Gradient hydraulic

The framework for the solution of porous media flow problems was estabUshed by the experiments of Henri Darcy in the 1800s. The relationship between fluid volumetric flow rate, hydraulic gradient, and cross-sectional area, yi, of flow is given by the Darcy formula ... 

Hydraulic Gradient Hydraulic gradient, the head of hquid necessary to overcome the frictional resistance to hquid (froth) passage across the plate, is impoiTant for plate stabihty inasmuch as it is the only liquid head that varies across the length of passage. If the gradient is excessive, the upstream portion of the plate may be rendered inoperative because of increased resistance to gas flow caused by increased liqmd head (Fig. 14-34). In general the empirical criterion for stable operation is /j > 2.5/j/,g. 

Sieve plates usually have negligible hydraulic gradient. Bubble-cap plates can have significant gradient because of the blockage by the caps. Valve plates presumably are intermediate, with hydraulic-gradient characteristics approaching those of sieve plates. 

For bubble-cap plates, hydraulic-gradient must be given serious consideration. It is a function of cap size, shape, and density on the plate. Methods for analyzing bubble-cap gradient may be found in the chapter by BoUes (Smith, De.sign of Equilibrium Stage Proce.s.se.s, Chap. 14, McGraw-Hill, New York, 1963) or in previous edition of this handbook. 

Figure 11 shows a t pical liquid collector plate for a column that uses one side downcomer to withdraw the liquid. The maximum diameter for such a design is about 12 ft, which is limited by the hydraulic gradient necessary for such a liquid flow-path length, For larger diameter columns, two opposite side downcomers or a center downcomer normally is used unless the total amount of liquid collected is relatively small. 

Hydraulic gradient, permeability, and effective porosity from water level contours, pump test results, and laboratory analyses... 

This case serves to point out the importance of maintaining a constant hydraulic gradient on the inside and outside of a slurry wall. This can also become a factor if slurry walls are used with groundwater pumping systems (extraction wells). Then water must be reinjected to maintain a... 

For large towers (usually over 8 ft in diameter) check the hydraulic gradient for sections of the tray normal to liquid flow, adjusting each section by not more than one-half the gradient... 

Tests have indicated that the hydraulic gradient is negligible or very small for most tray designs. Ustial design practice is to omit its effect unle.ss the alue o( A is expected to be greater than 0.75 in. If hydraulic gradient is appreciable, then tbe holes nearer to the tray inlet (liquid) will tend to weep before those nearer the tiay outlet. 

For stable tray operation, the hydraulic gradient should be less than one half the dry tray pressure drop. For conditions of high weir height and high Vq (Pv) the greater... 

When hydraulic gradient is a factor in the tray design, the dynamic liquid seal should be used in place of hsi for the determination of effective head. 

For bubble cap trays the phenomenon is believed to be induced by excessive hydraulic gradient it is recommended to keep hydraulic gradient to less than 40% of the dry pressure drop. 

Figure 5.9. Hydraulic gradient-velocity curves tor 200 fim sand in 25 mm diameter hydraulic conveying line...

Figure 5.10. Hxecss hydraulic gradient due to solids as function of modified Fronde number. Comparison ot results of different workers... 

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