Читать книгу Hydraulic Fluid Power - Andrea Vacca - Страница 33

Each fluid particle can experience surface forces, due to pressure or friction that are generated by contact with other particles or a solid surface. These surface forces lead to stresses. The concept of stress helps in describing how forces acting on the boundaries of a medium are transmitted throughout the medium itself. The concept of stress is very intuitive for a solid: stresses develop when the material is elastically deformed or strained. For example, when a force is applied to a solid part, such as a cantilever beam, stresses are generated within it. In contrast, if the medium is a fluid, stresses can be generated by motion rather than by deflection. In particular, shear stresses in fluids arise due to viscous flow. For this reason, while solids are elastic, fluids are viscous.

The shear effects can be visualized through the classic example of a flow between parallel plates (Figure 2.6). For a fluid at rest, there will be no shear stresses. This corresponds to the rest condition for a fluid element highlighted in Figure 2.6a. Now suppose that a rightward force dF is applied to the upper plate, dragging it across the fluid at a certain velocity. The relative shearing of the plates produces a shear stress τ, which acts on the fluid element:

(2.13)

where dA is the area of contact of the fluid element with the plate.

Figure 2.6 Shear stress in a fluid: initial rest condition (a) and (b) after a force is applied.

As one can guess from Figure 2.6, under the action of the force applied to the plate, the fluid element will continue deforming, with a rate that can be measured by the angle dα. It is possible to demonstrate that deformation rate can be expressed in terms of the velocity of the upper plate du [15]:

(2.14)

Therefore, the fluid element subjected to a shear stress τ experiences a rate of deformation (or shear rate) given by du/dy. This fact is valid for any fluid. However, the relationship between τ and du/dy varies for different types of fluids. Fluids in which the shear stress is proportional to the shear rate are called Newtonian fluids. Common fluids, such as water and air, and hydraulic fluids behave as Newtonian fluids in most conditions.

The constant of proportionality between shear rate and shear stress is defined as absolute or dynamic viscosity, τ:

(2.15)

The value of dynamic viscosity can be reported with different units: the SI system uses kg/(m s) (or Pa · s), but it is also common to find the dynamic viscosity expressed in poise, where 1 P corresponds to 1 g/(cm s) ¹. One centipoise (cP) corresponds to 0.001 kg/(m s).

Sometimes, the viscosity can be expressed as ratio between absolute viscosity and density. This ratio is also referred to as kinematic viscosity:

(2.16)

The common unit for ν is the Stoke, where 1 Stoke corresponds to 1 cm²/s. At room temperature (300 K), the dynamic viscosity of the water is 0.89 cP, while typically hydraulic fluids have much higher viscosity, typically higher than 30 cP.

Usually, viscosity cannot be estimated well from theoretical relations, and experimental devices (viscometers) are commonly used to determine the value of viscosity of a given fluid.