Viscosity

Suppose we have two parallel plates with fluid filling the gap between them, and the top plate moving at a velocity ux relative to the bottom one, as shown in Figure 2.4. We choose axes as shown, with x in the direction of motion, and y across the gap between the plates. It is found experimentally at a macroscopic scale that fluid does not slip at a solid surface. Thus the bulk fluid immediately adjacent to each plate is considered to have the same speed and direction of movement as the plate.

However, at much smaller scale in the fluid, the molecules have the velocity of the fluid plus additional random (thermal) motion. This random molecular motion has the effect of transferring larger momentum (acquired from the top plate) downwards and smaller momentum (acquired from the bottom plate) upwards. This net diffusion of momentum limits the velocity v

Figure 2.4 Flow between two parallel plates.

Figure 2.4 Flow between two parallel plates.

gradient that the fluid can sustain, producing an internal friction opposing the horizontal slip in the flow. It is found that the shear stress (i.e. the force per unit area, in the direction indicated in Figure 2.4) is t = f (du/'dy) (2.9)

where f is the dynamic viscosity (unit Nsm-2). This viscosity is independent of t and 'du/'dy, and depends only on the composition and temperature of the fluid.

A closely related fluid parameter is kinematic viscosity, defined as v = f/p (2.10)

In incompressible fluids, the flow pattern often depends more directly on v than on f. By combining (2.9) and (2.10), we find that the units of v are

Thus v has the character of a diffusivity. That is to say, the time taken for a change in momentum to diffuse a distance x is x2/v (cf. thermal diffusivity k defined in (3.15)). Typical values of v are given in Appendix B.

Renewable Energy 101

Renewable energy is energy that is generated from sunlight, rain, tides, geothermal heat and wind. These sources are naturally and constantly replenished, which is why they are deemed as renewable. The usage of renewable energy sources is very important when considering the sustainability of the existing energy usage of the world. While there is currently an abundance of non-renewable energy sources, such as nuclear fuels, these energy sources are depleting. In addition to being a non-renewable supply, the non-renewable energy sources release emissions into the air, which has an adverse effect on the environment.

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