Cross-sectional area of fluid

G, G> Mass flowrate per unit cross sectional area of fluid, solid kg/m2s ML-2 -1... 

Here, A is the cross-sectional area of fluid flow, V is the interstitial velocity of liquid, and M is the mass of tracer added. Michell and Furzer61 and Furzer and Michell35 claim that an accurate estimation of Ez can be obtained by fitting the experimental RTD with Eq. (3-8) by nonlinear regression techniques. The first and second moments are given by the relations... 

At Cross-sectional area of fluid CctCf, Concentration in dilute phase... 

In a two-phase flow system, the different affinity of the two fluids for the wall makes (me fluid preferentially flow along comers due to the capillarity. As the number of the polygon sides decreases and the comers sharpen, the cross-sectional area of fluids held in comers increases, and comer flow becomes more important. Therefore, comer flow must be considered carefully in such processes as evaporation and drying of micro- and nanochannels with small angular polygonal cross sections. 

The cross-sectional area of the wick is deterrnined by the required Hquid flow rate and the specific properties of capillary pressure and viscous drag. The mass flow rate is equal to the desired heat-transfer rate divided by the latent heat of vaporization of the fluid. Thus the transfer of 2260 W requires a Hquid (H2O) flow of 1 cm /s at 100°C. Because of porous character, wicks are relatively poor thermal conductors. Radial heat flow through the wick is often the dominant source of temperature loss in a heat pipe therefore, the wick thickness tends to be constrained and rarely exceeds 3 mm. 

The degree of swelling and shrinking is important for design of ion-exchange columns, especiaUy for the location of the distributors used to disperse incoming fluids, and coUect outgoing ones, evenly over the cross-sectional area of the resin bed. Once placed, these distributors are not adjustable. The upper distributor should be above (the lower one below) the resin bed, even in the bed s swoUen form. 

The bulk fluid velocity method relates a blending quaUty Chemscale number to a quaUtative description of mixing (Table 3). The value of is equal to one-sixth of the bulk fluid velocity defined by pumping rate divided by cross-sectional area of the tank (4). 

Two-fluid U tube (Fig. 10-14). This is a highly sensitive device for measuring small gas heads. Let A be the cross-sectional area of each of the resei voirs and a that of the tube forming the U let Pi be... 

In general, cavitation damage can be anticipated wherever an unstable state of fluid flow exists or where substantial pressure changes are encountered. Susceptible locations include sharp discontinuities on metal surfaces, areas where flow direction is suddenly altered (Fig. 12.5), and regions where the cross-sectional areas of the flow passages are changed. 

Hicks et al. [8] developed a correlation involving the Pumping number and impeller Reynolds number for several ratios of impeller diameter to tank diameter (D /D ) for pitched-blade turbines. From this coiTclation, Qp can be determined, and thus the bulk fluid velocity from the cross-sectional area of the tank. The procedure for determining the parameters is iterative because the impeller diameter and rotational speed N appear in both dimensionless parameters (i.e., Npe and Nq). 

A = cross section area of orifice, nozzle or pipe, sq ft h = static head loss, ft of fluid flowing AP = differential static loss, Ibs/sq in. of fluid flowing, under conditions of Al above... 

The specific displacement per revolution of the rotor is equal to the cross-sectional area of the fluid multiplied by the distance the fluid advances. The specific displacement s (in. ) is... 

Torque. Equation 4-160 gives the fluid cross-sectional area of the motor, which is... 

Suppose you have determined that two cylinders have the same volume and that one cylinder is twice as long as the other. In this case, the cross-sectional area of the longer tube will be half of the cross-sectional area of the other tube. If fluid is pumped into each cylinder at the same rate, both pistons will reach their full travel at the same time. However, the piston in the smaller cylinder must travel twice as fast because it has twice as far to go. There are two ways of controlling the speed of the piston, (1) by varying the size of the cylinder and (2) by varying the volume of flow (gpm) to the cylinders. 

The superficial gas velocity is the air flow rate per unit cross sectional area of the column. The superficial gas velocity is less than 0.4m s 1 and media flow rate is based on liquid velocity. Then, the column may have a hydraulic retention time that is a function of fluid velocity and column diameter. The liquid velocity is given by 4... 

