Introduction to Fluid Mechanics and Dynamics

• Mechanics is the oldest physical science, dealing with both stationary and moving bodies influenced by forces.
• Statics deals with bodies at rest, while dynamics focuses on bodies in motion; fluid mechanics, a subcategory, studies fluid behavior at rest (fluid statics) or in motion (fluid dynamics) and interactions with solids or other fluids.
• Fluid mechanics is also known as fluid dynamics when fluids at rest are seen as a special case of motion with zero velocity.
• Hydrodynamics studies the motion of fluids that are nearly incompressible, like liquids and gases at low speeds.
• Hydraulics, a hydrodynamics subcategory, focuses on liquid flows in pipes and open channels; gas dynamics studies fluids with significant density changes, like gases through high-speed nozzles.
• Aerodynamics studies gas flows, especially air, around objects like aircraft and cars, at various speeds.
• Meteorology, oceanography, and hydrology are specialized categories dealing with naturally occurring flows.

What Is a Fluid?

• Substances exist in three primary phases: solid, liquid, and gas, with liquid and gas phases referred to as fluid.
• The distinction between solids and fluids is based on the substance's ability to resist shear stress.
• Solids resist shear stress by deforming, while fluids deform continuously, no matter how small the stress.
• In solids, stress is proportional to strain, but in fluids, stress is proportional to strain rate.
• Solids stop deforming at a fixed strain angle under constant shear force, while fluids never stop and approach a constant strain rate.
• Shear strain, or angular displacement, increases in proportion to the applied force.
• When the force is removed, solid returns to its original position but fluid layer moves continuously with plate.

Stress

• Stress is defined as force per unit area.
• Normal stress is the normal component of force on a surface per unit area.
• Shear stress is the tangential component of force on a surface per unit area.
• In a fluid at rest, normal stress is called pressure, and there is zero shear stress.

Liquids vs Gases Molecular level

• In liquids, groups of molecules can move relative to each other, but the volume remains relatively constant.
• Liquids take the shape of their container and form a free surface in a gravitational field.
• Gases expand to fill the available space because gas molecules are widely spaced, and cohesive forces are very small.
• Gases cannot form a free surface in an open container.
• Intermolecular bonds are strongest in solids and weakest in gases due to molecule spacing.
• Molecules in solids are arranged in a repeating pattern, kept in fixed positions by attractive forces; liquids have similar molecular spacing.

Pressure

• Practical fluid systems consist of a large number of molecules, and the properties of the system naturally depend on the behavior of these molecules.
• Pressure of a gas in a container results from momentum transfer between molecules and container walls.
• Macroscopic approach does not require knowledge of gas molecule behavior to determine container pressure
• It is sufficient to attach a pressure gauge to the container
• The microscopic or statistical approach is complex and used in a supporting engineering role

Application Areas of Fluid Mechanics

• It is important to develop a good understanding of the basic principles
• Fluid mechanics is widely used both in everyday activities and modern engineering systems such as vacuum cleaners
• Fluid mechanics plays a vital role in the human body.
• The heart constantly pumping blood to all parts of the human body through the arteries and veins.
• The lungs are the sites
• Fluid dynamics applications include artificial hearts, breathing machines, and dialysis systems.
• Fluid mechanics also impact areas such as piping systems for water, natural gas, and sewage
• Heating and air-conditioning systems, refrigerators, components, and ordinary faucets also employ fluid mechanic principles
• Automotive components associated with fuel transportation also utilize fluid mechanics.
• Designs for aircraft, boats, submarines, rockets, jet engines and transportation systems are also designed using fluid mechanics
• Fluid mechanics impacts natural phenomena such as the rain cycle and ocean waves

History of Fluid Mechanics

• One of the first engineering problems humankind faced as cities were devel- oped was the supply of water for domestic use and irrigation of crops.
• Our urban lifestyles can be retained only with abundant water, and it is clear from archeology that every successful civilization of prehistory invested in the construction and maintenance of water systems.
• The Hellenistic Pergamon civilization built pressurized lead and clay pipelines (Fig. 1–9), up to 45 km long that operated at pressures exceeding 1.7 MPa (180 m of head).
• The earliest recognized contribution to fluid mechanics theory was made by the Greek mathematician Archimedes
• Romans built great aqueducts and educated many conquered people on the benefits of clean water, but overall had a poor understanding of fluids theory.
• Benedict Casteli published the continuity principle for fluids.
• Sir Isaac Newton: applied his laws to fluids and explored fluid interia.
• Bernoulli's 1738 classic treatise Hydrodynamica.

No-Slip Condition

• Fluid flow is often confined by solid surfaces, and it is important to under- stand how the presence of solid surfaces affects fluid flow.
• A fluid in direct contact with a solid "sticks" to the surface, and there is no slip.
• The fluid property responsible for the no-slip condition and the development of the boundary layer is viscosity
• ALL velocity profiles have ZERO values at the point of contact between liquid and solid surface.
• A fluid flowing over a stationary surface comes to complete stop.
• The layer that sticks to surface slows fluids nearby because of viscous forces.
• No-slip condition contributes to the development of velocity profile.
• Flow region adjacent to the wall called boundary layer
• It is the region with high viscous effects and velocity gradients
• Another consequence of the no-slip condition is the surface drag or "skin friction drag"
• This is the force a fluid exerts on a surface in the flow direction
• Flow separation occurs when fluid flows over a curved surface - boundary layer may no longer remain attached to the surface.
• Surface is same temperature at ALL contacts points between SOLID and FLUID.

