Air Pollution by R. S. Scorer and R. S. Scorer (Auth.)

By R. S. Scorer and R. S. Scorer (Auth.)

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T h i s m e a n s that the r a t e o f c h a n g e o f the p l u m e w i d t h , r, is p r o p o r t i o n a l to r~^', a n d so rat^ (6) w h e r e / is the t i m e f r o m release i n t o the air. S i n c e the h o r i z o n t a l t r a v e l is m o r e o r less w i t h the w i n d , U, the distance χ d o w n w i n d is g i v e n b y x = Ut (7) raxi (8) a n d so AIR 30 POLLUTION I n c a l c u l a t i n g this k i n d o f diffusion ( c a l l e d F i c k i a n ) the p l u m e w i d t h has t o b e d e f i n e d b y the c o n t o u r c o n t a i n i n g , say, 9 0 % o f the m a t e r i a l in a n y section transverse t o the w i n d , o r the c o n t o u r o n w h i c h the c o n c e n t r a t i o n is, say, 5 % o f the m a x i m u m .

T h e b u o y a n c y p e r unit l e n g t h o f p l u m e is p r o p o r t i o n a l to i / - ^ , a n d i f ( ¿ is the q u a n t i t y o f b u o y a n c y ( i . e . v o l u m e X fractional absolute temperature excess) e m i t t e d in unit time, a more c o m p l e t e version o f the second o f e q u a t i o n s ( 2 0 ) is w h e r e g is g r a v i t y . T h e p l u m e w i l l rise n o further but will be passively diffused w h e n w has decreased t o a c e r t a i n m u l t i p l e o f the v e l o c i t y o f the e n v i r o n m e n t a l eddies.

T h e m i x i n g is r a p i d so that the p l u m e v e r y q u i c k l y takes o n the h o r i z o n t a l v e l o c i t y o f the e n v i r o n m e n t . T h u s for the b e n t o v e r p l u m e X, the h o r i z o n t a l distance t r a v e l l e d , is e q u a l t o Ut after D I L U T I O N : F O R M U L A E A N D MECHANISMS 43 t i m e /, w h i l e (22) w h i c h i m p l i e s that Ζ (23) α<2/3αΛ;2/3 F I G . 12. The width of a bent-over hot plume in a neutral turbulencefree environment is proportional to its height above an origin close to the chimney top.

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