Design Theory of Fluidic Components by Joseph M. Kirshner

By Joseph M. Kirshner

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I n t h i s c a s e t h e f o r c e a c t i n g o n t h e s p r i n g is A p d(p — Pi) i n s t e a d o f A 2 p dp a n d w e define t h e c a p a c i t a n c e a c r o s s t h e p i s t o n d u e t o c o m p l i a n c e a s c _ \qdt A i 2 = j-j. 61) s T h e c o m p r e s s i b i l i t y c a p a c i t a n c e a s s o c i a t e d w i t h e a c h s i d e o f t h e p i s t o n is as before [qdt 1 = J Φι V_ "Pi' j g d t c V = \dp 2 np 2 2 T h e e q u i v a l e n t c i r c u i t is s h o w n in F i g .

F o r e x a m p l e , a l o n g c y l i n d e r ( F i g . 2. 2. 48 2 Passive Components Fig. 30 Polytropic e x p o n e n t for sin­ usoidal signals in air-filled cylindrical e n ­ closures. Fig. 31 Polytropic e x p o n e n t for sin­ usoidal signals in air-filled spherical e n ­ closures. 9 Capacitance 49 Fig. 32 Polytropic exponent for sin­ usoidal signals in air-filled narrow b o x enclosures. 59b) shows the relation between capacitance a n d polytropic e x p o n e n t . S i n c e t h e p o l y t r o p i c e x p o n e n t [ E q .

34) T h e s u b s t i t u t i o n o f E q s . 34) i n t o E q . 35) Since u ri is m u c h s m a l l e r t h a n u ei we m a y select t h e r e f e r e n c e v e l o c i t y U = u ei a n d t h u s E q . 36) F r o m E q s . 37) i n d i c a t e s t h a t w e c a n a c h i e v e l a r g e r e v e r s e flow coefficients by simply m a k i n g the radius ratio large. H o w e v e r , because of viscosity t h e loss coefficients will b e m u c h less t h a n p r e d i c t e d b y E q . ( 2 . 3 7 ) . I n t h e f o r w a r d flow d i r e c t i o n t h e loss coefficient is e s s e n t i a l l y t h e r e s u l t o f t w o s u d d e n e n l a r g e m e n t s .

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