Linear drag

Equations (13.89) and (13.91) describe the projectile trajectories of a volcanic bomb for linear drag. 

Substituting the linear drag velocity profile (dvz/dy) = Vq/H into Eq. 2.7-1, and defining / = y/H subsequent to integration, yields ... 

In drop-breakup experiments with polymers, the shear viscosity is typically shear-rate-dependent. So in plots such as Fig. 9-11, the viscosities are taken to be those of the melts at a nominal shear rate in the mixer. In the experiments of Sundararaj and Macosko, for example, the nominal shear rate y at a given motor speed is estimated from the linear drag flow that is assumed to exist in the narrowest gap of the mixer. 

For free solution electrophoresis. Gel based electrophoresis results in a non-linear drag which can increase the dependence of on a Approximate, based on assumption of proportionality between hydrodynamic volume and molecular weight ... 

The linear dependence of C witii temperahire agrees well with experiment, but the pre-factor can differ by a factor of two or more from the free electron value. The origin of the difference is thought to arise from several factors the electrons are not tndy free, they interact with each other and with the crystal lattice, and the dynamical behaviour the electrons interacting witii the lattice results in an effective mass which differs from the free electron mass. For example, as the electron moves tlirough tiie lattice, the lattice can distort and exert a dragging force. 

La.mina.r Flow Elements. Each of the previously discussed differential-pressure meters exhibits a square root relationship between differential pressure and flow there is one type that does not. Laminar flow meters use a series of capillary tubes, roUed metal, or sintered elements to divide the flow conduit into innumerable small passages. These passages are made small enough that the Reynolds number in each is kept below 2000 for all operating conditions. Under these conditions, the pressure drop is a measure of the viscous drag and is linear with flow rate as shown by the PoiseuiHe equation for capilary flow ... 

Additioaal uses for higher olefias iaclude the productioa of epoxides for subsequeat coaversioa iato surface-active ageats, alkylatioa of benzene to produce drag-flow reducers, alkylation of phenol to produce antioxidants, oligomeriza tion to produce synthetic waxes (qv), and the production of linear mercaptans for use in agricultural chemicals and polymer stabilizers. Aluminum alkyls can be produced from a-olefias either by direct hydroalumination or by transalkylation. In addition, a number of heavy olefin streams and olefin or paraffin streams have been sulfated or sulfonated and used in the leather (qv) iadustry. 

The hydrodynamic forces are usually described by a linear relation between drag resistance and relative fluid velocity ... 

Setting An established analytical method consisting of the extraction of a drag and its major metabolite from blood plasma and the subsequent HPLC quantitation was precisely described in a R D report, and was to be transferred to three new labs across international boundaries. (Cf. Section 4.32.) The originator supplied a small amount of drug standard and a number of vials containing frozen blood plasma with the two components in a fixed ratio, at concentrations termed lo, mid, and hi. The report provided for evaluations both in the untransformed (linear/linear depiction)... 

A transition linearly coupled to the phonon field gradient will experience, from the perturbation theory perspective, a frequency shift and a drag force owing to phonon emission/absorption. Here we resort to the simplest way to model these effects by assuming that our degree of freedom behaves like a localized boson with frequency (s>i. The corresponding Hamiltonian reads... 

Several copolymers of or-olelins are used as drag reducers. Suggested recipes are summarized in Table 12-1. Linear low-density polyethylene is a copolymer of ethylene and a-olefins. It is obtained by copolymerization utilizing Ziegler-Natta catalysts or metallocene catalysts. Concentrates may be prepared by... 

For viscous dominated flows, it can be assumed that the gas inertia and the gas gravitational forces are negligible. By dropping the gas inertia and gravity time from the gas momentum equation and simplifying the dimensionless drag coefficient to the linear viscous term, the set of dimensionless equations does not include gas-to-solid density ratio as a parameter. 

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