Pressure in fluids is a crucial concept in fluid mechanics. It's the force per unit area exerted by a fluid on surfaces. Understanding pressure helps us design everything from dams to submarines.

Hydrostatic pressure, caused by a fluid's weight, increases with depth. This principle explains why our ears pop underwater and why deep-sea creatures need special adaptations. It's key to many engineering applications, from water towers to hydraulic systems.

Pressure Fundamentals

Pressure in fluids

• Pressure is the force per unit area exerted by a fluid on a surface perpendicular to the force (water pressing against a dam)
• Mathematically, pressure ($P$) is defined as $P = \frac{F}{A}$, where $F$ is the force and $A$ is the area
• Pressure acts perpendicular to any surface in contact with the fluid (walls of a swimming pool)
• Pressure is a scalar quantity has magnitude but no direction (unlike force which is a vector)
• The SI unit for pressure is the Pascal (Pa), where 1 Pa = 1 N/m² (atmospheric pressure is about 101,325 Pa at sea level)

Hydrostatic pressure concept

• Hydrostatic pressure is the pressure exerted by a fluid at rest due to its weight (water at the bottom of a lake)
• In a static fluid, pressure varies linearly with depth increases as depth increases (pressure is higher at the bottom of a swimming pool than at the surface)
• The hydrostatic pressure at a given depth depends on the fluid density and the height of the fluid column above that point (mercury is denser than water, so a shorter column of mercury can exert the same pressure as a taller column of water)
• The change in pressure with depth is given by $\frac{dP}{dz} = -\rho g$, where $\rho$ is the fluid density, $g$ is the acceleration due to gravity (9.81 m/s²), and $z$ is the vertical coordinate positive upward (pressure decreases as you move upward in a fluid)

Hydrostatic Pressure Applications

Hydrostatic equation applications

• The hydrostatic equation calculates the pressure at a specific depth in a fluid $P = P_0 + \rho g h$, where $P$ is the pressure at depth $h$, $P_0$ is the pressure at the reference level (atmospheric pressure at the surface of a lake), $\rho$ is the fluid density, and $g$ is the acceleration due to gravity
• To calculate the pressure difference between two points in a fluid, use $\Delta P = \rho g \Delta h$, where $\Delta h$ is the vertical distance between the two points (pressure difference between the top and bottom of a water tower)
• When solving hydrostatic pressure problems, clearly define the reference level and the direction of the vertical coordinate z-axis (choose the surface of a liquid as the reference level and positive z-axis pointing upward)

Atmospheric pressure effects

• Atmospheric pressure is the pressure exerted by the Earth's atmosphere on objects at the surface (air pressing down on us)
• At sea level, the standard atmospheric pressure is 101,325 Pa (1 atm) or 14.7 psi (pounds per square inch)
• Atmospheric pressure acts as a reference pressure for many fluid systems
  1. Gauge pressure is the pressure measured relative to atmospheric pressure (tire pressure)
  2. Absolute pressure is the sum of gauge pressure and atmospheric pressure (pressure inside a pressurized gas cylinder)
• Changes in atmospheric pressure can affect the behavior of fluids in open systems (lower atmospheric pressure at high altitudes causes water to boil at a lower temperature)