Overview
This lecture covers the measurement and types of pressure in fluids, Pascal's law, hydrostatic law, and the concept of hydrostatic paradox within the context of fluid statics.
Types of Pressure
- Absolute pressure is measured above absolute zero pressure (pressure in outer space).
- Gauge pressure is measured above atmospheric pressure using atmospheric pressure as a reference.
- Atmospheric pressure is measured by a barometer and in absolute terms equals 101.3 kPa.
- Vacuum pressure occurs when a pressure is lower than atmospheric pressure.
- Vacuum pressure = atmospheric pressure – absolute pressure at the point.
Kinetic Theory of Pressure
- Pressure arises from collisions of fluid particles with surfaces, as per the kinetic theory of gases.
- In a vacuum (no particles or medium), the pressure is absolute zero.
Pascal's Law
- States that pressure at a point in a fluid at rest is the same in all directions (Px = Py = Pz).
- Proven via equilibrium of forces on a wedge-shaped fluid element.
- Normal stress at a point in a fluid at rest equals the pressure there.
- Law of transmissibility: externally applied pressure on a fluid is transmitted equally throughout the fluid.
- Used in hydraulic jacks: F1/A1 = F2/A2; larger area yields amplification of force (F2 > F1).
Hydrostatic Law
- Describes how fluid pressure varies with depth: dP/dz = ρg (downward z) or dP/dz = –ρg (upward z).
- Pressure at a depth h:
- Absolute pressure = atmospheric pressure + ρgh.
- Gauge pressure = ρgh (if atmospheric pressure is the reference).
- At equal depths, pressure is the same regardless of vessel shape (hydrostatic paradox).
- Force on the base of a vessel = pressure × area; differs if base areas differ.
Fluid at Rest vs. Motion
- A fluid at rest will only flow if there is a pressure difference.
- Fluid in motion (dynamics) depends on energy differences (to be covered in fluid dynamics).
- When two vessels are connected, flow occurs until pressure (height) equalizes in both.
Key Terms & Definitions
- Absolute Pressure — Pressure measured above absolute vacuum (zero pressure).
- Gauge Pressure — Pressure measured relative to atmospheric pressure.
- Atmospheric Pressure — Pressure exerted by the earth’s atmosphere (101.3 kPa).
- Vacuum Pressure — Pressure below atmospheric pressure.
- Pascal's Law — Pressure at a point in a stationary fluid is equal in all directions.
- Hydrostatic Law — The rate of change of pressure with depth in a fluid is equal to the fluid’s weight density.
- Hydrostatic Paradox — Fluid pressure at a given depth is independent of vessel shape/area.
Action Items / Next Steps
- Review and memorize pressure formulas: absolute, gauge, and hydrostatic.
- Practice problems involving Pascal’s law and hydraulic machines.
- Prepare for upcoming manometer and pressure measurement topics.