Question

The container shown in FIGURE EX14.11 is filled with oil. It is open to the atmosphere on the left. What is the pressure difference between points 1 and 2? Between points 1 and 3?

Accepted Answer

Step 1: Understand the problem. The container is filled with oil and open to the atmosphere on the left. We need to calculate the pressure difference between points 1 and 2, and between points 1 and 3. The pressure difference in a fluid is determined by the hydrostatic pressure equation, which depends on the depth and density of the fluid. Step 2: Recall the hydrostatic pressure equation: $$ P = P_0 + \rho g h $$, where $$ P  is $$the pressure at a given depth, $$ P_0  is $$the pressure at the surface (atmospheric pressure in this case), $$ \rho  is $$the density of the fluid, $$ g  is $$the acceleration due to gravity, and $$ h  is $$the depth below the surface. Step 3: For the pressure difference between points 1 and 2, identify the vertical distance $$ h_{12} $$ between these two points. The pressure difference $$ \Delta P_{12}  is $$given by $$ \Delta P_{12} = \rho g h_{12} . $$Substitute the values for $$ \rho $$, $$ g $$, and $$ h_{12}  to $$calculate the pressure difference. Step 4: For the pressure difference between points 1 and 3, identify the vertical distance $$ h_{13} $$ between these two points. The pressure difference $$ \Delta P_{13}  is $$given by $$ \Delta P_{13} = \rho g h_{13} . $$Again, substitute the values for $$ \rho $$, $$ g $$, and $$ h_{13}  to $$calculate the pressure difference. Step 5: Note that atmospheric pressure $$ P_0 $$ cancels out when calculating pressure differences, as it is the same at all points exposed to the atmosphere. Focus only on the contribution from the fluid's weight ($$ \rho g h ) to $$determine the pressure differences.

The container shown in FIGURE EX14.11 is filled with oil. It is open to the atmosphere on the left. What is the pressure difference between points 1 and 2? Between points 1 and 3?

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Hydrostatic Pressure

Pascal's Principle

Atmospheric Pressure