Question

Figure shows an ideal fluid flowing through a uniform cross-sectional tube in the vertical tube with liquid velocities $v_A$ and $v_B$ and pressure $P_A$ and $P_B$. Knowing that tube offers no resistance to fluid flow then which of the following is true?

• A. $P_A>P_B$
  
• B. $P_A=P_B$
  
• C. $P_A<P_B$
  
• D. None

Answer 1

The correct option is C $P_A<P_B$


For a streamline flow of an ideal liquid in uniform cross-section tube,
$v_A=v_B$

According to Bernoulli’s principle,
Total head at $A=$ total head at $B$

$\frac{P_A}{\rho g}+\frac{v_{A^2}}{2g}+h=\frac{P_B}{\rho g}+\frac{v_{B^2}}{2g}+0$

$P_B-P_A=\rho gh$

$\Rightarrow P_A<P_B$

Therefore, $P_A<P_B$
Final Answer: $\left(b\right)$