Pressure in Fluids

Introduction

Pressure in fluids is a measure of the force exerted per unit area. It is a fundamental concept in fluid mechanics and is crucial in many engineering and scientific applications.

Definition

The pressure$P$ in a fluid is defined as the force$F$ applied per unit area$A$:

The SI unit of pressure is the Pascal (Pa), which is equivalent to newtons per square meter (N/m²).

Types of Pressure

1. Absolute Pressure: The total pressure exerted by a fluid, including atmospheric pressure.
2. Gauge Pressure: The pressure measured relative to the atmospheric pressure. Gauge pressure is often what is measured by pressure gauges.

Bernoulli's Principle

Bernoulli's principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy.

Hydrostatic Pressure

In a static fluid (where the fluid is not moving), the pressure at a given depth is given by:

Where:
-$\rho$ is the density of the fluid.
-$g$ is the acceleration due to gravity.
-$h$ is the depth below the surface of the fluid.

Key Points:

• Pressure at a Depth: The pressure at a depth$h$ in a fluid is directly proportional to the density of the fluid and the height of the fluid column.
• Atmospheric Pressure: The pressure at the surface of a fluid is the sum of the hydrostatic pressure and the atmospheric pressure.

Example:

• Consider a fluid with a density of $1000{\text{kg/m}}^3$ (e.g., water) at a depth of $10\text{m}$.
• The acceleration due to gravity$g$ is approximately $9.81{\text{m/s}}^2$.

The hydrostatic pressure at this depth is: