Introduction to Fluid Mechanics

Fluid Mechanics

• Fluids are liquids and gases, sharing the property of being able to flow

Properties of Fluids

• Fluids move or flow when force is applied due to their inability to resist deformation
• Fluid mechanics is the study of fluid behavior when still (statics) and when in motion (dynamics)
• Fluid mechanics applies to mechanical and aerospace engineering and biological systems

Fluid Statics

• Deals with fluids at rest, which can be gases (aerostatics) or liquids (hydrostatics)
• Used to determine forces on floating/submerged objects and in devices like hydraulic presses
• Essential for designing water dams and liquid storage tanks

Properties of Solids, Liquids, and Gases

Solids

• Atoms are closely packed and vibrate but don't change position.
• Solid atoms are arranged in specific patterns
• Solids resist all types of stress and are not easily deformed

Liquids

• Intermolecular forces are weaker than solids but stronger than gases
• Liquids deform easily under stress and don't return to their original shape due to free-sliding atoms

Gases

• Atoms have large separations
• Gases have very weak inter-atomic forces
• Gases are easily compressed due to space between atoms
• Gases expand to fill available space

Pressure

• Defined as force per unit area
• Normal stress is the normal component of force acting on a surface per unit area
• Shear stress is the tangential component acting on a surface per unit area.
• In a fluid at rest, shear stress is zero, so pressure is the only stress.
• Pressure (p) equals force (F) divided by area (A): p = F/A
• SI unit of pressure is N/m², also known as Pascal (Pa)
• Other pressure units: mmHg, torr, atm, psi
• Conversion formula: Pother = (Pcons * Ppascal) / 101.3kPa
  • Pcons is a constant pressure value in another system, excluding Pascal
  • Ppascal is the given pressure value in Pascals
  • Pother is the pressure value in the new system

Pressure in Gases

• Air particles move randomly and collide with surfaces, exerting force
• Each collision exerts an impulsive force, similar to a tennis ball hitting a wall
• Countless gas particles collide each second, creating a constant force

Absolute, Gage, and Vacuum Pressure

• Absolute pressure is the actual pressure at a location, relative to absolute zero pressure
• Gage pressure is the difference between absolute pressure and local atmospheric pressure; it can be positive or negative: Pgage = Pabs - Patm
• Vacuum pressure is the difference between atmospheric pressure and absolute pressure: Pvac = Patm - Pabs
• Typical car tire pressure ranges from 32-35 psi

Density

• Density indicates whether an object will sink or float in a fluid
• Density measures how tightly packed the particles or molecules are in a substance
• Density (ρ) is defined as mass (m) per unit volume (V): ρ = m/V
• Gas density is proportional to pressure and inversely proportional to temperature
• Density helps explain phenomena like oil forming films on water

Measuring Density

Regular Solids

• Measure mass and volume using dimensions to find density: v = L × W × H

Irregular Solids

• Measure mass, then find volume by measuring water displacement when the solid is submerged

Relative Density (Specific Gravity)

• Relative density is the ratio of a substance's density to a reference substance (usually water)
• Water density at specific temperature is 1000 kg/m³
• If SG > 1, the object sinks; if SG < 1, the object floats
• SG = ρ / ρH2O

Ideal Gas Law Relationship

• Ideal gas equation relates density and pressure: pv = nRT = (m/M) RT = mRspecificT
• Rspecific = 0.287kPa*(m³/kg*K)
• Rspecific is the specific gas constant, varying for different gases.

Pascal's Principle

• A change in pressure applied to a static fluid is transmitted undiminished to every point in the fluid and container walls

Hydraulic Press

• Simple machine using Pascal's principle to convert small force into larger force
• p1 = p2 and (F1/A1) = (F2/A2)
• Hydraulic brakes in cars are an example

Pressure and Depth

• Pressure in a liquid depends on both depth and density
• Total pressure is pabs = patm + ρgh

Pressure Due to Depth

• Pressure due to liquid depth is independent of the container's shape and size
• Pressure depends only on depth

Atmospheric Pressure

• Atmospheric pressure is due to the weight of air molecules pulled towards the Earth by gravity
• Atmospheric depth is greatest at sea level and decreases with altitude
• Cooking takes longer at higher altitudes because of decreased air pressure

Measuring Atmospheric Pressure

• A barometer measures atmospheric pressure
• A mercury barometer uses a glass tube filled with mercury, inverted in a mercury bath
• Vacuum forms at the top of the tube due to the mercury column falling
• Standard atmospheric pressure supports a 76cm mercury column at sea level: pa = 13600 kg/m³ × 0.76cm × 9.8 m/s² = 101.3kPa
• For every 120m altitude increase, the mercury column decreases by 1cm: Altitude = (76cm-h / 1cm) × 120m

Factors Affecting Barometer Readings

• The length or cross-section of the barometer tube doesn't affect the fluid column height
• The tube diameter should be large enough to minimize surface tension and capillary effects

