Water is flowing through a horizontal pipe of irregular cross section . If the pressure at a point where the velocity is `0.2ms^(-1)` is 30 mm Hg , what will be the pressure at a point where the velocity is `1.2ms^(-1)` ? (Density of mercury `=13.6gcm^(-3),g=1000cms^(-2)` , Density of water `=1gcm^(-3))`

Explanation

`v_(1)=0.2m//s=20cm//s`
`v_(2)=1.2m//s=120cm//s`
`h_(1)=30mmHg=3cmHg`
`rho.=13.6gcm^(-3)`
`rho=1gcm^(-3)`
`g=1000cm//s^(2)`
`h_(2)=?`
For horizontal pipe `y_(1)=y_(2)`, using Bernoulli.s equation,
`P_(1)+(1)/(2)rhov_(1)^(2)=P_(2)+(1)/(2)rhov_(2)^(2)`
`P_(2)=P_(1)+(1)/(2)rho(v_(1)^(2)-v_(2)^(2))`
`=h_(1)rho.g+(1)/(2)rho(v_(1)^(2)-v_(2)^(2))`
`=30xx10^(-1)xx13.6xx10^(3)+(1)/(2)xx1(20^(2)-120^(2))`
`=40.8xx10^(3)-140xx50`
`40.8xx10^(3)-7xx10^(3)`
`P_(2)=33.8xx10^(3)dyn//cm^(2)`
`h_(2)=(P_(2))/(rhog)=(33.8xx10^(3))/(13.6xx10^(3))`
`thereforeh_(2)=2.485cm-Hg`