TAILIEUCHUNG - Mechanical Engineering Systems 2008 Part 7

Tham khảo tài liệu 'mechanical engineering systems 2008 part 7', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 142 Fluid mechanics this effect is caused by the gravitational attraction between the two planets but initially Newton thought that it was due to viscous drag in the celestial fluid or ether that was held to fill the universe. When Venus passed the earth it would shear this fluid in the relatively small gap between the two planets and there would be a resistance or drag force which would act to slow Venus down while speeding up the earth. Newton pursued this theory to the point of tabletop experiments with liquids and plates and produced an equation which basically describes and defines viscosity before discarding the idea in favour of gravity. The equation that Newton developed to define the viscosity of a fluid is Viscous shear stress viscosity X velocity gradient In its simplest form this can be applied to two flat plates one moving and one stationary in the following equation p - A h Here the force F applied to one of the plates each of area A and separated by a gap of width h filled with fluid of viscosity p produces a difference in velocity of u. The viscosity is correctly known as the dynamic viscosity and has the units of Pascal seconds Pa s . These are identical to N s m2 and kg m s. For the case where these two plates are adjacent lamina or layers F pA X velocity gradient We have replaced the term u h with something called the velocity gradient which will allow us later to apply Newton s equation to situations where the velocity does not change evenly across a gap. We can apply this to pipe flow if we now wrap the lamina into cylinders. Laminar flow in pipes Figure We said earlier that most fluid flow applications of interest to mechanical engineers involve turbulent flow but there are some increasingly important examples of laminar flow where the pipe diameter is small and the liquid is very viscous. The field of medical engineering has many such examples such as the flow of viscous blood along the small diameter tubes of a kidney dialysis .

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