An ideal fluid is flowing through the given tubes which is placed on a horizontal surface. If the liquid has velocities `V_(A)` and `V_(B)` and pressure `P_(A)` and `P_(B)` at point `A` and `B` respectively, then the correct relation is (`A` and `B` are at same height from ground level. the figure shown is as in the system is seen from the top):

Options

A. `V_(A) gt V_(B), P_(A) lt P_(B)`
B. `V_(A) lt V_(B), P_(A) gt P_(B)`
C. `V_(A) = V_(B), P_(A) = P_(B)`
D. `V_(A) gt V_(B), P_(A) = P_(B)`

Answer

C

Explanation

Applying continuity equation :
`V_(1)A_(1)=V_(2)A_(2)`
`A_(1)=A_(2)` so `V_(1)=V_(2)`
Applying bernaulli's equation :
`P +rho gh_(1)+1//2 rho v_(1)^(2) = P_(2)+ rho gh_(2)+1//2 rhov_(2)^(2)`
since `V_(1)=V_(2)`, and `h_(1)=h_(2) rArr P_(1)=P_(2)`