Manometer

• Manometers measure gas supply pressure using a U-shaped glass tube with liquid (oil, water, or mercury)

Applications of Atmospheric Pressure

• Syringes, water pumps, droppers, and drinking straws operate using atmospheric pressure

Archimedes' Principle

• An object immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced

Buoyant Force

• Buoyant force is the upward force a fluid exerts on immersed objects
• It’s due to pressure increasing with depth, resulting in a greater upward force on the bottom of the object
• Fb = W - W', where W is actual weight and W' is apparent weight
• Fb = ρfluid × g × Vdisp, where ρfVdis equals the mass of the displaced fluid

Submerged Objects

• When an object is totally submerged, the displaced fluid volume equals the object's volume
• Buoyant force: Fb = ρf × g × Vobj
• Object weight: Fg = Mg = ρobj × g × Vobj
• Net force: Fb - Fg = (ρf - ρobj)gVobj
  • Object floats if its density is less than the fluid's density
  • Object sinks if its density is greater than the fluid's density

Floating Objects

• A floating object displaces fluid equal to its weight
• Boats are designed to displace a large volume of water, allowing them to float
• Upward buoyant force equals downward gravitational force for floating objects
• Displaced volume is the same as the volume of the object beneath the surface
• Fb = ρf × g × Vdis and weight of object F㎏ = ρobj×g× Vobj Fg=Fg, where the ratio of volume and density is (Vdis/Vobj) = (ρobj/ρf)

Ocean Icebergs

• If ice made of pure water melts in an ocean of pure water, sea level does not change
• If ice made of pure water melts in salty ocean, sea level rises
• If ice made of salty water melts in an ocean of pure water, the level goes down
• If ice made of salty water melts in a salty ocean, the sea level does not change

Fluid Dynamics

• Fluid flow is caused by pressure differences
• Fluid tends to flow from high to low pressure regions
• Examples: Rivers, air over a bird's wing, blood circulation, fuel in an engine

Fluid Flow Regimes

• Laminar (steady) flow
• Turbulent flow
• Transition flow

Laminar Flow

• Fluid flows in infinitesimal parallel layers with no disruption
• Fluid layers slide parallel with no eddies or swirls
• Movement is smooth and regular
• Fluid particles arriving at a given point have the same velocity
• Typically occurs with low velocity fluids in smaller diameter pipes

Turbulent Flow

• Fluid undergoes irregular fluctuations
• Fluid velocity at a point changes continuously in magnitude and direction
• Movement is irregular and zigzag
• Occurs at high velocities or large diameter pipes
• Turbulent flow has more energy and can withstand adverse pressure gradients longer than laminar flow
• Viscosity transforms kinetic energy into internal energy between adjacent fluid layers
• A streamline is the path taken by a fluid particle under steady flow

Flow Rate

• Flow rate is the quantity of fluid passing through a pipe's cross-section per unit of time
• Q = volume / time

Equation of Continuity

• In steady flow, the product of a cross-sectional area and fluid velocity is constant
• Volume flow rate entering a pipe equals the volume flow rate leaving it
• This is valid for incompressible fluids: Q1 = Q2 and A1V1 = A2V2

Safety and High Pressure

High Pressure

• Pressure greater than 1 atm, often above 50 atm
• Used in thermal power plants (e.g., Velox boilers), cooking, gas cylinders, tire inflation, and high-pressure washers
• Pascalization diminishes microorganism activity, increasing shelf life

High Pressure Equipment

• Compressors or pumps
• Piping (fitting, seals, tubing, and valves)
• Vessels
• Steam generators
• Safety accessories
• Instrumentation

High Pressure Compressors

• A compressor increases the pressure of a gas by reducing its volume and transporting it through a pipe

High Pressure Vessels

• Housing designed to contain fluids under pressure, with direct attachment to a coupling point

Safety Accessories

• Include safety valves, bursting discs, and limiting devices that activate correction or shut down pressure/temperature switches

High Pressure Instrumentation

• Used for measuring pressure, temperature, flow, and level

Safety for High-Pressure Equipment

• Failure can cause serious injury or property damage
• Common causes include:
  • Damaged equipment or system design
  • Poor maintenance
  • Unsafe work systems
  • Operator error
  • Incorrect installation
  • Inadequate repair

Safety Measures for High-Pressure Systems

• Depend on the nature of the system

High Pressure Gas Cylinders

• Are filled with liquefied petroleum gas (LPG)
• Should be sealed
• Safety Measures*
  • Kept vertical in ventilated areas
  • Away from flammable materials
  • The knob is turned offafter use
  • Out of children's reach
  • Do not use cylinder for long periods while cooking

High Pressure Washers

• Used in industry and homes to clean large areas and vehicles.

Washer - Safety Measures

• Wear safety glasses or goggles
• Wear work boots
• Wear safety gloves
• Wear ear protection
• Never point the pressure washer at people or pets
• Stand properly when using the pressure washer