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

`76.12`

Explanation

Length of tube A, `l_(A) = 100 cm`
Radius of tube A, ` r_(A) = 0.1 ` m m = 0.01 cm
Pressure at which liquid enters tube A
`p_(A) = 80 ` cm of Hg
Let pressure at the junction of A and B = p
Rate of flow through tube A
`Q_(A) = (pi (p_(A) - p_(J)) r_(A)^(4))/( 8 eta l_(A)) = (pi (80 - p_(J)) (0.01)^(4))/(8 eta xx 100 ) cm^(3) s^(-1)`
Length of tube B, `l_(B) = 50 cm`
Radius of tube B, `r_(B)` = 0.2 m m = 0.02 cm
Pressure at which liquid leaves tube B
`p_(B) = 76 cm` of Hg
Rate of flow through tube B
`Q_(B) = (pi (p_(J) - p_(B)) r_(B)^(4))/( 8 eta l_(B)) = (pi (p_(J) - 76 ) (0.02)^(4))/( 8 eta xx 50) cm ^(3) s^(-1)`
But `Q_(A) = Q_(B)`
`:. ( pi (80 - p_(J)) (0.01)^(4))/(8 eta xx 100) = (pi ( p_(j) - 76 0.02)^(4))/( 8 eta xx 50)`
or` (80 - p_(J))(0.01)^(4) = 2 (p_(J) - 76 ) (0.02) ^(4)`
or `80 - p_(J) = 32 (p_(J) - 76 ) or = 76 .12 ` cm of Hg