Question

An ideal fluid is flowing through the given tubes which are placed on a horizontal surface. If the liquid has velocities $V_A$ and $V_B$, and pressure $P_A$ and $P_B$ at points A and B respectively, then the correct relation is (A and B are at the same height from ground level, the figure shown is as if the system is seen from the top):

• A. $V_A=V_B,P_A=P_B$
• B. $V_A>V_B,P_A<P_B$
• C. $V_A>V_B,P_A=P_B$
• D. $V_A<V_B,P_A>P_B$

Answer 1

The correct option is A $V_A=V_B,P_A=P_B$

Applying continuity equation:

$v_A{A}_A=v_B{A}_B,A_A=A_B,\text{So}{v}_B=v_A$

Applying Bernoulli's equation:
$P_A+\rho g{h}_A+\frac{1}{2}\rho v_A^2=P_B+\rho g{h}_B+\frac{1}{2}\rho v_B^2$

Since $v_A=v_B$ and pipes are placed on a horizontal surface $(h_A=h_B)$

$\Rightarrow P_A=P_B$

Hence, Option $\left(C\right)$ is the correct answer.