Fluids and Their Properties - Comprehensive Notes

1953 PWC

• Innovation Is Our Tradition.
• Fluids and Their Properties
• Module 3

Production Line for milk processing

• Pasteurized Milk
• Raw Milk
• Milk Tank
• 10 D-Pump
• Chilled Water
• Cold Water
• Steam-
• IIM
• Heated water
• Holding Tube
• Homogenizer

Fluid Mechanics Overview

• Fluid Mechanics
  • Gas
    • Air, He, Ar,
    • N₂, etc.
    • Compressibility
  • Liquids
    • Water, Oils
    • Alcohols,
    • etc.
    • Density Viscosity
    • Surface
    • Tension
    • Vapor
    • Pressure
  • Statics
    • $\Sigma F = 0$
    • Stability
    • Buoyancy
    • Pressure
    • Fluid Statics
  • Dynamics
    • \Sigma F_i > 0, Flows
    • Compressible/
    • Incompressible
    • Laminar/
    • Turbulent
    • Steady/Unsteady
    • Viscous/Inviscid
    • Fluid Dynamics

WHAT IS A FLUID?

• Substance exists in three primary phases: solid, liquid, and gas. A substance in the liquid or gas phase is referred to as a fluid.

• Distinction between a solid and a fluid is made on the basis of the substance's ability to resist an applied shear (or tangential) stress (force per unit area) that tends to change its shape.

• Distinction between solid and fluid?

  • Solid: can resist an applied shear by deforming but will not continuously deform.
  • Fluid: deforms continuously under applied shear.

• Fig. 1.1 Difference in behavior of a solid and a fluid due to a shear force.

WHAT IS A FLUID? cont.

• Stress is defined as force per unit area and is determined by dividing the force by the area upon which it acts. The normal component of the force acting on a surface per unit area is called the normal stress, and tangential component of a force acting on a surface per unit area is called shear stress. In a fluid at rest, the normal stress is called pressure.
• $Normal stress: \sigma = \frac{F_N}{dA}$
• $Shear stress: \tau = \frac{F_T}{dA}$
• A fluid at rest is at a state of zero shear stress. When walls are removed or a liquid container is tiled, a shear develops as the liquid moves to re-establish a horizontal free surface.

WHAT IS A FLUID? cont.

• Liquid
  • Group of molecules can move relative to each other, but the volume remains relatively constant because of strong cohesive forces between the molecules. As a result, a liquid takes the shape of the container it is in, and it forms a free surface in a larger container in a gravitational field.
• Gas
  • Expands until it encounters the walls of the container and fills the entire available space because cohesive forces are very small.
  • Gases cannot form a free surface.
  • Compressible.
  • Density not constant with pressure
  • Gas and vapor are often used as synonymous words

Properties of Fluids

• Any characteristic of a system is called a property.
  • Familiar: pressure P, temperature T, volume V, and mass m.
  • Less familiar: viscosity, thermal conductivity, modulus of elasticity, thermal expansion coefficient, vapor pressure, surface tension.
• Intensive properties are independent of the mass of the system. Examples: temperature, pressure, and density.
• Extensive properties are those whose value depends on the size of the system. Examples: Total mass, total volume, and total momentum.
• Extensive properties per unit mass are called specific properties. Examples include specific volume $v = \frac{V}{m}$ and specific total energy $e = \frac{E}{m}$.

What is rheology anyway?

• Rheology = the study of deformation and flow.

Applications of Rheology

• Process engineering calculations – Pumping requirements, extrusion, mixing, heat transfer, homogenization, spray coating
• Determination of ingredient functionality – Consistency, stickiness etc.
• Quality control of ingredients or final product – By measurement of viscosity, compressive strength etc.
• Determination of shelf life – By determining changes in texture
• Correlations to sensory tests – Mouthfeel

What is rheology anyway? Cont.

