k42w — dz And from these we have 42P = 2 dx dA dB dC + + dy dz ( 27 ) ( 28 ) It is easy to see that an equation of precisely the same form will hold in the case where the motion is not supposed to be steady ...
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