Introduction to Fluid Mechanics

• Mechanics is the oldest physical science, dealing with stationary and moving bodies influenced by forces.

Branches of Mechanics

• Statics deals with bodies at rest.
• Dynamics deals with bodies in motion under forces.

Fluid Mechanics Defined

• It studies the behavior of fluids at rest (fluid statics) or in motion (fluid dynamics), plus their interactions with solids or other fluids at boundaries.
• Fluid mechanics can be referred to fluid dynamics when fluids at rest are seen as a special case of motion with zero velocity.

Categories of Fluid Mechanics

• Hydrodynamics studies the motion of incompressible fluids like liquids and low-speed gases.
• Hydraulics specifically deals with liquid flows inside pipes and open channels.
• Gas dynamics studies the flow of fluids with significant density changes, such as gases through nozzles at high speeds.
• Aerodynamics studies the flow of gases, like air, over objects such as aircraft, rockets, and vehicles at varying speeds.

Definition of a Fluid

• In physics, the three primary phases of matter are solid, liquid, and gas, with plasma existing at very high temperatures.
• A fluid refers to a substance in either the liquid or gas phase.
• The ability to resist shear stress distinguishes solids from fluids.
• Solids resist shear stress by deforming but fluids deform continuously under any shear stress.
• Stress is proportional to strain in solids, while stress is proportional to strain rate in fluids.
• Under constant shear force, a solid stops deforming at a fixed strain angle, but a fluid continues deforming, approaching a constant strain rate.

Fluid Applications

• Both gases and liquids are classified as fluids and have numerous engineering applications.
• Examples include breathing, blood flow, pumps, fans, turbines, airplanes, ships, rivers, missiles, and even natural occurrences like wind and ocean currents.
• Most things on the planet are either fluids or move within or near a fluid.

Applications of Fluid Mechanics

• It is used in everyday activities and engineering designs from vacuum cleaners to supersonic aircraft.
• The human body relies on fluid dynamics, with the heart pumping blood and lungs facilitating airflow; artificial hearts and breathing machines also use fluid dynamics.
• Houses and cities use fluid mechanics for water, natural gas, and sewage piping; even faucets rely on fluid mechanics.
• Heating and air-conditioning systems use piping and ducting networks designed using fluid mechanics.
• Refrigeration involves refrigerant flowing through tubes, a compressor, and heat exchangers.
• Automobiles use fluid mechanics in fuel transportation components, fuel-air mixing, exhaust purging, and in the design of heating, brakes, steering, transmission, lubrication, cooling, and tires.
• Fluid mechanics is critical for designing aircraft, boats, submarines, rockets, jet engines, wind turbines, biomedical devices, cooling systems, and transportation systems for liquids and gases.
• It helps design stable buildings and bridges, considering wind loading, and explains natural phenomena like weather patterns, groundwater movement, and ocean currents.

Viscous vs. Inviscid Flow

• Friction develops between fluid layers moving at different speeds.
• Viscosity measures a fluid's internal resistance to flow or "stickiness.”
• Viscosity results from cohesive forces in liquids and molecular collisions in gases.
• All fluid flows have some viscous effects, but flows with significant friction are viscous flows.
• Inviscid flow regions are where viscous forces are very small compared to inertial or pressure forces, typically away from solid surfaces.

Internal vs. External Flow

• Fluid flow is either internal or external based on whether the fluid is confined or flows over a surface.
• External flow is the flow of an unbounded fluid over a surface such as a plate, wire, or a pipe.
• Internal flow occurs in pipes or ducts where the fluid is enclosed by solid surfaces.
• Open-channel flow is a type of internal flow where a duct is partially filled with liquid and has a free surface.
• Viscosity dominates internal flows but viscous effects in external flows are limited to boundary layers and wake regions.

Compressible vs. Incompressible Flow

• Flow is either compressible or incompressible, based on density variation.
• Incompressible flow means the density stays nearly constant and is typical for liquids, which are considered incompressible substances.
• Compressible flow means density changes are significant, which occurs when the fluid moves near the speed of sound.

Laminar vs. Turbulent Flow

• Laminar flows are smooth and orderly, with fluid moving in smooth layers.
• Turbulent flows are chaotic and characterized by velocity fluctuations, usually at high speeds.
• Transitional flow alternates between laminar and turbulent states.

Natural (Unforced) vs. Forced Flow

• A flow is natural or forced, depending on how it starts
• Forced flow is when a fluid is moved by external devices like pumps or fans.
• Natural flows occur due because of buoyancy, where warmer fluid rises and cooler fluid falls.

Steady vs. Unsteady Flow

• Steady implies no change in properties like velocity or temperature at a given point over time.
• Unsteady is a broad term for any flow that isn't steady.

Uniform vs. Nonuniform Flow

• Uniform flow means fluid properties like velocity, pressure, and temperature do not change with position.
• Wind tunnels aim for uniform airflow but non uniformity occurs near the walls due to the no-slip condition and boundary layers.

Dimensions vs. Units

• A dimension is how a physical variable is measured quantitatively.
• A unit is a way of assigning a number to a quantitative dimension.
• Length is a dimension; centimeters and inches are units for measuring it.
• Fluid mechanics uses four primary dimensions: mass, length, time, and temperature.
• Secondary dimensions like velocity, energy, and volume are expressed using primary dimensions.
• The English system (USCS) and the metric SI system are two common unit systems.

Example problem

• A body weighs 1000 lbf under standard Earth gravity (g=32.174 ft/s²).

Part A

• What is the mass in kg?

Solution

• F = W = mag, 1000 lbf = mag = (m)(32.174 ft/s²)
• m = 1000 lbf/(32.174 ft/s2), m = 1000 lbf/(32.174 ft/s2) = 31.08 slugs
• m = (31.08 slugs)(14.5939 kg/slug) = 454 kg

Part B

• What will the weight of this body be in N if it is exposed to the moon’s standard acceleration gmoon = 1.62 m/s2?

Solution

• F = Wmoon = magmoon = (454 kg)(1.62 m/s2) = 735 N

Part C

• How fast will the body accelerate if a net force of 400 lbf is applied to it on the moon or on the earth?

Solution

• F = ma, 400 lbf = ma = (31.08 slugs) (a)
• a = 400 lbf/(31.08 slugs), a = 12.87 ft/s2
• a = (12.87 ft/s2)(0.3048 m/ft) = 3.92 m/s2

Overview of fluid mechanics, covering statics and dynamics. Includes categories such as hydrodynamics, hydraulics, gas dynamics and aerodynamics. Focuses on fluid behavior at rest and in motion, plus their interactions with boundaries.