Drag, engineering term

The verb "to drag" is a poor engineering term. The correct technical terminology describing this well-known phenomenon is that the rushing water sucked the air down the toilet s drain. But the sucking of air out of my bathroom could only happen if the pressure in the toilet s drain was less than the pressure in my bathroom. This idea bothered me for two reasons ... 

While we laud the virtue of dynamic modeling, we will not duphcate the introduction of basic conservation equations. It is important to recognize that all of the processes that we want to control, e.g. bioieactor, distillation column, flow rate in a pipe, a drag delivery system, etc., are what we have learned in other engineering classes. The so-called model equations are conservation equations in heat, mass, and momentum. We need force balance in mechanical devices, and in electrical engineering, we consider circuits analysis. The difference between what we now use in control and what we are more accustomed to is that control problems are transient in nature. Accordingly, we include the time derivative (also called accumulation) term in our balance (model) equations. 

Many engineering operations involve the separation of solid particles from fluids, in which the motion of the particles is a result of a gravitational (or other potential) force. To illustrate this, consider a spherical solid particle with diameter d and density ps, surrounded by a fluid of density p and viscosity /z, which is released and begins to fall (in the x = — z direction) under the influence of gravity. A momentum balance on the particle is simply T,FX = max, where the forces include gravity acting on the solid (T g), the buoyant force due to the fluid (Fb), and the drag exerted by the fluid (FD). The inertial term involves the product of the acceleration (ax = dVx/dt) and the mass (m). The mass that is accelerated includes that of the solid (ms) as well as the virtual mass (m() of the fluid that is displaced by the body as it accelerates. It can be shown that the latter is equal to one-half of the total mass of the displaced fluid, i.e., mf = jms(p/ps). Thus the momentum balance becomes... 

Engineering Estimates of the Drag- and Pressure-Flow Terms of the Screw Characteristic Lines of Co-TSE Conveying Screws and Kneading Elements... 

The MRS closures will attract most interest for use wherever MTE methods fail. For example, in flows with rotation the Coriolis terms enter the Rij equations, but drop out in the equation for Ru — q Therefore, an MRS method probably will be essential for including rotation effects, which are of considerable importance in many practical engineering and geophysical problems. Other effects that have not yet been adequately modeled and for which MRS methods may offer some hope include additive drag reduction, ultrahigh Reynolds numbers, separation, roughness, lateral and transverse curvature, and strong thermal processes that affect the hydrodynamic motions. 

For non-ideal systems, on the other hand, one may use either D12 or D12 and the corresponding equations above (i.e., using the first or second term in the second line on the RHS of (2.498)). In one interpretation the Pick s first law diffusivity, D12, incorporates several aspects, the significance of an inverse drag D12), and the thermodynamic non-ideality. In this view the physical interpretation of the Fickian diffusivity is less transparent than the Maxwell-Stefan diffusivity. Hence, provided that the Maxwell-Stefan diffusivities are still predicable for non-ideal systems, a passable procedure is to calculate the non-ideality corrections from a suitable thermodynamic model. This type of simulations were performed extensively by Taylor and Krishna [96]. In a later paper, Krishna and Wesselingh [49] stated that in this procedure the Maxwell-Stefan diffusivities are calculated indirectly from the measured Fick diffusivities and thermodynamic data (i.e., fitted thermodynamic models), showing a weak composition dependence. In this engineering approach it is not clear whether the total composition dependency is artificially accounted for by the thermodynamic part of the model solely, or if both parts of the model are actually validated independently. 

The effect of shape of non-spherical particles on their drag coefficient has proved difficult to define. This is probably due to the difficulty in describing particle shape for irregular particles. Engineers and scientist often require a single number to describe the shape of a particle. One simple approach is to describe the shape of a particle in terms of its sphericity, the ratio of the surface area of a sphere of volume equal to that of the particle to the surface area of the particle. For example, a cube of side one unit has a volume of 1 (cubic units) and a surface area of 6 (square units). A sphere of the same volume has a diameter, Xp of 1.24 units. The surface area of a sphere of diameter 1.24 units is 4.836 units. The sphericity of a cube is therefore 0.806 (= 4.836/6). 

In the engineering literature, the term drag reduction is commonly used for denoting the reduction of friction in turbulent flow through pipes. The main concern here is the drag reduction achieved by adding small doses of polymers [few parts per million (ppm)] to turbulently flowing water. Indeed, reductions in frictional losses of up to 80% have been documented in the literature [e.g., see Kulicke et al. (1989) for an up-to-date review of the pertinent literature]. 

---