Classification of Fluid Flows

• Viscosity measures a fluid's internal stickiness.
• Viscosity is caused by cohesive forces between molecules in liquids and by molecular collisions in gases
• All fluid floes involve viscosity Flows in which the frictionnal effects are signficant are viscous flows. Neglecting the viscous terms greatly simplifies analysis. The fluid sticks to the plate because of the no-slip condition.

Internal vs External Flow

• Internal flow fluid is completely bounded by solid surfaces
• External flow fluid is unbounded over a surface like ball or pipe
• Internal flows are dominated by viscosity
• The flow of liquids in a duct is called open-channel flow
• Flows of water in rivers and irrigation ditches are examples of such flows.

Compressible vs Incompressible Flow

• Incompressible flow requires constant density throughout the flow
• The volume of fluid remains unchanged throughout motion when it is imcompressible
• Liquids have constant densities - thier flow is typically incompressibke
• Gases have highly compressible flows. Air is compressible beyond 100 m/s.

Mach Numbers

• A dimensionless Mach number (Ma) is defined as the ratio of the speed of flow to the speed of sound.
• The value of the speed of sound is 346 m/s in air at room temperature at sea level.
• Ma = 1 = Sonic flows
• Ma < 1 = Subsonic flows
• Ma > 1 = Supersonic flows
• Ma >> 1 = Hypersonic flows.

Laminar vs Turbulent Flow

• Highly ordered fluid motion characterized by smooth layers of fluid is known as laminar flow
• The word laminar comes from the movement of adjacent fluid particles together in “laminae".
• High viscosity fluids such as oils at low velocities is typically laminar
• Highly disordered fluid motion that occurs at high velocities and and are characteristerized by turbulent fluctuations
• Turbulent flows often occur at high velocities
• The flow of low-viscosity fluids such as air at high velocities is typically turbulent.
• Flows that alternates between laminar and turbulent are called transitional.
• The experiments conducted by Osborne Reynolds in the 1880s resulted in the establishment of the dimensionless Reynolds number

Natural vs Forces Flow

• Fluid flow is classified as natural or forces based on how fluid motion is initiated
• Forced - Fluid motion is driven by external source such as pump or fan over a surface
• Natural flow arises from buoyancy effect, which is warm fluid rising and cool fluid falling.
• Thermosiphoning effects are used in solar water heaters to replace pumps
• The rise of lighter warmer air indicates thermal plumes surrounds humans

Steady and Unsteady flow

• Steady implies "no change" of properties at a point with time, like steady girlfriend
• Opposite of steady is unsteady
• Uniform "no change" with location over a region
• Unsteady and transient are often used as interchangeable syncnonyms though they are NOT synonyms.
• Transient applies only to developing flows such as rocket engine startup
• Periodic applies to unsteady flows that oscillate about steady mean
• Steady flows are used in turbines, compressors, boilers, condensers
• Volume, mass and total energy content remains constant
• Properties can vary WITHIN the system

Dimensionality

• A flow is one-, two-, or three-dimensional if the flow velocity varies in one, two, or three dimensions, respectively.
• At the pipe surface is zero because of the no-slip condition, and the flow is two-dimensional in the entrance region of the pipe.
• The flow in a circular pipe is one-dimensional since the velocity varies in the radial r-direction but not in the angular θ- or axial z-directions
• Axisymmetric have rotational symmetry along the axis.

System vs Control Volume

• A system - A quantity of matter OR a region in space for study All mass
• Surroundings - rest of mass
• Boundary - surface separating system an surroundings - can have fixed or movable boundaries. and is Mathematically 0 thickness - so it has neither mass nor volume.
• Closed system ALSO known as "control mass" and simply a "system" when context is clear = it has a fixed amount of mass, so no mass can cross its boundary. Closed system can have moving boundaries Energy travels in as HEAT or WORK.
• A system can be considered "isolated" if no energy can cross its boundary either

Open System

• Open - AKA "Control volume" - It is also a selected region in SPACE. It involves mass flow like turbines and nozzles
• Best to select a study with CONTROL VOLUME - BOTH mass and energy can cross boundary here Examples: water heater, car radiators

importance of dimension and units

• dimension includes mass, length, time and temp
• The magnitudes assigned to the dimensions are called units.
• These are considered fundamental dimensions, while velocity, energy and volume are expressed in terms of the primary dimensions and are called secondary dimensions, or derived dimensions.

Explore the principles of mechanics, including statics and dynamics. Learn about fluid mechanics, covering both fluid statics and fluid dynamics. Discover hydrodynamics, hydraulics, gas dynamics, aerodynamics, and their real-world applications in meteorology, oceanography, and hydrology.