Question

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 pressures $P_A$ and $P_B$ at points $A$ and $B$ respectively, then the correct relation is:
(The figure shown below 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 C $v_A=v_B,P_A=P_B$

Applying continuity equation:
$v_A{A}_A=v_B{A}_B$
$A_A=A_B$, 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 $(h_A=h_B)$
$\Rightarrow P_A=P_B$