Water flows through a vertical tube of varible cross-section. The area of cross-section at A and B 6 and 3 `mm^(2)` respectively. If 12c c of water enters per second through A, find the pressure difference `P_(A)-P_(B).(g=10 m//s^(2))`. The separation between the cross-section at A and B is 100 cm.

Options

A. `1.6xx10^(5) dyn e//cm^(2)`
B. `2.29xx10^(5) dyn e//cm^(2)`
C. `5.9xx10^(5) dyn e//cm^(2)`
D. `3.9xx10^(5) dyn e//cm^(2)`

Answer

A

Explanation

`P_(A) - P_(B) =g(h_(2)-h_(1))rho +(1)/(2)rho (v_(2)^(2) - v_(1)^(2))`
Volume of liquid flowing per second through A,
`A_(1)v_(1) =12 cm^(3)//s`
or `v_(1) =(12)/(A_(1)) =(12cm^(3)//s)/(6xx10^(-2)cm^(2)) =200 cm//s`
From equation of continuity,
`A_(1)v_(1) =A_(2)v_(2)`
or `v_(2)=(A_(1)v_(1))/(A_(2)) =(12cm^(3)//s)/(3xx10^(-2)cm^(2)) =400 cm//s`.
`h_(2)-h_(1) =100 cm`
`:. P_(A) - P_(B) =1000xx100xx1 + (1)/(2)xx1xx[(400)^(2) - (200)^(2)]`
`=10^(5) +(1)/(2)xx12xx10^(4)`
`=1.6xx10^(5) dyn e//cm^(2)`