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Question Number 52787 by peter frank last updated on 13/Jan/19

	Answered by tanmay.chaudhury50@gmail.com last updated on 13/Jan/19

	$f l o w o f f l u i d i n p i p e f o r m u l a$ $\frac{d V}{d t} = \frac{△ p \times π r^{4}}{8 η l} = \frac{△ p}{\frac{8 η l}{π r^{4}}}$ $c o m p a r e i t w i t h f l o w o f c u r r e n t i n r e s i s t a n c e . .$ $h e r e c u r r e n t i \to \frac{d V}{d t}$ $p o t e n t i a l d i f f e r e n c e \to △ p$ $r e s i s t a n c e \to \frac{8 η l}{π r^{4}}$ $s o c a p p i l a r y j o i n e d i n s e r i e s i s e q u i v a l a n t$ $t o r e s i s t a n c e i n s e r i e s c o n n e c t i o n$ $(R_{e q} = R_{1} + R_{2} + R_{3} + . . . R e s i s t a n c e i n s e r i e s)$ $s a m e w a y e q u i v a l a n t v i s c o u s r e s i t a n c e$ $\frac{8 η l_{1}}{π r_{1}^{4}} + \frac{8 η l_{2}}{π r_{2}^{4}} + \frac{8 η l_{3}}{π r_{3}^{4}}$ $n o w u s e f o r m u l a c u r r e n t = \frac{p . d}{r e s i s t a n c e} = \frac{V}{R_{1} + R_{2} + R_{3}} = i$ $s i m i l a r w a y$ $r a t e o f f l o w \frac{d V}{d t} = \frac{△ p}{\frac{8 η l_{1}}{π r_{1}^{4}} + \frac{8 η l_{2}}{π r_{2}^{4} +} + \frac{8 η l_{3}}{π r_{3}^{4}}} = \frac{π △ p}{8 η (\frac{l_{1}}{r_{1}^{4}} + \frac{l_{2}}{r_{2}^{4}} + \frac{l_{3}}{r_{3}^{4}})}$ $s o a n s w e r i s$ $\frac{d V}{d t} = \frac{π p}{8 η (\frac{l_{1}}{r_{1}^{4}} + \frac{l_{2}}{r_{2}^{4}} + \frac{l_{3}}{r_{3}^{4}})} [g i v e n △ p = p]$
	Commented by peter frank last updated on 13/Jan/19

	$t h a n k s$
	Answered by peter frank last updated on 13/Jan/19

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