Inertia forces

Reynolds number is the ratio of the inertia forces to the viscous forces... 

For conditions approaching constant flow through the orifice, a relationship derivea by equating the buoyant force to the inertia force of the liquid [Davidson et al., Tran.s. In.stn. Chem. Engr.s., 38, 335 (I960)] (dimensionally consistent),... 

Inertial forces are developed when the velocity of a fluid changes direction or magnitude. In turbulent flow, inertia forces are larger than viscous forces. Fluid in motion tends to continue in motion until it meets a sohd surface or other fluid moving in a different direction. Forces are developed during the momentum transfer that takes place. The forces ac ting on the impeller blades fluctuate in a random manner related to the scale and intensity of turbulence at the impeller. 

The interfacial area between gases and hquids, immiscible liquids, and solids and hquids may be enlarged or reduced by these viscous and inertia forces when interacting with interfacial forces such as surface tension. 

Tabic 9-1 is a handy little chart to visualize a vertical, single-cylinder compressor and the basic functions. The functions are normalized to keep them in a dimensionless form [4]. With the following set of equations, the X and y components of the inertia forces for a single cylinder can be calculated. For the derivation, the reader is referred to references [4,. 5], Figure 9-4 depicts the generalized stage to aid in the definitioii of terms... 

At this point, as far as shaking forces go, the gas forces do not make a contribution. If the rod load or bearing loads are to be analyzed, the gas forces must be calculated and added vectorially to the inertia forces to... 

Therefore, the inertia forces have an insignificant influence on the sedimentation process in this regime. Theoretically, their influence is equal to zero. In contrast, the forces of viscous friction are at a maximum. Evaluating the coefficient B in equation 55 for a = 1 results in a value of 24. Hence, we have derived the expression for the drag coefficient of a sphere, = 24/Re. 

The turbulent regime for Cq is characterized by the section of line almost parallel to the x-axis (at the Re" > 500). In this case, the exponent a is equal to zero. Consequently, viscosity vanishes from equation 46. This indicates that the friction forces are negligible in comparison to inertia forces. Recall that the resistance coefficient is nearly constant at a value of 0.44. Substituting for the critical Reynolds number, Re > 500, into equations 65 and 68, the second critical values of the sedimentation numbers are obtained ... 

The slope of the curve in the transitional zone changes from 135 to 180°. It shows that the exponent in changes as follows 0 a 1. This means that the friction and inertia forces are commensurable in the process of sedimentation. Several empirical formulas have been proposed for estimating the resistance coefficient in the transition zone. One such correlation is... 

Reynolds number A dimensionless parameter that represents the ratio of the inertia forces to the viscous forces in a flow. Its magnitude denotes the actual flow regime, such as streamline (laminar), transitional, or turbulent. 

In addition to the gas load, the rod and cros.shead pin bushing is subject to the inertia forces created by the acceleration and deceleration of the compressor reciprocating mass. The inertia load is a direct function of crank radius, the reciprocating weight, and speed squared. The total load imposed on the crosshead pin and bushing is the sum of the gas load and the inertia load and is referred to as the combined rod load. ... 

Due to the basic design of the compressor, its rotating and reciprocating masses produce inertia forces and moments tha cannot be completely eliminated and must be absorbed by the foundation. The manufacturer has the ability to minimize the magnitude of these forces and moments by adding counterweights to the crossheads but cannot totally eliminate them. 

Can operate at higher speeds (rpm). Less inertia forces due to lighter components. 

The Reynolds number is the ratio of the inertia forces acting on the fluid to the viscous forces acting on the fluid. It is dimensionless and may be calculated as... 

The system is still comprised of the inertia force due to the mass and the spring force, but a new force is introduced. This force is referred to as the damping force and is proportional to the damping constant, or the coefficient of viscous damping, c. The damping force is also proportional to the velocity of the body and, as it is applied, it opposes the motion at each instant. 

Subscripts 1 = inertia force v = viscosity force G = gravity C = interfacial tension R = ratio m = model p = prototype... 

For a fluid flowing through a pipe the momentum per unit cross-sectional area is given by pu2. This quantity, which is proportional to the inertia force per unit area, is the force required to counterbalance the momentum flux. 

The ratio u/d represents the velocity gradient in the fluid, and thus the group (pu/d) is proportional to the shear stress in the fluid, so that (pu2)/(pu/d) = (dup/p) = Re is proportional to the ratio of the inertia forces to the viscous forces. This is an important physical interpretation of the Reynolds number. 

In turbulent flow with high values of Re, the inertia forces become predominant and the viscous shear stress becomes correspondingly less important. 

In large tubes, as well as in tubes of a few millimeters in diameter, two-phase flow patterns are dominated in general by gravity with minor surface tension effects. In micro-channels with the diameter on the order of a few microns to a few hundred microns, two-phase flow is influenced mainly by surface tension, viscosity and inertia forces. The stratified flow patterns commonly encountered in single macro-channels were not observed in single micro-channels. 

These studies consider the dynamics of a single bubble that grows in infinity space, which is filled by superheated liquid. Under these conditions the bubble expansion depends on inertia forces or on intensity of heat transfer. In the case when inertia forces are dominant the bubble radius grows linearly in time (Carey 1992) ... 

If we ignore inertia force and follow the conventional assumptions in liquid lubrication, motion equation (here we consider the incompressible fluids in the absence of volume force and volume momentum) is ... 

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