Fluid Properties: Density, Specific Volume & Gravity

Fundamentals of Fluid Mechanics

Introduction and Basic Concepts

• Fluid is any substance capable of flow. Solid is any substance that cannot flow
• Liquids, gases, and plasmas share characteristics that differentiate them from solids, and are categorized as fluids
• Plasma, the fourth state of matter, is a fluid, but is excluded from the scope of study.
• Focus is restricted to liquids and gases.
• Fluid molecules have relatively large spacing, are deformable, and are capable of flow
• Fluids conform to the shape of their container.
• In contrast to fluids, solid molecules are closely spaced and resist shearing forces
• Solids exhibit elasticity and have a defined shape.
• Liquids and gases are both categorized as fluid because they are both capable of flowing and deforming continuously under shear stress
• Liquids are difficult to compress, have a definite volume, and form a free surface
• Gases are easily compressed, lack a definite volume, and expand to fill any closed container
• Fluid mechanics is the study of fluids either in motion (fluid dynamics) or at rest (fluid statics)
• Fluid statics studies the behavior of fluids at rest
• Kinematics studies velocity, acceleration, and motion patterns without considering forces or energies
• Fluid dynamics studies the behavior of fluids in motion, divided into hydrodynamics (flow of water) and aerodynamics (flow of air)
• Fluid is important for life. Examples include air for breathing, water for drinking, and blood flow within bodies.
• Fluids influence comfort, transportation, recreation, and entertainment
• Knowledge of fluid mechanics is crucial in internal combustion engines, aerospace propulsion systems, waste disposal, pollution dispersal, power generation, pipelines, and more

