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However, many studies concern the motion of a free particle in a turbulent fluid, probably because of the broad application of a turbulent suspension. The Tchen equation is, in reality, a kinetic transport equation with both position and velocity as independent variables besides time. That is, it describes motion in the phase space. Worse still, it is in the range where statistical ergodic hypothesis does not apply. Hence, it was recognized by Lumley (1957) that unless we have a complete knowledge of the relation between Eulerian and Lagrangian correlations of turbulence, we cannot expect to solve this equation with rigor.
P t . 1. T h e C o n c e p t of C a p s u l e P i p e l i n i n g " , The Canadian J. of Chemical Engineering 4 1 , 155-61 ( A p r . 1963). C H A R L E S , M . E . , " T h e Pipeline F l o w of C a p s u l e s . P t . 2. T h e o r e t i c a l A n a l y s i s of t h e C o n c e n t r i c F l o w of Cylindrical F o r m s " , The Canadian J. of Chemical Engineering 4 1 (2), 4 6 - 5 1 ( A p r . 1963). E L L I S , H . , R E D B E R G E R , P . J. a n d B O L T , L . M . , " T r a n s p o r t i n g S o l i d s b y P i p e L i n e : C a p s u l e s a n d S l u g s " , Industrial Engineering Chemistry 5 5 (9), 2 9 - 3 4 (Sept.
P t . 5. A n E x p e r i m e n t a l I n v e s t i g a t i o n of t h e T r a n s p o r t b y W a t e r of Single S p h e r i c a l C a p s u l e s w i t h D e n s i t y G r e a t e r t h a n t h a t of t h e W a t e r " , The Canadian J. of Chemical Engineering 4 2 , 155-61 ( A u g . 1964). N E W T O N , R . , R E D B E R G E R , P . J. a n d R O U N D , G . F . , " T h e P i p e l i n e F l o w of C a p s u l e s . P t . 6. N u m e r i c a l Analysis of S o m e V a r i a b l e D e t e r m i n i n g F r e e F l o w " , Canadian J.
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