• Rheology affects:
  • Processing (design, costs, production rates)
  • End use (food texture, product pour, motor-oil function)
  • Product quality (surface distortions, anisotropy, strength, structure development)

Examples of Types of Fluids

• Newtonian: Water, clear fruit juices, milk, honey, vegetable oil, corn syrup
• Shear thinning (Pseudoplastic): Applesauce, banana puree, orange juice concentrate, French mustard, dairy cream
• Dilatant: Some types of honey, 40% raw corn starch solution
• Bingham plastic: Tomato paste, toothpaste
• Herschel-Bulkley: Minced fish paste, raisin paste

Strain and Strain (Shear) Rate

• Strain
  • a dimensionless quantity representing the relative deformation of a material
  • Normal Strain
  • Shear Strain

Shear Stress

• Shear Stress is the intensity of force per unit area

Measures of Fluid Mass and Weight: Density

• The density of a fluid is defined as mass per unit volume.
• $\rho = \frac{m}{v}$
• m = mass, and v = volume.
• Different fluids can vary greatly in density
• Liquids densities do not vary much with pressure and temperature
• Gas densities can vary quite a bit with pressure and temperature
• Density of water at 4° C: $1000 \frac{kg}{m^3}$
• Density of Air at 4° C : $1.20 \frac{kg}{m^3}$
• Alternatively, Specific Volume:
  • $\frac{1}{\rho}$

Measures of Fluid Mass and Weight: Specific Weight

• The specific weight of fluid is its weight per unit volume.
• $\gamma = \rho g$
• g = local acceleration of gravity, $9.807 \frac{m}{s^2}$
• Specific weight characterizes the weight of the fluid system.
• Specific weight of water at 4° C: $9.80 \frac{kN}{m^3}$
• Specific weight of air at 4° C : $11.9 \frac{N}{m^3}$

Measures of Fluid Mass and Weight: Specific Gravity

• The specific gravity of fluid is the ratio of the density of the fluid to the density of water @ 4° C.
• $SG = \frac{\rho}{\rho<em>{H</em>2O}}$
• Gases have low specific gravities
• A liquid such as Mercury has a high specific gravity, 13.2
• The ratio is unitless.
• Density of water at 4° C : $1000 \frac{kg}{m^3}$

Viscosity: Kinematic Viscosity

• $\nu = \frac{\mu}{\rho}$
• Kinematic viscosity is another way of representing viscosity
• Used in the flow equations.
• The units are of $L^2/T$ or $m^2/s$ and $ft^2/s$

EXAMPLE

• Calculate the weight of a reservoir of oil if it has a mass of 825 kg.
• Solution
  • $w = 825 kg \times 9.81 \frac{m}{s^2} = 8093 kg \frac{m}{s^2}$
  • $w = 8093 N = 8.093 \times 10^3 N = 8.093 kN$
• EXAMPLE
  • 5. 6m³ of oil weighs 46 800 N. Find its mass density, p, and relative density, g.
• Solution
  • Weight 46 800 mg
  • $\text{Mass } m = \frac{46800}{9.81} = 4770.6 kg$
  • $\text{Mass density, } \frac{\text{Mass}}{\text{volume}} = \frac{4770.6}{5.6} = 852 \frac{kg}{m^3}$
  • $\text{Relative density } SG = \frac{\rho}{\rho<em>{H</em>2O}} = \frac{852}{1000} = 0.852$

EXAMPLE cont.

• The density of an oil is $850 \frac{kg}{m^3}$. Find its relative density and Kinematic viscosity if the dynamic viscosity is $5 \times 10^{-3} \frac{kg}{ms}$.
• Solution
  • $\rho_{oil} = 850 \frac{kg}{m^3}$
  • $\rho_{water} = 1000 \frac{kg}{m^3}$
  • $SG_{oil} = \frac{850}{1000} = 0.85$
  • Dynamic viscosity = m = $5 \times 10^{-3} \frac{kg}{ms}$
  • Kinematic viscosity = $\nu = \frac{\mu}{\rho} = \frac{5 \times 10^{-3}}{1000} = 5 \times 10^{-6} \frac{m^2}{s}$

Examples of Surface Tension

• Water droplets from rain hang from branches or leaves of trees (Picture)

WHAT IS SURFACE TENSION

• The cohesive forces between molecules down into a liquid are shared with all neighboring atoms. Those on the surface have no neighboring atoms above, and exhibit stronger attractive forces upon their nearest neighbors on the surface. This enhancement of the intermolecular attractive forces at the surface is called surface tension.

Drops Spherical

• Why are drops spherical?

Capillary Effect

• Capillary effect: The rise or fall of a liquid in a small-diameter tube inserted into the liquid.
• Capillaries: Such narrow tubes or confined flow channels.
• The capillary effect is partially responsible for the rise of water to the top of tall trees.
• Meniscus: The curved free surface of a liquid in a capillary tube.
• The strength of the capillary effect is quantified by the contact (or wetting) angle, defined as the angle that the tangent to the liquid surface makes with the solid surface at the point of contact.

