Fluid mech

• Fluid Mechanics


  The study of fluids and the forces acting on them
• Fluid Mechanics in Education


  • Knowledge of fluid mechanics is essential because the majority of different processes and operations in the laboratory are conducted either partly or totally in the fluid phase
  • Fluids are more efficient and cost-effective to work with compared to solids
• Fluid


  A substance that will deform continuously when subjected to a tangential or shear force

  
• Newtonian fluids


  • Fluids that behave according to simple laws, such as water, oil, and air
  • Exhibit constant viscosity but virtually no elasticity
• Non-Newtonian fluids


  • Fluids whose viscosity is not constant or which exhibit significant elasticity
  • Examples include polymeric materials, drilling mud, and toothpaste
• States of matter


  • Liquids
  • Gases
• Liquid


  Characterized by relatively high densities and viscosities, with molecules close together, and volumes that tend to remain constant
• Gas


  Characterized by relatively low densities and viscosities, with molecules far apart, and will rapidly tend to fill the container in which they are placed
• The transition from liquid to gas is a continuous and gradual process, not a single point
• Stress


  A force per unit area, including normal stress (perpendicular to the surface) and shear stress (tangential to the surface)
• Pressure


  A scalar quantity that measures the degree of compression of a fluid, independent of the orientation of the surface

  
• Velocity


  The rate of change of the position of a fluid particle with time, having both magnitude and direction
• Volumetric flow rate, mass flow rate, and momentum flow rate


  1. Volumetric flow rate (Q = uA)

  2. Mass flow rate (m = ρQ = ρuA)

  3. Momentum flow rate (Ṁ = mu = ρu²A)
• Conservation laws


  Conservation of mass, energy, and momentum
• To solve a fluid mechanics problem, information is needed on the physical properties of the fluid and a constitutive equation relating stresses to the flow pattern
• The Law of Conservation of Energy and the Law of Conservation of Momentum
• Density


  Mass per unit volume, indicates inertia or resistance to an accelerating force

  
• Viscosity


  Resistance to flow under an applied shear stress
• Surface tension


  Tendency of the surface of a liquid to behave like a stretched elastic membrane
• Physical properties depend primarily on the particular fluid
• For liquids, viscosity depends strongly on temperature
• For gases, viscosity is approximately proportional to the square root of the absolute temperature
• The density of gases depends almost directly on the absolute pressure
• For most other cases, the effect of pressure on physical properties can be disregarded
• Typical processes often run almost isothermally, and in these cases the effect of temperature can be ignored
• Except in certain special cases, we shall ignore any variation of physical properties with pressure and temperature
• Density of liquids


  Depends on the mass of an individual molecule and the number of such molecules that occupy a unit of volume
• Degrees A.P.I. (American Petroleum Institute)


  Related to specific gravity s, by the formula: ◦A.P.I. = 141.5/s - 131.5
• For water, ◦A.P.I. = 10, with correspondingly higher values for liquids that are less dense
• For the crude oil listed in Table 1.1, ◦A.P.I. = 35
• Density of ideal gases


  Depends on the molecular weight, absolute pressure, and absolute temperature

  
• Compressibility factor Z


  Introduced for nonideal gases to account for deviation from ideal gas behaviour
• Isothermal compressibility of a gas


  Fractional decrease in volume caused by a unit increase in pressure
• Coefficient of thermal expansion α

  Isobaric (constant pressure) fractional increase in volume per unit rise in temperature
• Specific gravity s


  Ratio of the density ρ to the density ρSC of a reference fluid at some standard condition
• For liquids, ρSC is usually the density of water at 4 ◦C, which equals 1.000 g/ml or 1,000 kg/m3
• For natural gas, the gas gravity is defined as the ratio of the molecular weight of the gas to that of air (28.8 lbm/lb-mol)
• Viscosity


  Resistance to flow under an applied shear stress, measured by the proportionality constant μ between shear stress and velocity gradient
• Kinematic viscosity ν


  Ratio of the viscosity to the density, important when viscous and gravitational forces coexist
• Viscosity of liquids


  Varies approximately with absolute temperature T according to the formula: μ = a * exp(b/T)