Water flowing steadily through a horizontal pipe of non-unifrom cross-section. If the pressure of water is `4xx10^(4)N//m^(2)` at a point where cross-section is `0.02 m^(2)` and velocity of flow is `2 ms^(-1)` . The pressure at a point where cross-section reduces to `0.01 m^(2)` is `3.4xx10^(n)` Pa. What is the value of n ?

Answer

4

Explanation

Here, `a_(1) =0.02 m^(2), a_(2) =0.01 m^(2)`,
`v_(1) =2 ms^(-1), v_(2)= ?`
From Bernoullis theorem for horizontal flow
`P_(1) +(1)/(2)rho v_(1)^(2) = P_(2) +(1)/(2)rho v_(2)^(2)`
or `P_(2) = P_(1) + (1)/(2)rho 9v_(1)^(2) - v_(2)^(2)`
`=4xx10^(4) + (1)/(2)xx10^(3) (2^(2) - 4^(2))`
`=3.4xx10^(4)` Pa
`=3.4xx10^(n)` Pa (Given)
`:. n=4`