Fluid Properties: Pressure

Definition

Pressure is defined as the physical force exerted on an object or a surface per unit area. In the context of fluid mechanics, it represents the normal force exerted by a fluid (liquid or gas) at rest per unit area of the surface in contact with the fluid.

Main Content

1. Pascal’s Law

• Pascal’s Law states that a change in pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and to the walls of the container.
• This principle explains why pressure acts equally in all directions at a specific point within a static fluid.

2. Hydrostatic Pressure

• Hydrostatic pressure is the pressure exerted by a fluid at equilibrium at a given point within the fluid, due to the force of gravity.
• It increases in direct proportion to the depth of the fluid because of the increasing weight of the fluid column above the point.
• The formula is $P = \rho gh$, where $\rho$ is fluid density, $g$ is gravity, and $h$ is depth.

3. Absolute vs. Gauge Pressure

• Gauge pressure is the pressure measured relative to the ambient atmospheric pressure.
• Absolute pressure is the total pressure exerted by the fluid, calculated as the sum of gauge pressure and atmospheric pressure ($P_{abs} = P_{gauge} + P_{atm}$).

       Atmosphere (Patm)
      ___________________
      |                 |
      |     Fluid       |  h (depth)
      |    (Density ρ)  |
      |        * Point  |
      |_________________|

Working / Process

1. Determining Pressure at a Point

• Identify the density ($\rho$) of the fluid and the gravitational constant ($g \approx 9.81 m/s^2$).
• Measure the vertical distance ($h$) from the free surface of the liquid to the point of interest.

2. Applying the Hydrostatic Formula

• Multiply the three variables (density, gravity, and depth) together to calculate the pressure exerted by the fluid column.
• Ensure all units are in SI standard (kg/m³, m/s², and meters) to obtain the result in Pascals (Pa).

3. Accounting for Atmospheric Effects

• If the container is open to the air, add the atmospheric pressure (approximately 101,325 Pa) to your calculated hydrostatic pressure to find the absolute pressure.
• If the container is sealed, the pressure will be dictated solely by the fluid and the pressure of the gas trapped above it.

Advantages / Applications

• Hydraulic Systems: Used in braking systems and heavy machinery lifts where Pascal's Law allows small forces to create massive output forces.
• Engineering Design: Essential for calculating the structural integrity of dams, tanks, and submarine hulls against water pressure.
• Meteorology: Measurement of atmospheric pressure variations helps in predicting weather patterns and storm fronts.

Summary

Fluid pressure is the manifestation of force distributed over an area, governed by gravity and depth in static conditions. It is a fundamental concept in engineering that dictates how fluids interact with structures and how mechanical energy is transferred in hydraulic systems.

Key terms to remember: Pascal (unit of pressure), Hydrostatic, Density, Gauge Pressure, and Atmospheric Pressure.