Pressure gradient measurements

This is in excellent agreement with equation 2.70, considering that equation 3.47 was derived from flow rate and pressure gradient measurements rather than from direct measurement of the velocity profiles. 

Figure 15 shows typical results of axial voidage profile measurements (Li and Kwauk, 1980 Li et al, 1981). Experiments were conducted by using different solids materials in a Type A apparatus, 90 mm i.d. and 8 m high. Voidages were calculated from pressure gradient measurements. Solids circulation rate was controlled by a pneumatically actuated pulse feeder (see Section III in Chapter 7). 

Hicken, B.L., Sharara, A.I., Abrams, G.A., Eloubeidi, M., Fallon, M.B., Arguedas, M.R. Hepatic venous pressure gradient measurements to assess response to primary prophylaxis in patients with cirrhosis A decision analytical study. Alim. Pharm. Ther. 2003 17 145-153... 

FIG. 21-25 iFluid" fluidization permeameter, illustrating powder bed supported by distributor plate fluidized at a gas velocity U, with associated pressure taps for multiple pressure gradient measurements dP/dh. Courtesy iPowder Systems, EhG, Associates, Inc.)... 

Figures 2 to 5 show examples of mobility reduction factors measured in oil-free Berea cores containing high-salinity, high-hardness brines under reservoir conditions. (An explanation of surfactant names used in these figures appears in the Appendix.) Nitrogen was used as the gas phase. MRF values presented in these figures were obtained from pressure gradients measured after pseudosteady-state flow through the linear cores had...

Pressure gradient measurements for setthng slurries show that the total frictional drag at the pipe wall can be expressed as the sum of kinetic and Coulombic components. In term of shear stresses,... 

Let us first consider experiments without composition gradients. These are permeability measurements, in which flow is induced by a pressure gradient Consider first the flow of pure substance 1, setting x = 1, = 0 and... 

Demonstration. The transition zone is clearly indicated at 12,000 ft. The trend line is determined as an exponential function. The difference between the trend line value (2.48 g/cm ) and the measured value (2.28 g/cm ) at 13,000 ft can be correlated to the formation pressure gradient using the empirical correlation curve established by Boatman and shown in Figure 4-337 [101]. 

In the absence of a direct measurement of the in-line concentration of solids ey. it is necessary to make an estimate of its value in order that the hydrostatic pressure gradient in the pipe may be calculated. This can be done for a given mixture velocity u and delivered concentration C, provided that the velocity of the particles relative to the liquid UR is known. 

The conveying of fine particles in vertical pipes of diameters 25 mm, 50 mm, and 75 mm has been studied by BoOTHROYD(75 . He measured the pressure gradient in the pipeline, and found that the frictional pressure drop was less than that for air alone in the 25 mm pipe, but was greater in the larger pipes. This effect was attributed to the fact that the extent to which the fluid turbulence was affected by the presence of the particles was markedly influenced by pipe size. 

Measured Flow rate. Pressure gradient. Mean velocity, rms of velocity fluctua-... 

It was found that the pressure gradient and flow friction in micro-channels were higher than that predicted by the conventional laminar flow theory. In a low Re range, the measured pressure gradient increased linearly with Re. For Re > 500, the slope of the /(c-Re relationship increases with Re. The ratio C was about 1.3 for micro-channels of hydraulic diameter 51.3-64.9pm and 1.15-1.18 for microchannels of hydraulic diameter 114.5-168.9pm. It was also found that the ratio of C depends on the Reynolds number. 

A general case of heat transfer under the conditions of combined action of electro-osmotic forces and imposed pressure gradient was considered by Chakra-borty (2006). The analysis showed that in this case the Nusselt number depends not only on parameters z and S, but also on an additional dimensionless group, which is a measure of the relative significance of the pressure gradient and osmotic forces. 

Chisolm, D., and L. A. Sutherland, 1969, Prediction of Pressure Gradients in Pipeline Systems during Two-Phase Flow, Symp. on Fluid Mechanics and Measurements in Two-Phase Flow Systems, Leeds, pp. 24-25. (3)... 

Experimental measurements must be interpreted in connection with all external influences, including fluid flow, bulk viscosity, and pH of the system. Consideration must be given to whether the mass transport is occurring in one or more dimensions and whether mass transport is affected by pressure gradients and/or osmotic pressure gradients. 

A pipeline has been proposed to transport a coal slurry 1200 mi from Wyoming to Texas, at a rate of 50 million tons/yr, through a 36 in. diameter pipeline. The coal slurry has the properties of a Bingham plastic, with a yield stress of 150dyn/cm2, a limiting viscosity of 40 cP, and an SG of 1.5. You must conduct a lab experiment in which the measured pressure gradient can be used to determine the total pressure drop in the pipeline. 

In Section II.B of Chapter 3, the tube flow viscometer was described in which the viscosity of any fluid with unknown viscous properties could be determined from measurements of the total pressure gradient (— A4>/L) and the volumetric flow rate (Q) in a tube of known dimensions. The viscosity is given by... 

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). 

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