Fluid Mechanics Essentials

This cheat sheet covers the fundamental properties of liquids and gases, pressure, buoyancy, and fluid flow, providing key formulas and concepts for quick reference.

Core Principles

• Fluids (liquids and gases) flow and take the shape of their container.
• Liquids are nearly incompressible and form a horizontal surface.
• Gases are easily compressible, have no surface, and fill the entire container.
• Pressure is force applied over an area.
• Pascal's Law states that pressure applied to an enclosed fluid is transmitted undiminished throughout.
• Hydrostatic pressure depends on depth and fluid density.
• Atmospheric pressure decreases with altitude.
• Buoyancy force equals the weight of the fluid displaced by an object (Archimedes' Principle).
• Fluid flow speed increases in constricted areas (Continuity Law).
• Faster fluid flow corresponds to lower pressure (Bernoulli's Principle).

Action Steps

• Identify if the substance is a liquid or a gas.
• Calculate pressure using force and area ($p = F/S$).
• Apply Pascal's Law for enclosed fluids under external force.
• Determine hydrostatic pressure based on depth and density ($p_h = h \cdot \rho \cdot g$).
• Measure atmospheric pressure, noting its decrease with altitude.
• Calculate buoyancy force using displaced fluid volume and density ($F_{vz} = V \cdot \rho \cdot g$).
• Compare object and fluid densities to predict sinking, floating, or hovering.
• Analyze fluid flow using the Continuity Law and Bernoulli's Principle.

Formulas

• $p = \frac{F}{S}$
• $p_h = h \cdot \rho \cdot g$
• $F_{vz} = V \cdot \rho \cdot g$
• $\frac{F_1}{S_1} = \frac{F_2}{S_2}$

Key Terms

• Tekutiny (Fluids): Substances that flow and take the shape of their container (liquids and gases).
• Tlak (Pressure): Force exerted per unit area.
• Pascalův zákon (Pascal's Law): Pressure applied to an enclosed fluid is transmitted equally in all directions.
• Hydrostatický tlak (Hydrostatic Pressure): Pressure exerted by the weight of a fluid at rest.
• Atmosférický tlak (Atmospheric Pressure): The pressure exerted by the weight of the atmosphere.
• Vztlaková síla (Buoyancy Force): The upward force exerted by a fluid that opposes the weight of an immersed object.
• Archimédův zákon (Archimedes' Principle): The buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
• Zákon kontinuity (Continuity Law): In a pipe, fluid speed increases where the cross-sectional area decreases.
• Bernoulliho rovnice (Bernoulli's Equation): Relates fluid speed, pressure, and elevation; faster flow means lower pressure.

Real World Examples

• Hydraulic brakes or lifts: Utilize Pascal's Law to multiply force using different piston areas.
• Water in a kettle or U-tube: Demonstrates the principle of connected vessels where the surface levels equalize.
• Mercury barometer: Torricelli's experiment proving atmospheric pressure using a column of mercury.
• A stone dropped in water: Sinks because its density is greater than the water's density.
• A fish in water: Hovers because its density equals the water's density.
• A piece of wood floating: Floats because its density is less than the water's density.
• Putting your thumb over a garden hose: The water speeds up due to the reduced area (Continuity Law).
• Airplane wings: Generate lift due to faster airflow over the top surface creating lower pressure (Bernoulli's Principle).