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.