MC

Chapter 5: Fluid Mechanics

Fluid Mechanics Overview

  • Understanding key concepts related to fluid mechanics, including density, pressure, buoyancy, and principles that govern fluid behavior.

Key Concepts Covered

  • Density

  • Pressure

  • Buoyancy in a Liquid

  • Archimedes’ Principle

  • Pressure in a Gas

  • Atmospheric Pressure

  • Pascal’s Principle

  • Buoyancy in a Gas

  • Bernoulli’s Principle

Fluid Mechanics

Definition of Fluids

  • Fluids are materials capable of flowing, including gases and liquids.

  • Properties of fluids are influenced primarily by density and pressure.

Density

Importance of Density

  • Density is an essential property of solids, liquids, and gases, indicating how compact a substance is.

  • Represents the "lightness" or "heaviness" of materials of equal size.

Density Calculation

  • Formula: Density = Mass / Volume

  • Units:

    • Mass: grams (g) or kilograms (kg)

    • Volume: cm³ (cubic centimeters) or m³ (cubic meters)

    • Density often expressed in kg/m³ or g/cm³.

  • Example: The density of mercury is 13.6 g/cm³, indicating it's 13.6 times denser than water (1 g/cm³).

Weight Density

  • Weight Density = Weight / Volume

  • Example:

    • Density of salt water: 64 lb/ft³, greater than fresh water at 62.4 lb/ft³.

Density Comparison Exercise

  1. 100 kg of lead vs 100 kg of water:

    • Both have the same mass, but lead is denser due to smaller volume.

Pressure

  • Pressure is the force exerted per unit area by one object on another.

  • Formula: Pressure = Force / Area

  • Units: lb/ft², N/m² (Newtons per square meter), or Pascals (Pa).

Pressure in Liquids

  • Pressure in a liquid is depth-dependent rather than volume-dependent.

  • As depth increases, pressure due to liquid weight increases.

  • Example: Swimming deeper doubles the pressure exerted on the body due to the weight of water above.

  • Pressure is exerted equally in all directions within a liquid.

Effects of Water Pressure

  • Water pressure acts perpendicular to the surfaces of containers, and liquid spurts at right angles from holes in the container.

  • Greater depth results in higher exiting speeds of water.

Behavior of Fluids in Containers

  • Pressure at any depth within a container is the same regardless of container shape.

  • Equation for liquid pressure: Liquid pressure = Weight Density × Depth

  • Example: The force of gravity acting on water in a tower generates reliable water pressure in pipes.

Buoyancy in a Liquid

  • Buoyancy refers to the apparent loss of weight experienced by submerged objects, equal to the weight of the fluid displaced.

Concepts of Buoyant Force and Floatation

  • If a buoyant force exceeds an object’s weight, the object floats.

  • If the weight surpasses the buoyant force, the object sinks.

  • Equal buoyant force and weight allow an object to remain at a constant depth.

Archimedes’ Principle

  • An immersed body is buoyed up by a force equal to the weight of the fluid it displaces.

  • This applies to both gases and liquids.

Displacement Rule

  • A submerged object displaces a volume of fluid equal to its own volume, leading to the concept of buoyant force resulting from pressure differences.

Pressure in a Gas

Characteristics

  • Molecules in gases are spaced further apart than in liquids, and gases expand to fill available space.

  • Gas pressure is related to the motion of bouncing gas molecules against walls.

Boyle’s Law

  • Definition: For a fixed amount of gas at constant temperature, the product of pressure and volume remains constant.

  • Equation: P1 × V1 = P2 × V2

Atmospheric Pressure

Overview

  • Atmospheric pressure arises from the weight of air pressing down due to gravity.

  • Varies with altitude—most atmosphere is below 30 km.

Measurement

  • Average atmospheric pressure at sea level is approximately 101 kPa (kilopascals).

  • Barometers measure atmospheric pressure and can indicate altitude.

Pascal’s Principle

  • States that changes in pressure applied to an enclosed fluid are transmitted uniformly throughout the fluid.

  • Example: Pressure applied on one piston in a hydraulic system increases pressure in another piston.

Bernoulli’s Principle

  • States that an increase in fluid speed results in a decrease in pressure within the fluid.

  • Can be observed with streamlines: closer streamlines indicate faster flow and lower pressure.

Applications

  • Applied in various fields such as aerodynamics (aircraft wings) and fluid flow measurement.