The reading of pressure meter attached with a closed pipe is `5 xx 10^(5) Nm^(-2)`. On opening the valve of the pipe, the reading of the pressure meter is `4.5 xx 10^(5) Nm^(-2)`. Calculate the speed of the water flowing in the pipe.

Explanation

Initial pressure `P_(2)=5xx10^(5)Nm^(-2)`
Final pressure `P_(1)=4.5xx10^(5)Nm^(-2)`
Initial velocity `v_(1)=0`
Final velocity `v_(2)=v_(2)`
Density of water `rho=10^(3)kg//m^(3)` Using Bernoulli's theorem, we can write,
`P_(2)+(1)/(2)rhov_(2)^(2)=P_(1)+(1)/(2)rhov_(1)^(2)`
`5xx10^(5)+(1)/(2)xx10^(3)xxv_(2)^(2)=4.5xx10^(5)+(1)/(2)xx10^(3)xxv_(2)^(2)`
`5xx10^(5)-4.5xx10^(5)=(1)/(2)xx10^(3)xxv_(2)^(2)`
`0.5xx10^(5)=(1)/(2)xx10^(3)xxv_(2)^(2)`
`5xx10^(4)=(10^(3)v_(2)^(2))/(2)`
`10^(3)v_(2)^(2)=10xx10^(4)=10^(5)`
`v_(2)^(2)=(10^5)/(10^3)=10^(2)`
`thereforev_(2)=sqrt(10^2)=10ms^(-1)`
Speed of water `=10ms^(-1)`