Question

Figure 4.220 shown a container filled with a liquid of density $\rho$. Four point $A$, $B$, $C$ and $D$ lie on the vertical of a vertical square. Point $A$ and $C$ lie on a vertical line and point $B$ and $D$ lies on a horizontal line. Choose the correct statement(s) about the pressure at the four points.

• A. $P_D=P_B$
• B. $P_A<P_B=P_D<P_c$
• C. $P_D=P_B=\frac{P_c-P_A}{2}$
• D. $P_D=P_B=\frac{P_c+P_A}{2}$

Answer 1

Answer: (A), (B), (D)

The correct options are
A $P_D=P_B$
B $P_A<P_B=P_D<P_c$
D $P_D=P_B=\frac{P_c+P_A}{2}$

The pressure of the point will depend on its depth. If a point is at 'h' depth under water then the pressure at that point will be $P_0+\rho gh$

${}_B=h_0\Rightarrow P_D=P_B$ option A

$h_C>h_A\Rightarrow P_C>P_A{h}_B=h_D>h_A\Rightarrow P_B=P_D>P_A{h}_B=h_D<h_C\Rightarrow P_B=P_D<P_C$

$\frac{P_A+P_C}{2}=\frac{P_D+\rho gh+P_0+\rho g(h+l\sqrt{2})}{2}=P_0+\rho gh+\frac{\rho gl}{\sqrt{2}}{P}_B=P_D=P_D+\rho g(h+l/sqrt2)=P_D+\rho gh+3g\frac{l}{\sqrt{2}}\Rightarrow P_B=P_D=\frac{P_A+P_C}{2}$

Option D