Unit 8: Fluids
8.2: Pressure
Introduction
Pressure is a fundamental concept in fluid mechanics that describes the force exerted by a fluid over a given area. It plays a critical role in understanding buoyancy, fluid dynamics, and real-world applications such as hydraulics and atmospheric science.
Key Concepts
- Definition of Pressure: \[ P = \frac{F}{A} \] where P is pressure (Pa), F is force (N), and A is area (m²).
- Units of Pressure:
- Pascal (Pa) = 1 N/m²
- Atmospheric Pressure: 1 atm = 101,325 Pa
- Other units: mmHg, torr, bar
- Pressure in a Fluid:
\[
P = P_0 + \rho g h
\]
where:
- P₀ = atmospheric pressure
- ρ = fluid density (kg/m³)
- g = acceleration due to gravity (9.81 m/s²)
- h = depth in the fluid (m)
- Gauge vs. Absolute Pressure:
- Absolute pressure includes atmospheric pressure.
- Gauge pressure measures pressure above atmospheric pressure.
- Pascal’s Principle: A change in pressure applied to a confined fluid is transmitted undiminished throughout the fluid: \[ P_{\text{in}} = P_{\text{out}} \] This principle is the basis for hydraulic systems.
Mathematical Routines
- Use P = F/A to calculate pressure on a surface.
- Apply P = P₀ + ρgh to determine pressure at different depths.
- For hydraulic systems: \[ \frac{F_1}{A_1} = \frac{F_2}{A_2} \]
Tip: Pressure increases with depth in a fluid, regardless of container shape.
Creating Representations
- Diagrams: Draw force and pressure distributions in a container.
- Graphs: Plot pressure vs. depth to show the linear relationship.
Scientific Questioning & Argumentation
- Why does pressure increase with depth in a fluid?
- How does Pascal’s Principle enable hydraulic lifts?
Use pressure equations and diagrams to support your answers.
Exam Tip: Know the difference between absolute and gauge pressure for solving fluid problems.
Practice Activities
Activity 1: Pressure at Depth
A diver descends 10 m underwater. Given ρ = 1000 kg/m³, calculate the total pressure acting on the diver.
Activity 2: Hydraulic Lift
A small piston (A₁ = 0.01 m²) in a hydraulic lift applies a force of 200 N. If the large piston (A₂ = 0.5 m²) supports a car, what is the maximum weight it can lift?
Summary & Exam Preparation Tips
- Pressure is force per unit area and measured in Pascals.
- Fluid pressure increases with depth: P = P₀ + ρgh.
- Pascal’s Principle explains hydraulic systems.
- Distinguish gauge pressure vs. absolute pressure in problems.