Please remember all the unit that you use in your calculation. There are no marks for correct answer without unit.

Transcription

1 CHAPTER 1 : PROPERTIES OF FLUIDS What is fluid? A fluid is defined as a substance that deforms continuously when acted on by a shearing stress at any magnitude. In a fluid at rest, normal stress is called pressure. Unit: Please remember all the unit that you use in your calculation. There are no marks for correct answer without unit. Please be careful about this.

2 DENSITY Designated by the Greek symbol ρ (rho). Defined as its mass per unit volume. ρ = mass volume = kg m _ Specific volume, ν is the volume per unit mass. This property is not commonly used in fluid mechanics but is used widely in thermodynamics. ν = volume mass = 1 ρ = m_ kg Please remember all the basic properties of common fluids

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4 Density also change with temperature!

5 SPECIFIC WEIGHT Designated by the Greek symbol γ (gamma). Defined as its weight per unit volume. γ = weight volume = mass gravity volume = kg g m _ = ρg Unit: jk l m n m atau o l p

6 SPECIFIC GRAVITY Designated as SG. Defined as the ratio of the density of the fluid to the density of water at some specified temperature. Usually the specified temperature is taken as 4 C. SG = ρ vwxyz ρ { }~ } Unit: Dimensionless

7 THE PERFECT GAS All the common gases follow with reasonable accuracy, at least in some finite region, the so-called ideal or perfect gas law: p = ρrt R is called the gas constant which is the ratio of Boltzmann s constant to the mass of a single molecule: R = K m alternatively, R may be written in terms of the molecular weight, M of the gases: R k n = R Œ 8314 (J/kg mol K) = M k n M k n (mol) Unit: J kg K

8 VISCOSITY Viscosity is a measure of a fluid's resistance to flow. It describes the internal friction of a moving fluid. A fluid with large viscosity resists motion because its molecular makeup gives it a lot of internal friction. A fluid with low viscosity flows easily because its molecular makeup results in very little friction when it is in motion. Gases also have viscosity, although it is a little harder to notice it in ordinary circumstances.

9 No slip condition: Particles close to a surface do not move along with a flow when adhesion is stronger than cohesion. At the fluid-solid interface, the force of attraction between the fluid particles and solid particles (Adhesive forces) is greater than that between the fluid particles (Cohesive forces). This force imbalance brings down the fluid velocity to zero. For a given motion V of the upper plate, τ is constant, hence zx z is constant, so that the resulting velocity profile is linear across the plate.

10 τ = μ du dy The quantity μ, called the coefficient of viscosity of a Newtonian fluid. Also called as dynamic viscosity. Unit: N s/m or kg/m s Example: water, common oils, common gases

11 If the coefficient μ nonlinear, the fluid is said to be non-newtonian. Example: toothpaste, shampoo, paint or blood.

12 Pseudoplastic fluid or shear-thinning fluid: Its local viscosity decreases with increasing stress. Dilatant fluid or shear-thickening fluid: Its local viscosity increases with increasing stress. In this situation, there is only a single finite strain rate in this flow. ε = 1 2 u y + v x = 1 u 2 y = 1 du 2 dy τ = 2με = μ du dy

13 A simple but often effective analytic approach to non-newtonian behavior is the power-law approximation of Ostwald and de Waele: τ 2Kε where K and n are material parameters which in general vary with the pressure and temperature (and composition in the case of mixture). The exponent n delineates three cases. n < 1 Pseudoplastic n = 1 Newtonian K = μ n > 1 Dilatant

14 COMMON DIMENSIONLESS PARAMETERS Consider a relatively general relationship between the pressure drop p, a length L, a characteristic velocity V, the density ρ, the viscosity μ, the gravity g, the surface tension σ, the sound of speed c and an angular frequency ω, written as: The pi-theorem applied to this problem, with L, V and ρ as repeating variables, results in: p ρv = f ρvl μ, V gl, V c, Lω V, V ρl σ

15 Euler number: Reynolds number: Froude number: Eu = p ρv Re = ρvl μ Fr = V gl Mach number: M = V c

16 Strouhal number: St = Lω V Weber number: We = V ρl σ

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