Two tubes A and B of length 80 cm and 40 cm have radii 0.1 mm and 0.2 mm respectively are connected in series end to end. If a liquid passing through tow tubes is entering A at a pressure of 82 cm of mercury and leaving B at a pressure of 76 cm of mercury. Find the pressure at the junction of A and B.

Answer

76.18 cm of Hg

Explanation

Let `P_(j)` (in cm of Hg) be the pressure at the junction of A and B.
For of flow of liquid through tube A,
`Q_(1)=(pi(P_(A)-P_(j))r_(1)^(4))/(8 eta l_(1))=(pi(82-P_(j))(0.01)^(4))/(8 etaxx80)`
For tube `B:l_(2)=40 cm, r_(2)=0.02 cm`,
Pressure at which liquid leaves tube B,
`P_(B)=76` cm of Hg
Rate of flow of liquid through tube B
`Q_(2)=(pi(P_(j0-P_(B))r_(2)^(4))/(8 eta l)=(pi(P_(j)-76)(0.02)^(4))/(8 etaxx40))`
Here,
`:. (pi(82-P_(j))xx(0.01)^(4))/(8 etaxx80) =(pi(P_(j)-76)(0.02)^(4))/(8 etaxx40)`
or `(82-P_(j))=(P_(j)-76)xx32`
On solving, `P_(j)=76.18` cm of Hg