Fluid Mechanics

Weight, Mass, and Density

Understanding the concepts of weight, mass, and density is fundamental in fluid mechanics. These properties determine how substances interact under the influence of gravity and pressure.

• Mass: The amount of matter in an object. Measured in kilograms (kg).

• Weight: The force of gravity acting on mass.

• Density: How much mass is packed into a certain volume.

Force and Pressure

Force and pressure are key concepts in fluid mechanics, describing how fluids exert influence on surfaces and objects.

• Force: A push or pull acting on an object.

• Pressure: Force spread over an area.

• Application: Smaller area results in higher pressure for the same force.

Buoyant Force and Pressure Differences

Buoyant force arises due to pressure differences in fluids, leading to the phenomenon of floating and sinking.

• Buoyant Force: Upward force exerted by a fluid, equal to the weight of the fluid displaced.

• Pressure Difference: Pressure increases with depth in a fluid.

• Example: A boat floats because the upward buoyant force equals the weight of the boat.

Volume and Pressure in Confined Gas

Gases in confined spaces obey specific laws relating pressure, volume, and temperature.

• Boyle's Law: For a fixed amount of gas at constant temperature, pressure and volume are inversely related.

• Application: If volume decreases, pressure increases (assuming temperature is constant).

Atmospheric Pressure

Atmospheric pressure is the force exerted by the weight of air above a surface.

• Standard Atmospheric Pressure: About 101,325 Pa at sea level.

• Application: Atmospheric pressure affects boiling points and weather patterns.

Pressure in a Confined Fluid

Pressure applied to a confined fluid is transmitted equally throughout the fluid.

• Pascals's Principle: Pressure applied at one point is transmitted equally to all parts.

• Example: Hydraulic lifts use this principle to multiply force.

Archimedes' Principle and Gases

Archimedes' Principle explains buoyancy in both liquids and gases.

• Archimedes' Principle: An object immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced.

• Application: Hot air balloons rise because the air inside is less dense than the surrounding air.

Fluid Speed and Pressure (Bernoulli's Principle)

Bernoulli's Principle relates the speed of a fluid to its pressure.

• Bernoulli's Equation:

• Application: Faster-moving fluid has lower pressure. Explains airplane lift and why shower curtains move inward.

Thermal Energy and Temperature

Thermal Energy vs. Temperature

Thermal energy is the total kinetic energy of all particles in a substance, while temperature measures the average kinetic energy per particle.

• Thermal Energy: Total energy due to particle motion.

• Temperature: Average kinetic energy per particle.

Lowest Possible Temperature

Absolute zero is the lowest temperature possible, where molecular motion stops.

• Absolute Zero:

Heat vs. Temperature

Heat is energy transferred due to temperature difference. Temperature is a measure of how hot or cold something is.

• Heat: Energy that moves because of a temperature difference.

• Temperature: Indicates thermal state, not energy transfer.

Calories, Calories, and Joules

Energy can be measured in calories or joules. These units are used to quantify heat energy.

• 1 calorie: Energy to heat 1 g of water by 1°C.

• 1 Calorie (food calorie): $1000$ calories.

• 1 calorie: joules.

Three Laws of Thermodynamics

The laws of thermodynamics govern energy transfer and transformation in physical systems.

• First Law: Energy cannot be created or destroyed, only transformed.

• Second Law: Heat flows naturally from hot to cold; disorder (entropy) always increases.

• Third Law: Impossible to reach absolute zero.

Energy Flow in Nature

Energy tends to spread out over time due to the increase in entropy.

• Ordered energy: Becomes disordered (heat) over time.

• Application: Explains why perpetual motion machines are impossible.

Specific Heat Capacity and Thermal Inertia

Specific heat capacity is the amount of heat required to change the temperature of a substance. Thermal inertia describes resistance to temperature change.

• Specific Heat Capacity:

• Heat Energy:

• Application: Water has high specific heat, moderating Earth's climate.

Thermal Expansion

Most materials expand when heated. This must be considered in engineering applications.

• Application: Bridges and railways have expansion joints to prevent damage.

Ice Structure and Water's Density

Ice has a unique hexagonal structure, making it less dense than liquid water.

• Application: Ice floats on water; water is densest at 4°C.

Heat Transfer and Changes of Phase

Conduction in Solids

Conduction is the transfer of heat through direct contact. Metals are good conductors due to free electrons.

• Application: Cooking pans are made of metals for efficient heat transfer.

Convection in Fluids

Convection involves the movement of fluid, carrying heat with it.

• Application: Boiling water and atmospheric currents.

Radiant Energy

Radiant energy is heat transfer by electromagnetic waves, requiring no medium.

• Application: Sunlight warming the Earth.

Newton's Law of Cooling

The rate of cooling depends on the temperature difference between an object and its environment.

• Newton's Law of Cooling:

Greenhouse Effect

The greenhouse effect describes how Earth's atmosphere traps heat, affecting climate.

• Application: Greenhouses and global warming.

Energy and Phase Changes

Phase changes involve energy transfer without changing temperature.

• Application: Melting, boiling, freezing, and condensation.

Boiling and Cooling

Boiling occurs when molecules gain enough energy to escape as vapor.

• Application: Boiling water for cooking.

Melting vs. Freezing

Melting absorbs energy; freezing releases energy. Both occur at the same temperature but in opposite directions.

• Application: Ice melting in a drink absorbs heat, cooling the drink.

Energy-Using and Energy-Releasing Changes

Evaporation, melting, and sublimation absorb energy. Condensation, freezing, and deposition release energy.

• Application: Sweating cools the body by evaporation.

Key Formulas and Laws