Here in Chapter 1 we make the additional assumptions that the fluid has constant density, that the cross-sectional area of the tube is constant, and that the walls of the tube are impenetrable (i.e., no transpiration through the walls), but these assumptions are not required in the general definition of piston flow. In the general case, it is possible for u, temperature, and pressure to vary as a function of z. The axis of the tube need not be straight. Helically coiled tubes sometimes approximate piston flow more closely than straight tubes. Reactors with square or triangular cross sections are occasionally used. However, in most of this book, we will assume that PFRs are circular tubes of length L and constant radius R. 

Figure 2.43 Model geometry for the CFD calculations on flow in curved micro channels (above) and time evolution of two initially vertical fluid lamellae over a cross-section of the channel (below), taken from [139].The secondary flow is visualized by streamlines projected on to the cross-sectional area of the channel. The upper row shows results for fC = 150 and the lower row for K = 300.

Fig. 4.3.3 (a) Shear flow of a Newtonian fluid defined as the ratio of the shear stress and trapped between the two plates (each with a shear rate, (b) A polymeric material is being large area of A). The shear stress (a) is defined stretched at both ends at a speed of v. The as F/A, while the shear rate (y) is the velocity material has an initial length of L0 and an gradient, dvx/dy. The shear viscosity (r s) is (instantaneous) cross-sectional area of A. 

An alternative to the stirred tank system is a column-type device which provides for constant fluid flow through a powder bed. The mass transport process was shown to be primarily determined by the length and cross-sectional area of the cylinder and the fluid flow rate [36],... 

The three-fluid manometer illustrated in Fig. 4-P11 is used to measure a very small pressure difference (P1 — P2). The cross-sectional area of each of the reservoirs is A, and that of the manometer legs is a. The three fluids have densities pa, ph, and pc, and the difference in elevation of the interfaces in the reservoir is x. Derive the equation that relates the manometer reading h to the pressure difference P1 — P2. How would the relation be simplified if A al... 

Here, p is the density of the fluid, V is the relative velocity between the fluid and the solid body, and A is the cross sectional area of the body normal to the velocity vector V, e.g., nd1/4 for a sphere. Note that the definition of the drag coefficient from Eq. (11-1) is analogous to that of the friction factor for flow in a conduit, i.e.,... 

The permeability of a porous medium (K) is defined as the proportionality constant that relates the flow rate through the medium to the pressure drop, the cross-sectional area, the fluid viscosity, and net flow length through the medium ... 

FIGURE 11.32 Flow profiles in microchannels, (a) A pressure gradient, - AP, along a channel generates a parabolic or Poiseuille flow profile in the channel. The velocity of the flow varies across the entire cross-sectional area of the channel. On the right is an experimental measurement of the distortion of a volume of fluid in a Poiseuille flow. The frames show the state of the volume of fluid 0, 66, and 165 ms after the creation of a fluorescent molecule, (b) In electroosmotic flow in a channel, motion is induced by an applied electric field E. The flow speed only varies within the so-called Debye screening layer, of thickness D. On the right is an experimental measurement of the distortion of a volume of fluid in an electroosmotic flow. The frames show the state of the fluorescent volume of fluid 0, 66, and 165 ms after the creation of a fluorescent molecule [165], Source http //www.niherst.gov.tt/scipop/sci-bits/microfluidics.htm (see Plate 12 for color version). 

In this definition, ps and pt are the solid and fluid densities, respectively. The characteristic diameter of the particles is ds (which is used in calculating the projected cross-sectional area of particle in the direction of the flow in the drag law). The kinematic viscosity of the fluid is vf and y is a characteristic strain rate for the flow. In a turbulent flow, y can be approximated by l/r when ds is smaller than the Kolmogorov length scale r. (Unless the turbulence is extremely intense, this will usually be the case for fine particles.) Based on the Stokes... 

In general, the velocity of the fluid varies across the diameter of the pipe but an average velocity can be defined. If the cross-sectional area of the pipe at a particular location is S, then the volumetric flow rate Q is given... 

In accordance with the sign convention, the forces acting on the fluid in the positive x-direction are the force due to the upstream pressure P and the shear force on the inner surface of the element. Those acting in the negative x-direction are the force due to the pressure Pi and the shear force on the outer surface of the element. The cross-sectional area of the element, on which the pressure acts, is equal to 2mrSr. As the fluid s momentum remains constant, the net force acting on the fluid is zero ... 

In equation 3.51, p is the density and n the power law flow behaviour index of the fluid. 51 and S2 are the cross-sectional areas of the smaller and larger pipes respectively and u the volumetric average velocity in the smaller pipe. 

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