Fluid Characteristics and Viscosity

A fluid is defined as a substance that deforms continuously under application of a shearing stress, regardless of how small the stress. Blood is the primary example of a biological material that behaves as a fluid about which I will write in this text. To study the behavior of materials that act as fluids, it is useful to define a number of fluid parameters. A list of important fluid characteristics would include density, specific weight, specific gravity, and viscosity.

Density is defined as the mass per unit volume of a substance and is given by the Greek character p (rho). The SI units for p are kg/m3 and the approximate density for blood is 1060 kg/m3. Blood is slightly denser than water, and red blood cells in plasma2 will settle to the bottom of a test tube, over time, due to gravity.

Specific weight is defined as the weight per unit volume of a substance. The SI units for specific weight are N/m3. Specific gravity, s, is the ratio of the weight of a liquid at a standard reference temperature to the weight of water. For example, the specific weight of mercury, SHG = 13.6 at 20 °C. Specific gravity is a unitless parameter.

Density and specific weight are measures of the "heaviness" of a fluid, but two fluids with identical density and specific weight can flow quite differently when subjected to the same forces. You might ask, "What is the additional property that determines the difference in behavior?" That property is viscosity.

1.2.1 Displacement

To understand viscosity, begin by imagining a hypothetical fluid between two parallel plates which are infinite in width and length. See Fig. 1.3.

The bottom plate A is a fixed plate. The upper plate B is a moveable plate, suspended above plate A on the fluid between the two plates. The vertical distance between the two plates is represented by h. A constant force F is applied to the moveable plate B causing it to move along at a constant velocity, VB, with respect to the fixed plate.

If we replace the fluid between the two plates with a solid, the behavior of the plates would be different. The applied force F would create a displacement, d, a shear stress, t, in the material, and a shear strain, g. After a small, finite displacement, motion of the upper plate would cease.

If we then replace the solid between the two plates with a fluid, and reapply force F, the upper plate will move continuously, with a velocity of VB. This behavior is consistent with the definition of a fluid; a material that deforms continuously under the application of a shearing stress, regardless how small the stress.

2Plasma has a density very close to that of water.

(constant)

(constant)

Figure 1.3 Moveable plate suspended over a layer of fluid.

Figure 1.3 Moveable plate suspended over a layer of fluid.

After some finite length of time, dt, a line of fluid that was vertical at time = 0 will move to a new position as shown by the dashed line in Fig. 1.3. The angle between the line of fluid at t = 0 and the line of fluid at t = t + dt, is defined as the shearing strain. Shearing strain is represented by the Greek character g (gamma).

The first derivative of the shearing strain with respect to time is known as the rate of shearing strain, dg/dt. For small displacements, tan(dg) is approximately equal to dg. The tangent of the angle of shearing strain can also be represented as follows:

tan(dg)

opposite _ VBdt adjacent h

Therefore, the rate of shearing strain, dg/dt can be written:

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