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# Definition Applied to Fluids in Motion

الكلية كلية الهندسة     القسم  الهندسة البيئية     المرحلة 3
أستاذ المادة عدي عدنان جهاد الخيكاني       05/10/2012 16:37:55
Definition Applied to Fluids in Motion
For example, consider the fluid shown flowing along a fixed surface. At the surface there will be little movement of the fluid (it will ‘stick’ to the surface), whilst further away from the surface the fluid flows faster (has greater velocity):

If one layer of is moving faster than another layer of fluid, there must be shear forces acting between them. For example, if we have fluid in contact with a conveyor belt that is moving we will get the behaviour shown:

Ideal fluid Real (Viscous) Fluid

When fluid is in motion, any difference in velocity between adjacent layers has the same effect as the conveyor belt does.
Therefore, to represent real fluids in motion we must consider the action of shear Forces.

Consider the small element of fluid shown, which is subject to shear force and has a dimension s into the page. The force F acts over an area A = BC×s. Hence we have a shear stress applied:
Stress = Force/Area

? = F/A
Any stress causes a deformation, or strain, and a shear stress causes a shear strain. This shear strain is measured by the angle ? .
Remember that a fluid continuously deforms when under the action of shear. This is different to a solid: a solid has a single value of ? for each value of ? . So the longer a shear stress is applied to a fluid, the more shear strain occurs. However, what is known from experiments is that the rate of shear strain (shear strain per unit time) is related to the shear stress:
Shear stress ? Rate of shear strain

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