Centripetal acceleration centrifugal force

Centripetal and Centrifugal Acceleration A centripetal body force is required to sustain a body of mass moving along a curve tra-jec tory. The force acts perpendicular to the direction of motion and is directed radially inward. The centripetal acceleration, which follows the same direction as the force, is given by the kinematic relationship ... 

Next we turn to the stability of Couette flow for parallel rotating cylinders. This is an important flow for various applications, and, though it is a shear flow, the stability is dominated by the centrifugal forces that arise because of centripetal acceleration. This problem is also an important contrast with the first two examples because it is a case in which the flow can actually be stabilized by viscous effects. We first consider the classic case of an inviscid fluid, which leads to the well-known criteria of Rayleigh for the stability of an inviscid fluid. We then analyze the role of viscosity for the case of a narrow gap in which analytic results can be obtained. We show that the flow is stabilized by viscous diffusion effects up to a critical value of the Reynolds number for the problem (here known as the Taylor number). 

The variables in (12-114) including the coefficients C[ and C 2 are all dimensional, as indicated by the fact that they are primed. We see that the fluid moves in circular paths and thus the fluid particles undergo a centripetal acceleration. However, the centrifugal force associated with this centripetal acceleration does not produce a secondary flow, because it is exactly balanced by a radial pressure gradient,... 

It was widely appreciated by Newton and his contemporaries that the compressive effect of the Cartesian aether was equivalent to some hypothetical force, often likened to gravity, that puUs a planet towards the central star and bends its rectilinear motion around into a closed curve. The magnitude of such a force had to be sufficient to balance the centrifugal, potter s wheel, effect and so prevent the rotating planet firom escaping. It became vitally important to calculate the centripetal acceleration that was needed to stabilize such a closed orbit. 

The wind Fgr satisfying this equation is called the gradient wind. Although the flow is steady, it is curved and hence there is a centripetal acceleratioa This acceleration is measured by the term V /r and may be considered to define a centrifugal force per unit mass. Therefore, the gradient wind may be seen as a balance between centrifugal, Coriolis, and pressure gradierrt forces. 

If we observe the element from a coordinate system, which is not fixed in space by rotating with the element, the centripetal acceleration will not be observed, but will appear as an apparent force directed away from the axis of rotation, the centrifugal force (Fig. 2.1.1 b). This latter force is similar in nature to the gravity force, and acts away from the axis of rotation with a magnitude equal to the mass of the element times the centripetal acceleration. 

Equation (2.A.12) is the balance between the centrifugal force (or the mass times the centripetal acceleration) and the pressure force, all on a per unit volume basis. It shows, as we also saw on basis of heuristic arguments in the main text, that the pressure in a vortex flow increases towards the periphery and more so the stronger the tangential velocity. The radial pressure distribution can be obtained by integrating the right-hand side over r. 

The Froude number is the ratio of the centrifugal acceleration to gravitational constant, and relates to the compaction forces experienced by the wet mass owing to centrifugal and centripetal forces generated by the plow. 

Introduction. Centrifugal separators make use of the common principle that an object whirled about an axis or center point at a constant radial distance from the point is acted on by a force. The object being whirled about an axis is constantly changing direction and is thus accelerating, even though the rotational speed is constant. This centripetal force acts in a direction toward the center of rotation. 

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