Fluid Dynamics: Matter and Characteristics

Fluid Dynamics (2.2.4)

Matter

• Matter is composed of several molecules
• A molecule is the smallest unit of a substance, exhibiting its physical and chemical properties
• All molecules of a particular substance are identical and unique to that substance
• Matter exists in three physical states: solid, liquid, and gas
• A physical state is the physical condition of a compound and doesn't alter its chemical structure
• Ice, water, and steam are all H2O, representing the same matter in different states

Characteristics of Matter

• Solids have a definite shape, independent of the container
• Solids have a defined volume
• Solids are not easily compressible due to little free space between particles
• Particles in solids do not flow easily past one another
• Liquids have an indefinite shape, taking the shape of the container
• Liquids have a defined volume
• Liquids are not easily compressible due to little free space between particles
• Particles in liquids flow easily , past one another
• Gases have an indefinite shape, taking the shape of the container
• Gases have an indefinite volume
• Gases are compressible due to lots of free space between particles
• Particles in gases flow easily, past one another
• Atoms and molecules in matter are constantly in motion due to heat energy
• The degree of motion determines the physical state of matter

Density

• Density is a substance's mass per unit volume
• Density of solids and liquids varies with temperature
• Density of a gas varies with temperature and pressure
• Density= Mass / Volume
• Example: If a liquid filling a container weighs 1497.6 lb and the container's volume is 24 ft³, the liquid's density is 62.4 lb/ft³
• A standard temperature of 4 °C is used when measuring the density of solids and liquids
• Temperature changes don't change mass but alter volume through thermal expansion/contraction altering mass per unit volume
• Pressure is a crucial consideration for gas density measurements
• Gas density increases in direct proportion to the pressure
• Standard conditions for gas density measurements are 0 °C and 76 cm of mercury (Hg) or average atmospheric pressure at sea level
• Gasses density is computed based on these conditions

Specific Gravity

• Specific gravity compares the density of one substance against a standard
• Water at 4 °C is the standard for liquids and solids, while air is the standard for gases
• Specific gravity (SG) calculates by comparing the mass of a substance of a define volume to the mass of an equal volume of water
• SG for liquids and solids = mass of a substance/mass of equal volume of water or density of a substance/density of water
• The same formulas are used to find the density of gases by substituting air for water.
• Specific gravity is a pure number without units
• A hydraulic liquid with a specific gravity of 0.8 means 1 cubic foot of the liquid weighs 0.8 times as much as a cubic foot of water
• Specific gravity is independent of sample size and varies only with the substance's material
• A hydrometer measures the specific gravity of liquids
• The hydrometer includes a glass float within a larger glass tube which is weighted so it floats vertical
• The hydrometer contains a vertically graduated scale
• When the outer tube has liquid denser than pure water, the float rises higher, showing greater specific gravity
• When the outer tube has liquid less dense, the float sinks lower, showing smaller specific gravity

Viscosity

• Viscosity is affected by changes in temperature and pressure
• As temperature rises, a liquid's viscosity decreases, making it flow more easily
• As pressure increases, a liquid's viscosity also increases
• A good hydraulic system liquid, must be thick enough for seals in: pumps, motors, valves
• These components rely on tight fits to maintain pressure so any leakage through clearances = pressure loss, control disruption, and reduced pump efficiency
• Thinner liquids(low viscosity) cause greater leakage losses and allow rapid wear on moving/heavily loaded parts
• If a liquid is too thick (high viscosity), internal friction = flow resistance through clearances, lines & passages
• The results of using liquid that is too thick are pressure drops, sluggish operation, increased power consumption
• Viscosity applies to gases as well as liquids & oils, with aerodynamics considering air viscosity
• It is important to note that viscosity effects can be velocity-dependent, so these are not simple fluids (non-Newtonian fluids)
• As a gas's temperature rises, its viscosity increases

Viscosity Index

• Viscosity Index represents changes in the viscosity of oil
• Low VI means large changes in viscosity with changing temperature
• High VI means minimal change in viscosity over a wide temperature range
• An ideal oil maintains constant viscosity during temperature changes
• Automotive lubricants need high VI to resist thickening when cold, promoting quicker starts & circulation
• High VI resists thinning at hot temperatures, providing complete lubrication to prevent excessive oil usage
• High-VI hydraulic oil is needed for aircraft to handle temperatures from below -65°F at high altitudes to over 100°F on the ground
• Hydraulic fluid for proper hydraulic control system operation needs a high VI to function at the extremes of it's expected temperature range

