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 Bernoulli's equation:
`p_(1)+rho gh_(1)+1/2 rho v_(1)^(2) = P_(2) + rhogh_(2) +1/2 rho v_(2)^(2)`
Since, `v_(1) = v_(2)`, and h_(1) = h_(2)`
`implies P_(1)=P_(2)`.