A Treatise on the Mathematical Theory of the Motion of FluidsThe University Press, 1879 - Broj stranica: 258 |
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Stranica 4
... dx dt + udt + dF dy vdt + wdt . dF dz OF pressed by F + Ət Since the new value of F for the moving particle is also ex- dt , we have OF dF dF = + u dF dF + v + w Ət dt dx dy dz .. ( 1 ) . 6. Let p be the pressure , p the density , X , Y ...
... dx dt + udt + dF dy vdt + wdt . dF dz OF pressed by F + Ət Since the new value of F for the moving particle is also ex- dt , we have OF dF dF = + u dF dF + v + w Ət dt dx dy dz .. ( 1 ) . 6. Let p be the pressure , p the density , X , Y ...
Stranica 5
... dx dy dz dv dv dv dt and , in like manner , dv + u dt dx dw dw dw dw + u dt dx dy dz + v + w dy dz Y. 1 dp 11 - P dx ' = y_1 dp p dy + v · + w⋅ = Z 1 dp - P dz .. ( 2 ) . 7. We have thus three equations connecting the five unknown ...
... dx dy dz dv dv dv dt and , in like manner , dv + u dt dx dw dw dw dw + u dt dx dy dz + v + w dy dz Y. 1 dp 11 - P dx ' = y_1 dp p dy + v · + w⋅ = Z 1 dp - P dz .. ( 2 ) . 7. We have thus three equations connecting the five unknown ...
Stranica 6
... d.x du ( u ( + 4d dx ) dydz , and - ( - 4d dx ) dydz , du dx which give together dxdydz . Calculating in the same way dx the parts due to the other faces , we find av du dv dw = at ( dx + dy + du ) dxdydz . dz Since we have also V ...
... d.x du ( u ( + 4d dx ) dydz , and - ( - 4d dx ) dydz , du dx which give together dxdydz . Calculating in the same way dx the parts due to the other faces , we find av du dv dw = at ( dx + dy + du ) dxdydz . dz Since we have also V ...
Stranica 7
... dx dy dz or , if l , m , n be the direction - cosines of the normal to the surface , = lu + mv + nw = 0 ... dx dF +21 dy dF and dt + Uq dx + V2 dy dF + w1 dz dF + wz dz = = 0 , 0 , where the suffixes are used to distinguish the two sides ...
... dx dy dz or , if l , m , n be the direction - cosines of the normal to the surface , = lu + mv + nw = 0 ... dx dF +21 dy dF and dt + Uq dx + V2 dy dF + w1 dz dF + wz dz = = 0 , 0 , where the suffixes are used to distinguish the two sides ...
Stranica 9
... dx the amount which leaves the region in the same time by the oppos- d . ite face is ( Qu + dx ) dy dz . The two faces together give a gain of - d . Qu dx dx dy dz per unit time . Calculating in the same way the effect of the flow ...
... dx the amount which leaves the region in the same time by the oppos- d . ite face is ( Qu + dx ) dy dz . The two faces together give a gain of - d . Qu dx dx dy dz per unit time . Calculating in the same way the effect of the flow ...
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angle angular velocity Ave Maria Lane axes axis C. J. CLAY Cambridge University Press centre Christ's College circle circuit CLAY & SONS co-ordinates constant corresponding Crown 8vo curves const cyclic Demy 8vo denote direction dt dt dx dx dx dy dz dy dy Edited element equation of continuity Fellow finite fluid forces formulæ given Green's Theorem Hence impulse infinitely small infinity integral internal boundary irrotational irrotational motion J. E. SANDYS liquid LL.D mass moving Notes obtain origin P. G. TAIT P₁ parallel particle plane xy portion pressure Professor quantities radius RENDEL HARRIS satisfied shews simply-connected solid sphere St John's College stream-lines surface theorem Thomson Trinity College University of Cambridge University Press Warehouse velocity-potential vertical vortex waves zero аф
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