Properties of Fluids

• Fluids have characteristics that help describe their condition and distinguish them from one another, known as fluid properties
• Fluid properties can be classified as physical, (general) thermodynamic, and transport properties
• Thermodynamic properties are considered with gas equations when fluids are influenced by temperature
• Transport properties include viscosity, thermal conductivity, and mass diffusivity
• Topics covered include viscosity, surface tension, capillarity, and compressibility
• Density is the mass amount per unit volume of a substance, expressible in different ways
• Mass density (ρ) is the mass of fluid per unit volume at standard temperature and pressure, measured in kg/m³
• Water's density is 1000kg/m³, while air's density is 1.23kg/m³ at P = 1.013×105N/m² and T = 15°C
• Specific Volume is the reciprocal of mass density, defined as volume per unit mass of a fluid, measured in m³/kg
• Weight density (w), also known as Specific Weight, is the weight of a fluid per unit volume at standard temperature and pressure.
• Weight is a force equal to mass times acceleration, w = ρg, where g is gravitational acceleration
• Specific Gravity (SG or σ), also known as Relative Density, is the ratio of a fluid's mass density to that of a standard reference fluid
• The standard reference fluid is water (at 4°C) for liquids and air for gases at atmospheric pressure.
• Relative density for liquid is SGliquid = ρliquid/ρwater = ρliquid / 998kg/m³
• Relative density for gas is SGgas = ρgas/ρair = ρgas / 1.205kg/m³
• Specific gravity has no dimensions and is dimensionless
• Viscosity is a fluid’s stickiness, or internal friction; viscous fluids resist shear stresses
• Viscosity measures internal friction and a fluid's resistance to flow
• Resistance is opposite to applied shear forces
• Under particular conditions fluids offer greater or lesser flow resistance
• Liquids like tar, treacle, and glycerine are commonly "thick," while water, petrol, and paraffin are "thin."
• Gases as well liquids exhibit viscosity
• Water is 55 times as viscous as air
• Viscosity determines a fluid's resistance to shearing stresses
• Fluid viscosity arises on molecular scales from intermolecular cohesion and interaction
• Molecular cohesion is dominant in liquids, while the latter is more important in gases
• The viscosity together with relative velocity causes a shear stress acting between fluid layers
• Shear stress (τ) is proportional to the rate of shear strain known as velocity gradient.
• Coefficient of dynamic is the constant of proportionality, viscosity.
• Coefficient of dynamic viscosity (u) is defined as shear stress (τ) or shear force unit area needed to drag fluid with unit velocity past another layer at unit distance
• Unit of dynamic viscosity is kgs⁻¹m⁻¹ or Nsm-2
• Viscosity can be measured in poise (P), where 10 P = 1 kgs⁻¹m⁻¹ = 1 Nsm-2
• Co-efficient of dynamic viscosity: water is 1.14×10-3 kg/ms and air is 1.78×10-5 kg/ms Kinematic vicosity is noted as water at 20°C = 1/100 poise = centipoises (CP)
• Kinematic viscosity (v) is the ratio of dynamic viscosity to fluid density, v = μ/ρ
• The unit of kinematic viscosity is m²/s; it can also measured in stoke and 1 stoke = 10⁻⁴m²/s
• Temperature changes have affects on fluid vicosity
• In liquids, viscosity decreases as temperature increases b/c intermolecular cohension decreases
• In gases, viscosity increases as temperature increases b/c intermolecular cohension increases
• Viscocity can also be effected under varying conditions changes in pressure. increased pressure increase viscosity of some oils
• Newton's Law of Viscosity states shear stress exerted on a fluid element's surface is directly proportional to the rate of shear strain
• Fluids following newton's law are know as newtonian fluids, if not they are non-newtonian fluids.
• Newtonian fluids are fluids that exhibit shear stress and a linearly dependent on velocity gradient
• Newtonian fluids include common fluids such as water, kerosene, and air
• Non-Newtonian fluids which the value of u is not constant are generally complex mixtures and relatively uncommon
• Non-newtonians are studied under the science of deformation of flow called “rheology”. such as slurries, mud flows, polymer solution, blood, etc.
• Thermodynamic properties are considered using the equation of state of a perfect gas when a fluid is influenced by temperature changes, PV = MRT or P = PRT
• Where, P = Absolute pressure, V = Volume of the fluid, T = Absolute temperature, m = mass of gas, and R = Characteristic gas constant
• Perfect gas equation can be derived as PV = nMRT in terms of kilogram-mole where m = nM
• Where, m = nM, n = number of moles, and M = molecular weight
• A change of density may be achieved both by a change of pressure and by a change of temperature
• When a change in a state of the fluid system is affected at constant pressure the process is known to be isobaric process
• When the change in a state of the fluid system is affected at constant temperature the process is known to be isothermal process
• When no heat is transferred to or from the fluid during the change in the state of the fluid system, the process is known to be adiabatic process. Here, Pv² or P/ρ = constant
• Where, y = Cp/Cv, Cp = Specific heat capacity at constant pressure, and cv = Specific heat capacity at constant volume
• Cohesion is is the intermolecular attraction between molecules of the same liquid
• Adhesion is the attraction between the molecules of a liquid and the molecules of its solid boundary
• Capillarity action is due to both cohesion and adhesion
• Surface tension comes from the force of cohesion between molecules; normally expressed in N/m
• Surface tension depends upon the nature of the liquid, surrounding matter, and kinetic energy
• Water has a surface tension of 0.073 Nm⁻¹; some organic liquids have values between 0.020-0.030 Nm⁻¹ and mercury is about 0.48 Nm⁻¹
• Increased temperature will decrease the surface tension of all liquids
• Surface tension of water may be reduced by organic solutes like soap/detergents; salts like sodium chloride raise the surface tension of water
• That tension which exists in the surface separating two immiscible liquids is known as interfacial tension
• Pressure inside a water droplet = P = 4σ/d
• Inside a soap droplet: P = 8σ/d
• Liquid jet: P = 2σ/d

