An ideal liquid is flowing in two pipes, AC is inclined and BD is horizontal. Both the pipes are connected by two vertical tubes of length `h_(1)` and `h_(2)` as shown in the fig. The flow is streamline in both the pipes. if velocity of liquid at A, B and C are `2m//s, 4m//s` and `4m//s` respectively, the velocity at D will be

Options

A. `4m//s`
B. `sqrt(14)m//s`
C. `sqrt(28)m//s`
D. none

Answer

C

Explanation

`P_(A)+(1)/(2)rhoV_(A)^(2)=P_(C)+(1)/(2)rhoV_(C)^(2)+rhog(h_(2)-h_(1))`
`P_(A)-P_(C)=(1)/(2)rho(V_(C)^(2)-V_(A)^(2))+rhog(h_(2)-h_(1))`
`P_(B)+(1)/(2)rhoV_(B)^(2)=P_(D)+(1)/(2)rhoV_(D)^(2)`
`P_(A)+rhogh_(1)+(1)/(2)rhoV_(B)^(2)=P_(C)+rhogh_(2)+(1)/(2)rhoV_(D)^(2)`
`P_(A)+(1)/(2)rhoV_(B)^(2)=P_(C)+rho(h_(2)-h_(1))+(1)/(2)rhoV_(D)^(2)`
`(1)/(2)(V_(C)^(2)-V_(A)^(2))+rhog(h_(2)-h_(1))+(1)/(2)rhoV_(B)^(2)`
`=rhog(h_(2)-h_(1))+(1)/(2)rhoV_(D)^(2)(1)/(2)xx12+(1)/(2)xx12+(1)/(2)xx16=(1)/(2)V_(D)^(2)`,
`V_(D)=sqrt(28)(m)/(s)`