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))

Water is flowing through a horizontal pipe of irregular cross section

1.	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))
Answer» SOLUTION :`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`