The figure shown a pipe of uniform cross-section inclined in a vertical plane. A U-tube manometer is connected between the point A and B. If the liquid of density `rho_(0)` flows with velocity `v_(0)` in the pipe. Then the reading h of the manometer is

Options

A. `h=0`
B. `h=(v_(0)^(2))/(2g)`
C. `h=(rho_0)/(rho)((v_(0)^(2))/(2g))`
D. `h=(rho_(0) H)/(rho-rho_(0))`

Answer

A

Explanation

From continuity equation,
`v_(A)=v_(B)=v_(0)`
`:. p_(A)=rhogh=p_(B)+0`
`:. p_(B)-p_(A)=rhogh` …(i)
Now, let us make pressure equation from manometer.
`p_(A)+rho g (h+H)=rho_(Hg) gh=p_(3)`
Putting `p_(B)-p_(A)=rhogh we get h=0`.