There capillaries of length l, `2l` and `l//2` are connected in series. Their radii are r, `r//2` and `r//3` respectively. If stream line flow is maintained and the pressure difference across the first capillary tube is `P_(1)`, find the pressure difference across (i) the second and (ii) the thired capillary tube.

Answer

[`32 P_(1); 40-5P_(1)`]

Explanation

Since the there tube are connected inseries, so the rate of flow of liquid throough all the there tubes is same say V. Let `P_(1), P_(2)` and `P_(3)` be pressure difference across the `1st`, second and third tube respectively.
Then `V=pi P_(1)(r_(1)^(4))/(8eta l_(1))=piP_(2)r_(2)^(4)0/(8eta l_(2))=(pi P_(3)r_(3)^(4))/(8eta l_(3))`
Here, `l_(1)=1, l_(2)=2, l_(3)=l//2,r_(1)=r, r_(2)=r//2, r_(3)=r//3`
so `(P_(1)r^(4))/(l)=(P_(2)((r)/(2))^(4))/(2l)=P_(3)((r)/(3))^(4)0/(l//2)`
or `P_(1)=(P_(2))/(32)=(2P_(3))/(81)` or `P_(2)=32P_(1)`
and `P_(3)=(81)/(2)P_(1)=40.5P_(1)`