Fluid inertia

Flow Past Bodies. A fluid moving past a surface of a soHd exerts a drag force on the soHd. This force is usually manifested as a drop in pressure in the fluid. Locally, at the surface, the pressure loss stems from the stresses exerted by the fluid on the surface and the equal and opposite stresses exerted by the surface on the fluid. Both shear stresses and normal stresses can contribute their relative importance depends on the shape of the body and the relationship of fluid inertia to the viscous stresses, commonly expressed as a dimensionless number called the Reynolds number (R ), EHp/]1. The character of the flow affects the drag as well as the heat and mass transfer to the surface. Flows around bodies and their associated pressure changes are important. 

The effect of fluid inertia manifests during abrupt change in velocity of the fluid mass. It is quantified by the Rossby number ... 

Dynamic simulation models include fluid inertia and compressibility and exchanger shell expansion to determine the pressure spikes associated with... 

Kale, D. D Mashelkar. R. A., and Ulbrecht, J. Chem. Ing. Tech. 46 (1974) 69. High speed agiiauon of non-Newtonian fluids Influence of elasticity and fluid inertia. 

These results suggest that simple parabolic flow is ensured only in the conductive airways where the Reynolds number is less than 1.0. There, the fluid inertia is negligible, and the convective fluid transport is less than the molecular transport. ... 

Comparison with the full Navier-Stokes equation, Eq. (1-1), shows that fluid inertia is completely neglected in Eq. (1-33). Problems arising from the nonlinearity of the convective acceleration term are thereby avoided. However, the order of the equation and hence the number of boundary conditions required are unchanged. 

For a nondimensional oscillation period of tp = 0.1, Fig. 4.15 shows the circumferential velocity profiles at four instants in the period. The wall velocity follows the specified rotation rate exactly, which it must by boundary-condition specification. The center velocity r — 0 is constrained by boundary condition to be exactly zero, incenter = 0. The interior velocities are seen to lag the wall velocity, owing to fluid inertia and the time required for the wall s influence to be diffused inward by fluid shearing action. 

The available correlations in the literature are not able to represent the experimental results derived from 1500 high pressure data on the liquid hold-up. To correlate all the data, the effects of fluid inertia, surface forces, and liquid shear stress have again been accounted for, by using the corresponding dimensionless groups in the following empirical correlation [37] ... 

REYNOLDS NUMBER. A dimensionless number that establishes the proportionality between fluid inertia and the sheer stress due to viscosity. The work of Osborne Reynolds has shown that the flow profile of fluid in a closed conduit depends upon the conduit diameter, the density and viscosity of the flowing fluid, and the flow velocity. 

The second term in the right-hand side of Eq. (5.392) represents the fluid inertia, whereas the first term represents the viscous contribution to the pressure drop. At low Reynolds numbers, the Ergun equation can be simplified by neglecting the inertial term. Under this condition, Eq. (5.392) can be expressed as... 

There are two distinct modes of flow, laminar and turbulent. Fluid inertia tends to allow fluctuations to grow and give rise to turbulent eddies. Viscosity on the other hand, tends to damp out these fluctuations. A ratio of forces, inertial to viscous, is used to characterise the nature of the flow and is called the Reynolds Number, Re. For pipe flow this takes the form ... 

The indeterminate character of some Stokes flow problems influence of a nonNewtonian suspending fluid, inertia and deformability. 

Clearly, fluid inertia is important in drop ejection, since Re >> 1 however, flow is still considered to be in the laminar regime, as the... 

Although this picture is remarkably generic, the mechanisms responsible for the formation of a particle-lean layer adjacent to the wall depend on the properties of the material under consideration. For the case of solid particle dispersions, wall depletion, particle migration, and solid-liquid separation are the most frequent sources of solvent layer lubrication. Wall depletion occurs whenever dispersions are brought into contact with smooth and solid surfaces because the suspended particles cannot penetrate rigid boundaries [147]. Particle migration is due to various forces arising from fluid inertia, fluid elasticity, and shear-induced diffusivity effects [165]. Solid-liquid separation, which frequently occurs in flocculated suspensions like... 

The flow of the continuous phase is considered to be initiated by a balance between the interfacial particle-fluid coupling - and wall friction forces, whereas the fluid phase turbulence damps the macroscale dynamics of the bubble swarms smoothing the velocity - and volume fraction fields. Temporal instabilities induced by the fluid inertia terms create non-homogeneities in the force balances. Unfortunately, proper modeling of turbulence is still one of the main open questions in gas-liquid bubbly flows, and this flow property may significantly affect both the stresses and the bubble dispersion [141]. 

Solve for the velocity field in this case. Also, calculate the shear stress at the moving wall. Does fluid inertia increase or decrease the average shear stress ... 

We wish to examine the influence of fluid inertia on the stress measured at the lower plate. 

Fluid inertia (acceleration forces, centrifugal forces in curved films, fluid gravity) is negligible compared to viscous shear and hence Vu/Vt = Vv/Vt = Vui/Vt = 0. 

We also have the effective shear modulus relation, = G, and the effective parameter, 0, which includes the effective fluid inertia in the relative motion parameter, p, i.e.. 

Thus, resistance to flow through a tube correlates directly with catheter length and fluid viscosity and inversely with the fourth power of catheter diameter. For steady flow, the delivery system can be modeled as a series of resistors representing each component, including administration set, access catheter, and circulatory system. When dynamic aspects of the delivery system are considered, a more detailed model including catheter and venous compliance, fluid inertia, and turbulent flow is required. Flow resistance may be defined with units of mm Hg/(L/h), so that 1 fluid ohm = 4.8 x 10 " Pa s/m. Studies determining flow resistance for several catheter components with distilled water for flow rates of 100, 200, and 300 mL/h appear in Table 25.1. 

The surface tension force counter acting the fluid inertia at the edges of the sheet is ... 

Fluid inertia effects have been found to be very small for the cone-and-plate geometries typically supplied with these instruments. While inertial corrections are foimd to be imimportant for the parallel plate geometries, for shearing gaps of the order of 2 mm or less (except possibly for very thin fluids), they must be taken into accoimt in the concentric cylinder geometry (especially for high-density, mobile fluids). Evaluation methods are available for p, in the case of cylindrical and plane Couette flow, taking into account fluid inertia [Aschoff and Schummer, 1993]. 

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