Course article ad
Fluids
Pressure
Definition
Pressure is the magnitude of the normal force applied perpendicular to the surface of an object per unit area over which that force is distributed.
---
### Detail
Pressure is a scalar quantity, meaning it has a magnitude but no specific direction. In fluid mechanics, pressure at a specific point acts uniformly in all directions. In solid mechanics, pressure is fundamentally tied to normal stress. While they share the same units, pressure typically refers to external forces acting on a surface, whereas stress refers to the internal distribution of forces within a continuous material.
When conducting analyses or taking real-world measurements, it is vital to distinguish between three primary reference states:
Absolute Pressure: The total pressure measured relative to a perfect, absolute vacuum.
Gauge Pressure: The pressure measured relative to the local ambient atmospheric pressure. This is what most common pressure gauges (like a tire pump gauge) read.
Atmospheric Pressure: The baseline pressure exerted by the weight of Earth's atmosphere, which is roughly 101325 Pa at sea level.
Formulas
The fundamental equation for determining pressure is:
$$P = \frac{F}{A}$$
Where:
$P$ is the pressure, typically measured in Pascals (Pa) or N/m².
$F$ is the magnitude of the normal force in Newtons (N).
$A$ is the contact area in square meters (m²).
To calculate the hydrostatic pressure exerted by a fluid column at rest:
$$P = \rho g h$$
Where:
$\rho$ is the density of the fluid (kg/m³).
$g$ is the acceleration due to gravity (m/s²).
$h$ is the depth or height of the fluid column (m).
To convert between reference states:
$$P_{abs} = P_{gauge} + P_{atm}$$
Examples
Mechanical Simulation: When setting up a finite element analysis (FEA) to evaluate the structural integrity of a pressurized pipe network, defining the exact internal surface pressure is required to observe the resulting hoop stresses and predict whether the material will yield under continuous operation.
Everyday Physics: A kitchen knife easily slices through a solid vegetable. Because the edge of the blade has a microscopic surface area, even a minor force applied by a human hand generates a massive localized pressure that overcomes the structural bonds of the vegetable.
Fluid Mechanics: A submarine descending into the ocean experiences an increase in hydrostatic pressure of approximately 1 atm for every 10 meters of depth. The hull must be engineered as a complex pressure vessel to resist these extreme compressive forces and prevent collapse.
Pressure is the magnitude of the normal force applied perpendicular to the surface of an object per unit area over which that force is distributed.
---
### Detail
Pressure is a scalar quantity, meaning it has a magnitude but no specific direction. In fluid mechanics, pressure at a specific point acts uniformly in all directions. In solid mechanics, pressure is fundamentally tied to normal stress. While they share the same units, pressure typically refers to external forces acting on a surface, whereas stress refers to the internal distribution of forces within a continuous material.
When conducting analyses or taking real-world measurements, it is vital to distinguish between three primary reference states:
Absolute Pressure: The total pressure measured relative to a perfect, absolute vacuum.
Gauge Pressure: The pressure measured relative to the local ambient atmospheric pressure. This is what most common pressure gauges (like a tire pump gauge) read.
Atmospheric Pressure: The baseline pressure exerted by the weight of Earth's atmosphere, which is roughly 101325 Pa at sea level.
Formulas
The fundamental equation for determining pressure is:
$$P = \frac{F}{A}$$
Where:
$P$ is the pressure, typically measured in Pascals (Pa) or N/m².
$F$ is the magnitude of the normal force in Newtons (N).
$A$ is the contact area in square meters (m²).
To calculate the hydrostatic pressure exerted by a fluid column at rest:
$$P = \rho g h$$
Where:
$\rho$ is the density of the fluid (kg/m³).
$g$ is the acceleration due to gravity (m/s²).
$h$ is the depth or height of the fluid column (m).
To convert between reference states:
$$P_{abs} = P_{gauge} + P_{atm}$$
Examples
Mechanical Simulation: When setting up a finite element analysis (FEA) to evaluate the structural integrity of a pressurized pipe network, defining the exact internal surface pressure is required to observe the resulting hoop stresses and predict whether the material will yield under continuous operation.
Everyday Physics: A kitchen knife easily slices through a solid vegetable. Because the edge of the blade has a microscopic surface area, even a minor force applied by a human hand generates a massive localized pressure that overcomes the structural bonds of the vegetable.
Fluid Mechanics: A submarine descending into the ocean experiences an increase in hydrostatic pressure of approximately 1 atm for every 10 meters of depth. The hull must be engineered as a complex pressure vessel to resist these extreme compressive forces and prevent collapse.