Hydraulic gradient laminar flow

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. 

COEFFICIENT OF PERMEABILITY The gross velocity of flow of water under laminar flow conditions through a porous medium under a unit hydraulic gradient and standard temperature conditions (usually 20° C). Laboratory test results are usually expressed in centimeters per second. 

In either laminar or turbulent flow, rotational circulation of a processed material around its own hydraulic center in each channel of the mixer causes radial mixing of the material. All processed material is continuously and completely intermixed, resulting in virtual elimination of radial gradients in temperature, velocity and material composition. 

At given gas and liquid superficial velocities Jg and ji that are defined by the volumetric flow rate of the respective phase divided by the cross-sectional area of the microchannel, de Mas et cd. [30] solved the force balance for the two co-flowing fluid phases. A capillary with a diameter equal to the hydraulic diameter of the microreactor was considered (Figure 11.2). The annular flow was assumed to be axisym-metric, laminar and fully developed. Using a constant pressure gradient in the gas and liquid phases along the streamwise direction, the flow satisfies the equations... 

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