Question

In the given figure there are three points $\text{A, B,}$ and $\text{C}$ having pressure ${\text{P}}_{\text{A}},{\text{P}}_{\text{B}}$, and ${\text{P}}_{\text{C}}$ respectively. Identify the correct option:

• A. ${\text{P}}_{\text{A}}={\text{P}}_{\text{B}}={\text{P}}_{\text{C}}$
• B. ${\text{P}}_{\text{B}}-{\text{P}}_{\text{A}}={\text{P}}_{\text{C}}-{\text{P}}_{\text{A}}$
• C. ${\text{P}}_{\text{A}}>{\text{P}}_{\text{B}}>{\text{P}}_{\text{C}}$
• D. ${\text{P}}_{\text{A}}={\text{P}}_{\text{B}}+{\text{P}}_{\text{C}}$

Answer 1

The correct option is B ${\text{P}}_{\text{B}}-{\text{P}}_{\text{A}}={\text{P}}_{\text{C}}-{\text{P}}_{\text{A}}$

In the given figure, the points $\text{B}$ and $\text{C}$ are at the same height, so, ${\text{P}}_{\text{B}}={\text{P}}_{\text{C}}\to \left(1\right)$
The pressure difference between the points $\text{A}$ and $\text{B}$ = ${\text{P}}_{\text{B}}-{\text{P}}_{\text{A}}\to \left(2\right)$
Comparing $\left(1\right)$ and $\left(2\right)$, we get
${\text{P}}_{\text{B}}-{\text{P}}_{\text{A}}={\text{P}}_{\text{C}}-{\text{P}}_{\text{A}}$