Consider the Navier-Stokes equations with constant density it their dimensional form: Consider the Navier-Stokes equations with constant density it their dimensional form:
The Reynolds number Re is the only dimensionless parameter which is always important in simplifying the equations of fluid motion for various applications. The Reynolds number Re is the only dimensionless parameter which is always important in simplifying the equations of fluid motion for various applications. Reynoldsification helps in simplifying NS equations by ingnoring less important terms.This simplification helps in obtaining analytical solutions to engineering parameters like friction factor.Better understanding of the complexity of real fluid flow is achieved by fitting the situation into Reynolds frame work.
These are flows with Reynolds number lower than unity, Re<< 1. Since Re = UL/, the smallness of Re can be achieved by considering by dealing with a highly viscous liquid, or
The choice Re << 1 is an very interesting and important assumption. The choice Re << 1 is an very interesting and important assumption.It is relevant to many practical problems, especially in a world where fluid devices are shrinking in size. A particularly interesting application is to the swimming of micro-organisms. This assumption, unveils a special dynamical regime which is usually referred to as Stokes flow.To honor George Stokes, who initiated investigations into this class of fluid problems. We shall also refer to this general area of fluid dynamics as the Stokesian realm.This is of extreme contrast to the theories of ideal inviscid flow, which might be termed the Eulerian realm.
Re is indicative of the ratio of inertial to viscous forces. Re is indicative of the ratio of inertial to viscous forces.The assumption of small Re means that viscous forces dominate the dynamics. That suggests that to drop entirely the term Dv/Dt from the Navier-Stokes equations.This renders the linear system. The linearity of the problem will be a major simplification.
Redefine the dimensionless pressure as pL/(2μU) instead of p/(U2).
The basic assumption of creeping flow was developed by Stokes (1851) in a seminal paper. The basic assumption of creeping flow was developed by Stokes (1851) in a seminal paper.This states that density (inertia) terms are negligible in the momentum equation.Under non-gravitational field.
How does sedimentation vary with the size of the sediment particles? How does sedimentation vary with the size of the sediment particles?What electric field is required to move a charged particle in electrophoresis?What g force is required to centrifuge cells in a given amount of time.What is the effect of gravity on the movement of a monocyte in blood?How rapidly do enzyme-coated beads move in a bioreactor?The flow geometry of all above mentioned applications is flow past a sphere. Define the term vorticity in spherical coordinate system.
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