Centrifugal force, fluid dynamics

Lubricity. In any mechanical seal design, there is rubbing motion between the dynamic seal faces. This rubbing motion is often lubricated by the fluid being pumped. Most seal mauufac turers hmit the speed of their seals to 90 ft/sec (30 m/sec). This is primarily due to centrifugal forces acting on the seal, which tends to restrict the seal s axial flexibihty. 

The flow model propounded by Bittins and Zehner [33] for a baffled tank equipped with radial-flow stirrers is based on the fluid-dynamic interaction between the stirrer and the stationary vessel wall as well as the fittings such as baffles, coils etc. In the case of the blade stirrer, the radial liquid discharge towards the vessel walls is produced by the centrifugal forces, which has increased to qb by the time it reaches the baffles as a result of the inclusion of surroimding liquid. There the tangential flow velocity, which has left the stirrer with a value of Ms2, is decelerated from M51 to Ms2. The flow is turned back and flows above and underneath the stirrer plane back to the stirrer, where it arrives with a value of Wjj. 

Answer Use the postulated form of the one-dimensional velocity profile developed in part (a) and neglect the entire left side of the equation of motion for creeping flow conditions at low rotational speeds of the solid sphere. The fact that does not depend on cp, via symmetry, is consistent with the equation of continuity for an incompressible fluid. The r and 9 components of the equation of motion for incompressible Newtonian fluids reveal that dynamic pressure is independent of r and 9, respectively, when centrifugal forces are negligible. Symmetry implies that does not depend on cp, and steady state suggests no time dependence. Hence, dynamic pressure is constant, similar to a hydrostatic situation. Fluid flow is induced by rotation of the solid and the fact that viscous shear is transmitted across the solid-liquid interface. As expected, the -component of the force balance yields useful information to calculate v. The only terms that survive in the (/ -component of the equation of motion are... 

Answer Based on the final result in part (e) for dFsoM on fluid, the normal stress is due to Xrr and fluid pressure. In the absence of centrifugal forces, one calculates fluid pressure from the hydrostatic situation where dynamic pressure is constant throughout the fluid. Hence,... 

The dynamics of the particle s relative movement with respect to the fluid is governed by the action of three forces oriented along the radial direction er (i) the centrifugal force Frc applied to the particle s mass, (ii) the pressure force Frp exerted by the fluid flow on the particle, and (iii) the friction force resisting the relative movement of the particle with respect to the fluid. 

Dynamic pumps infuse energy to the fluid in a manner that increases either its momentum (centrifugal pumps) or its pressure (electroosmotic and electrohydro-dynamic pumps) as shown in Table 4. They involve centrifugal or hydrodynamic actuations and, more specifically, are driven by electro-/magneto-hydrodynamic [257], electroosmotic [254-256], electrokinetic [251-253], electrowetting [258], and acoustic forces [259]. Centrifugal pumps are typically less effective for fluids with low Reynolds numbers and have limitation in miniaturization. 

---