Hydraulics and Fluid Mechanics

Hydraulics

• Derived from the Greek word 'Hudour' meaning water
• Branch of engineering science dealing with water at rest or in motion
• Branch of engineering science based on experimental observation of water flow

Fluid Mechanics

• Branch of engineering-science focused on fluid behavior under rest and motion conditions
• Divided into statics, kinematics, and dynamics

Statics

• Hydrostatics: Study of incompressible fluids under static conditions
• Aerostatics: Study of compressible static gases

Kinematics

• Deals with velocities, accelerations, and flow patterns

Dynamics

• Deals with relationships between velocities, accelerations of fluid, and the forces or energy causing them

Properties of Fluids – General Aspects

• Matter is classified based on the spacing between molecules: solid, liquid, and gaseous states
• Solids have closely spaced molecules while liquids have relatively large spacing, and gases have the largest spacing
• Inter-molecular cohesive forces are large in solids, smaller in liquids, and extremely small in gases
• Solids can resist tensile, compressive, and shear stresses up to a limit
• Fluids have little to no tensile strength and can resist compressive forces only when contained
• Fluids deform continuously under shearing force
• Shear stress depends on the rate of deformation of the fluid element
• Liquids are difficult to compress, whereas gases are readily compressible and expand indefinitely when external pressure is removed

Fluid Definition

• Substance capable of flowing
• Substance that deforms continuously when subjected to external shearing force

Fluid Characteristics

• Conforms to the shape of the containing vessel
• Undergoes continuous deformation under shear force

Fluid Classification

• Liquid, Gas, Vapour
• Ideal fluids, Real fluids

Liquid

• Fluid with a definite volume that varies slightly with temperature and pressure
• Possesses bulk elastic modulus under compression, storing energy like a solid
• Volume contraction under compression is usually ignored, assuming incompressibility
• Can withstand slight tension due to molecular attraction, causing apparent shear resistance (viscosity)

Gas

• No definite volume
• Compressible

Vapour

• Gas near its liquid state in terms of temperature and pressure (e.g., steam)

Ideal Fluids

• No viscosity or surface tension
• Incompressible
• No such fluid exists in nature
• Fluids with low viscosities (like water and air) can be treated as ideal fluids under certain conditions to simplify mathematical analysis
• Standard fluid for liquids is pure water at 4°C

Specific Weight, Mass, Volume & Gravity Example

• Liquid volume = 6 m3, Liquid weight = 44 kN
• Specific weight (w) = 7.333 kN/m3
• Specific mass/mass density (ρ) = 747.5 kg/m3
• Specific volume (v) = 0.00134 m3/kg
• Specific gravity (S) = 0.747

Viscosity

• Property determining a fluid's resistance to shearing stresses
• Measure of internal fluid friction causing resistance to flow
• Primarily due to cohesion and molecular momentum exchange between fluid layers
• Effects appear as shearing stresses between moving fluid layers
• An ideal fluid has no viscosity
• Fluids with very little viscosity are sometimes considered ideal fluids
• Viscosity is due to cohesion and interaction between particles
• Shear stress (τ) is proportional to the rate of change of velocity with respect to distance (y)
• The relationship is expressed as: τ = µ (du/dy) where µ is a constant of proportionality