Capillary Effect cont.

• When the attractive forces are between unlike molecules, they are said to be adhesive forces. The adhesive forces between water molecules and the walls of a glass tube are stronger than the cohesive forces (attraction between like molecules) lead to an upward turning meniscus at the walls of the vessel and contribute to capillary action.

Presure

• Pressure is the force on an object that is spread over a surface area. The equation for pressure is the force divided by the area where the force is applied. Although this measurement is straightforward when a solid is pushing on a solid, the case of a solid pushing on a liquid or gas requires that the fluid be confined in a container. The force can also be created by the weight of an object.
• $F = mg$
• $Pressure = \frac{F}{A} = \frac{\text{Weight}}{\text{Area}}$
• Unit of pressure is Pa

Vapor Pressure

• The pressure at which a liquid will boil is called its vapor pressure. This pressure is a function of temperature (vapor pressure increases with temperature). In this context we usually think about the temperature at which boiling occurs.
• For example, water boils at 100C at sea-level atmospheric pressure (1 atm abs). However, in terms of vapor pressure, we can say that by increasing the temperature of water at sea level to 100C, we increase the vapor pressure to the point at which it is equal to the atmospheric pressure (1 atm abs), so that boiling occurs.
• It is easy to visualize that boiling can also occur in water at temperatures much below 100°C if the pressure in the water is reduced to its vapor pressure. For example, the vapor pressure of water at 10°C is 0.01 atm.
• Therefore, if the pressure within water at that temperature is reduced to that value, the water boils. Such boiling often occurs in flowing liquids, such as on the suction side of a pump or tip regions of impellers. When such boiling does occur in the flowing liquids, vapor bubbles start growing in local regions of very low pressure (high velocity) and then collapse in regions of high downstream pressure (low viscosity). This phenomenon is called as cavitation. Cavitations must be avoided (or at least minimized) in most flow systems since it reduces performances, generates annoying vibrations and noise, and causes damage to equipment.

Evaporation Vs. Boiling

• Evaporation
  • Bubbles cannot form since the vapor pressure is less than atmospheric pressure.
• Boiling
  • Bubbles can form and rise since the vapor pressure can overcome atmospheric pressure.
• Saturation (or vapor) pressure of water at various temperatures

Force Equilibrium of a Fluid Element

• Fluid static is a term that is referred to the state of a fluid where its velocity is zero and this condition is also called hydrostatic.
• So, in fluid static, which is the state of fluid in which the shear stress is zero throughout the fluid volume.
• In a stationary fluid, the most important variable is pressure.
• For any fluid, the pressure is the same regardless its direction. As long as there is no shear stress, the pressure is independent of direction. This statement is known as Pascal's law

Force Equilibrium of a Fluid Element cont.

• Figure 2.1 Pressure acting uniformly in all directions
• Figure 2.2: Direction of fluid pressures on boundaries

Standard Atmosphere

• $P_{atm} = 1 atm = 101325 Pa = 760 mmHg = 760 torr = 1 bar$

Pressure Gauges

• The atmospheric pressure can be measured with a mercury barometer. Since the mass density of mercury is $\rho = 13600 \frac{kg}{m^3}$, the height of the mercury column is about
• $h = \frac{P_{atm}}{\rho g} = \frac{1.013 \times 10^5 Pa}{(13600 \frac{kg}{m^3})(9.8 \frac{m}{s^2})} = 760 mm = 0.76 m$
• The atmospheric pressure and sometimes other pressure are expressed in the unit of mm mercury. So $P_{atm} = 760 mm$ mercury.
• 1 mm mercury = 133.3 Pa = 1 torr

Pressure Gauges cont.

• Another kind of pressure gauges can be used to measure fluid pressure different from the atmospheric pressure:

• $P<em>{gauge} = P</em>2 - P_{atm} = \rho g h$

• Once the gauge pressure $P<em>{gauge}$ is measured, the value of the atmospheric pressure $P</em>{atm}$ is needed to calculate $P_2$ -- the absolute pressure:

• $P<em>1 = P</em>{gauge} + P<em>{atm} = \rho g h + P</em>{atm}$

Pressure Relationships

• $P<em>{abs} = P</em>{gages} + P_{atm}$