Forces in Static Fluids

• Study involves forces acting on or generated by fluids at rest
• General statics rules apply to fluids at rest
• Static fluid cannot have shearing force
• Force between fluid and boundary acts at right angles
• Statement is true for curved surfaces, force is normal to surface.
• Equilibrium is tested by resolving forces along three mutually perpendicular axes and planes
• Pressure is convenient force unit (per unit area) for fluids in vessels acting in normal force at contact point
• Pressure intensity is the ratio of normal force on unit area; pressure is uniform if force is same
• Pressure: P = F/A
• Liquid is subjected to pressure due to its own weight which increases with its depth of liquid
• A liquid at rest is contained by a vessel will exert pressure
• Height = h, area = A, w = specific weight, P = pressure intensity
• Pressure on the base of the cylinder = Weight of the liquid: PA = wAh
• Thus, P = wh
• P=pgh
• Equation shows that pressure depends on distance from the free surface known as the pressure head or static head
• Pressure over pgh is pressure head or static head Pascal's law says rate pressure acts equally in all directions
• Can be proven when considering element of fluid is triangular prism with point P: Px = Py = Ps
• Pressure in the horizontal direction is constant
• P=Pressure, Z = Elevation: dP/ds = pgcosQ
• Pressure variation with elevation integrated as P₂ - P₁ = -pg dz = − gdz or - w dz
• Absolute Pressureis P = -ρgz + constant where constant would is Atmospheric Pressure.
• Gauge pressure is the pressure measured with the help of pressure measuring instrument, in which the atmospheric pressure is taken as datum. Pressure is zero on the scale on the armosphere.

Fluid Dynamics

• In fluid dynamics, specific weight is important, nature of fluid motion is complex
• Kinematics studies motion of fluid without consideration for forces causing motion
• Kinetics studies the forces producing changes in fluid motion
• Study includes both kinematic and kinetic considerations
• Motion of fluids predicted in same ways as solids are predicted using physical laws and properties of fluid
• The flow of fluids can be classified in these ways: Steady / Unsteady, Uniform / Non-uniform, One, two, and three dimensional, Compressible / Incompressible,Laminar / Turbulent
• Uniform flow is when flow velocity is the same in magnitude direction
• Non-uniform flow is when is not the same at other points
• Steady Flow is when conditions that are not changing do not change with time
• Unsteady flow is when the conditions change with time
• Compressible is when density of the fluid is not constant -Incompressible is when fluid density is a constant
• Fluid flow is three-dimensional means that flow parameters change in the coordinate System
• Two dimensional if parameters alter in direction to flow
• An Empty bucket example, If the mass rate of water is 1.7Kg mass volume
• volume flow rate is Q = = vm density time time
• discharge v= A*U
• Conservation of mass is principle entering mass + leaving mass = increase of water in control density * ( delta)A * u1 + density (delta)u2 + water in control volume or = density * ( delta)a1,um1 += density *(delta)u2,um2
• Steady flow is incompressible and equation that governs is used again and again and throughout course. A1,U2= constant
• This equation applies to two pipes and cross sections which is constant over time Energy: the summery of pressure. Energy, kinetic energy and potential = Bernaulli equation
• p+ 1/ 2 pu ^2 - pgh

Dimensional Analysis and Hydraulic Similitude

• Introduces the combination of theory with experiment
• Dimensionless parameters provide are a way to get there
• Dimensionless Parameters can be generated from all those things Physical, Analysis and Symettry
• Model is used to define a system testing where it is to be predetermined and tested.
• Protype the opposite
• Dimensions are measureable physical quantities without numerical dimension is where units are that standards are use and the quantity has dimensions
• In fluid mechanics, the four dimensions are: mass, length, lime
• Buckingham theorm is important to know.
• Geometric similitude model to pratotype
• kinematic similitude time and geometry
• Dynamic simplitude is that rates are proportional to model rate
• Types of forces or parameters are Reynold. Froude. Eulet. weber numbers

Flow in Pipes and Ducts

• Flow of fluids depends of prevailing conditions. The rate is smooth or nor
• Flow of a pipe is either compressible or incompressible ( fluids though pipes is newtonian)
• Flow of a newton in is (laminar - turbo)
• Laminar is known as stream, Viscous and other examples include arteries Random. Irregular- Hanzord Movement = velocity grade near the sound Constant based on regulators' numbers

Test your knowledge of fluid properties including mass density, specific volume, weight density, and specific gravity. Understand fluid behavior under compression and explore different types of fluid flow.