Q. Three capillaries of length $L,\ \ L/2\ and\ L/3\ $ are connected in series. Their radii are $r,\ r/2\ \ and\ r/3$ respectively. Then, if stream-line flow is to be maintained and the pressure across first capillary is $p$, then the
A) pressure difference across the end of second capillary is 8$p$
B) pressure difference across the third capillary is 43$p$
C) pressure difference across the end of second capillary is 16$p$
D) pressure difference across the third capillary is 56$p$
Explanation
(a) Rate of flow of liquid is given by
$\frac{dQ}{dt} = \frac{\pi pr^{4}}{8ɳL}$
$As\ capillaries\ are\ joined\ in\ series\ ,\ so\ \left( \frac{dQ}{dt} \right)\ $
$\ \ \ \ will\ be\ same\ for\ each\ capillary.$
$Hence,\ \frac{{\pi\ pr}^{4}}{8ɳL} = \frac{\pi\ p^{'}(r/2)^{4}}{8ɳ\left( \frac{L}{2} \right)} = \frac{\pi\ p^{'}(r/3)^{4}}{8ɳ\left( \frac{L}{3} \right)}$
So, pressure difference across the ends of 2nd capillary
$\ \ p^{'} = 8p$
and across the ends of 3rd capillary
$\ \ p^{'} = 27p$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.