Properties: Density and Viscosity

The properties outlines below are general properties of fluids which are of interest in engineering. The symbol usually used to represent the property is specified together with some typical values in SI units for common fluids. Values under specific conditions (temperature, pressure etc.) can be readily found in many reference books. The dimensions of each unit is also give in the MLT system (see later in the section on dimensional analysis for more details about dimensions.)

  1. Density

    2. The density of a substance is the quantity of matter contained in a unit volume of the substance. It can be expressed in three different ways.

    1. Mass Density

      Mass Density, , is defined as the mass of substance per unit volume.

      Units: Kilograms per cubic metre, (or )

      Dimensions:

      Typical values:

      Water = 1000, Mercury = 13546 Air = 1.23, Paraffin Oil = 800.

      (at pressure =1.013and Temperature = 288.15 K.)

    2. Specific Weight

      Specific Weight , (sometimes , and sometimes known as specific gravity) is defined as the weight per unit volume.

      or

      The force exerted by gravity, g, upon a unit volume of the substance.

      The Relationship between g and can be determined by Newton's 2nd Law, since

      weight per unit volume = mass per unit volume g

      Units: Newton's per cubic metre, (or )

      Dimensions:.

      Typical values:

      Water =9814 , Mercury = 132943 , Air =12.07 , Paraffin Oil =7851

    3. Relative Density

      Relative Density, , is defined as the ratio of mass density of a substance to some standard mass density.

      For solids and liquids this standard mass density is the maximum mass density for water (which occurs at c) at atmospheric pressure.

      Units: None, since a ratio is a pure number.

      Dimensions: 1.

      Typical values: Water = 1, Mercury = 13.5, Paraffin Oil =0.8.

    4. Viscosity

      Viscosity, m, is the property of a fluid, due to cohesion and interaction between molecules, which offers resistance to sheer deformation. Different fluids deform at different rates under the same shear stress. Fluid with a high viscosity such as syrup, deforms more slowly than fluid with a low viscosity such as water.

      All fluids are viscous, "Newtonian Fluids" obey the linear relationship

      given by Newton's law of viscosity. , which we saw earlier.

      where is the shear stress,

      Units ;

      Dimensions.

      is the velocity gradient or rate of shear strain, and has

      Units: ,

      Dimensions

      is the "coefficient of dynamic viscosity" - see below.

      1. Coefficient of Dynamic Viscosity

        The Coefficient of Dynamic Viscosity, , is defined as the shear force, per unit area, (or shear stress ), required to drag one layer of fluid with unit velocity past another layer a unit distance away.

        Units: Newton seconds per square metre, or Kilograms per meter per second,.

        (Although note that is often expressed in Poise, P, where 10 P = 1 .)

        Typical values: Water =1.14 , Air =1.78 , Mercury =1.552 ,
        Paraffin Oil =1.9 .

        Kinematic Viscosity

        Kinematic Viscosity, , is defined as the ratio of dynamic viscosity to mass density.

        Units: square metres per second,

        (Although note that n is often expressed in Stokes, St, where St = 1 .)

        Dimensions: .

        Typical values: Water =1.14 , Air =1.46 , Mercury =1.145 ,
        Paraffin Oil =2.375 .