Title 1 Fluid Properties.pdf ✅

HGE 1: Fluid Properties 1.1. Introduction to Fluid Mechanics Fluid mechanics is the study of the behavior of fluids that are either at rest or in motion. Fluids refer to any homogeneous substance that can flow, such as liquids or gases. The following are the branches of fluid mechanics: • Hydrostatics. Study of liquids at rest. • Hydrodynamics. Study of liquids in motion. (Study of gases in motion is aerodynamics) • Hydraulics. Study of mechanical properties of liquids. (Study of mechanical properties of gases is pneumatics) • Hydrology. Study of water on Earth. 1.2. Basic Fluid Properties • Density (ρ). Refers to the mass of the fluid that is contained in a unit of volume. ρ = mass volume ρ = m V • Unit weight (γ). Also called specific weight. Refers to the weight of the fluid per unit volume. γ = weight volume γ = W V Recall that the weight of an object is its mass multiplied by the acceleration due to gravity. γ = mg V γ = ( m V ) g γ = ρg • Specific Gravity (SG or G). A dimensionless quantity defined as the ratio of the density to that of some other substance that is taken as standard. The most common standard substance is water for solids and liquids and air for gases. SG = ρsubstance ρstandard Multiplying both the numerator and denominator by the acceleration due to gravity (γ = ρg), SG = ρsubstanceg ρstandardg SG = γsubstance γstandard The common values for the density and unit weight of water are 1000 kg/m3 , 1 g/cm3 , 9810 N/m3 , 9.81 kN/m3 , and 62.4 lb/ft3 . Water also has its maximum unit weight at 4°C.
• Specific Volume. Refers to the volume occupied by a unit mass of fluid. spv = volume mass spv = V m = 1 ρ In terms of the unit weight, spv = g γ 1.3. Viscosity • Absolute Viscosity (μ). Also called dynamic viscosity. Refers to a fluid’s resistance to shearing stresses. absolute viscosity = shearing stress velocity gradient μ = τ dv dy τ = μ( dv dy) The velocity gradient is the change of velocity in the fluid at some point away from the force causing the shear stress. In ideally plastic fluids, the velocity gradient is linear. τ = μ ( v y ) (for ideally plastic fluids) Its common unit in the metric system is Pa-s. Another common unit is poise, equivalent to 0.1 Pa-s. • Kinematic Viscosity (ν). Refers to the ratio of the dynamic viscosity (μ) of the fluid to its mass density (ρ). ν = μ ρ Its common unit in the metric system is m2 /s. Another common unit is the stoke, equivalent to 0.0001 m2 /s.

For the pressure inside a bubble, there are two surfaces in contact with air (the air inside and outside the bubble). Thus, the surface tension is doubled. 2σ(πD) = P ( 1 4 πD 2) P = 8σ D For the pressure inside a droplet, there is only one surface in contact with air, so the pressure is halved. P = 4σ D Fluid Properties. • Density. ρ = m V • Unit Weight. γ = W V • Specific Gravity. SG = ρsubstance ρstandard • Specific Weight. spv = V m • Absolute Viscosity. τ = μ ( dv dy) • Kinematic Viscosity. ν = μ ρ • Capillary Rise. h = 4σ cos θ γD or 2σ cos θ γR • Pressure inside a bubble. P = 8σ D • Pressure inside a droplet. P = 4σ D