A liquid flows through two capillary tubes A and B connected in series. The length and radius of B are twice that of A. What is the ratio of the pressure difference across A to that across B ?

Answer

8

Explanation

Ac cording to poiseuille's formula, the rate of flow of liquid through a capillary tube is,
`V=(pi P r^(4))/(8 eta l)`
When tubes are connected in series, the rate of flow of liquid through them is the same. Therefore,
`V_(A) = V_(B)` or `(pi P_(A) r_(A)^(4))/(8 eta l_(A)) = (pi P_(B) r_(B)^(4))/(8 eta l_(B))`
`:. (P_(A))/(P_(B)) =((r_(B))/(r_(A)))^(4) ((l_(A))/(l_(B)))^(4) xx((l_(A))/(2l_(A)))` `=16xx(1)/(2) =8`