Question

Pressure of liquid inside a vessel depends on?

Hint:

Remember Pascal's principle and the hydrostatic paradox: The shape of the container does not matter at all. The pressure at the bottom of a wide bucket is identical to the pressure at the bottom of a thin capillary tube if they hold the same liquid at the exact same depth.

Answer 1

Step 1: Understanding the Concept:
The pressure exerted by a static fluid inside a container is known as hydrostatic pressure. It is caused by the weight of the fluid column above the point of measurement.
Step 2: Key Formula or Approach:
The fundamental formula for hydrostatic pressure at a depth inside a liquid is:
\[ P = P_0 + \rho g h \]
Where:
\(P\) = Total pressure at depth \(h\)
\(P_0\) = Atmospheric pressure at the surface
\(\rho\) = Density of the liquid
\(g\) = Acceleration due to gravity
\(h\) = Depth below the free surface of the liquid
The term "\(\rho g h\)" is the gauge pressure contributed by the liquid itself.
Step 3: Detailed Explanation:
Looking at the terms in the formula \(\rho g h\), we can identify what factors influence the liquid pressure:
1. Depth (\(h\)): Pressure increases linearly with the depth from the free surface. Deeper points experience higher pressure due to a taller column of liquid above them.
2. Density of liquid (\(\rho\)): Denser liquids are heavier per unit volume, so they exert more pressure at the same depth compared to less dense liquids.
3. Acceleration due to gravity (\(g\)): The gravitational pull creates the weight of the fluid. A stronger gravitational field leads to higher pressure.
Crucially, it does NOT depend on:
- The shape of the vessel.
- The total volume or amount of liquid in the vessel.
- The cross-sectional area of the vessel.
This independence from shape is known as the Hydrostatic Paradox.
Step 4: Final Answer:
The pressure of a liquid inside a vessel depends on the depth, the density of the liquid, and acceleration due to gravity.