12-10-2012, 12:03 PM
Fluid Dynamics
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Equations of Motion
The dynamics of fluid flow is the study of fluid motion with forces causing flow. The dynamic
behaviors of the fluid flow is analyzed by the Newton’s law of motion (F=ma), which relates
the acceleration with the forces. The fluid is assumed to be incompressible and non-viscous.
• The pressure force ‘Fp’ is exerted on the fluid mass, if there exists a pressure gradient
between the 2 parts in the direction of flow.
• The gravity force ‘Fg’ is due to the weight of the fluid and it is equal to ‘Mg’. The
gravity force for unit volume is equal to ‘g’.
• The viscous force ‘Fv’ is due to the viscosity of the flowing fluid and thus exists in the
case of all real fluid.
• The turbulent flow ‘Ft’ is due to the turbulence of the flow. In the turbulent flow, the
fluid particles move from one layer to other and therefore, there is a continuous
momentum transfer between adjacent layer, which results in developing additional
stresses(called Reynolds stresses) for the flowing fluid.
• The surface tension force ‘Fs’ is due to the cohesive property of the fluid mass. It is,
however, important only when the depth of flow is extremely small.
• The compressibility force ‘Fe’ is due to elastic property of fluid and it is important only
either for compressible fluids or in the cases of flowing fluids in which the elastic
properties of fluids are significant.