Streamlining

• All objects can have the same cross-sectional area when comparing streamlining
• A flats shape obstructs airflow
• Flat shapes cause more drag or resistance which is separated flow
• A curved shape allows smooth airflow in attached flow (Coanda effect)
• Streamlining shapes objects to reduce drag or viscosity-related air resistance for motion in airflow
• Streamlining reduces resistance and increases lift
• For less resistance during subsonic flight, objects must be well rounded like a teardrops
• For less resistance during subsonic flight bodies must gradually curve from the midsection to a tapered rear section

Compressibility

• Compressibility / incompressibility describes the ability of a fluid's molecules to be compressed (made more dense) and spring back
• An incompressible fluid can't be compressed, maintaining near constant density and is representative of Liquids
• A gaseous fluid such as a Aair can be either compressible/incompressible depending on conditions

Effects of Compressibility

• Gases are considered incompressible for theoretical/experimental purposes when moving slowly at under 220 mph
• Low speeds doesn't impact the density of the surrounding air
• Assumptions about air compressibility became invalid as aircraft speeds increased above 220 mph
• At these higher speeds some energy is used to compress air and it will also change density
• The air at higher altitudes also has a lower density than air closer to the surface of Earth
• Aerodynamic theories must account for both compressible/incompressible airflow
• Aerodynamic theories for compressible airflow characteristics are much more complex
• Air possesses a higher density at lower altitudes and considered to be incompressible for experimental/theories purposes

Static, Dynamic and Total Pressure

• When an aircraft flies, its moves through a fluid (air) which creates a pressure due to the weight of the atmosphere – otherwise known as static pressure
• When the aircraft has forward motion as well which strikes air molecules at a rate that increases with speed, which is known as dynamic pressure
• Total pressure (Pt or Po) is equal to static plus dynamic pressure also known as total pitot pressure/stagnation pressure
• Aircraft utilize pitot tubes to measure aircraft speed
• Static pressure is the actual pressure of the fluid with its state rather than motion
• In aircraft, static pressure is open to the atmosphere, and can be measured through a hole in the wall perpendicular to the external airflow Dynamic pressure is parallel to the air flow
• Bernoulli's equation can be used to calculate dynamic pressure

Bernoulli's Equation

• q = ½ rV² where r is the fluid density and V means the fluid velocity
• Static Pressure + Dynamic Pressure = Total Pressure(P_s+r/2 x V^2)= P_t
• Static pressure is used to calculate aircraft altitude

Bernoulli's Principle

• Daniel Bernoulli created a principle to explain potential/kinetic energy relationship in fluids
• All matter contains potential and/or kinetic energy.
• Fluid potential energy caused by its pressure, and kinetic energy from its movement
• Potential energy can exchange for kinetic energy although energy cannot be created/destroyed
• Bernoulli’s principle states the static pressure within a liquid/fluids decreases at points where the velocity increases.
• Fluids move at low velocity in wider sections of a venturi, resulting in high static pressure When the tube narrows the liquid has the same volume
• Fluids move at high velocity in narrow sections, resulting in lower pressure than the wider section

Bernoulli's Theorem Equation

• It can be applied to different types of fluid flow for different forms of Bernoulli's equation Its simple form valid for incompressible flows (liquids/gases) moving at low mach numbers Bernoulli's equation appears in many physics, fluid mechanic/aeroplane textbooks and can be describes as: Static Pressure + Dynamic Pressure = Total Pressure = Constant
• Derived from the principle of energy conservation, the sum of mechanical energy forms in fluid remains consistent in a streamline/points Sum of kinetic/potential energy remains constant
• Conditions are: steady, inciscid, incompressible (low velocity), no heat addition, small change in height
• static pressure + dynamic pressure = total P/ρ + v^2/2 + gz = constant

Venturi Effect

– Reduction in fluid pressure occurs when flowing through constricted pipe sections

• The conservation of energy states the fluid velocity must increase to satisfy continuity while the pressure drops
• The conservation of kinetic energy balances a drop in pressure
• An equation for a drop in pressure results with Bernoulli’s principle plus the equation of continuity
• Choked flow results in low total flow because pressure drops below 0
• Named for Italian physicist Giovanni Battista Venturi (1746–1822)/Venturis are found in many applications