Hydraulic friction gradient

The hydraulic friction gradient of water in rubber-lined pipes in the range of 2" to 18" is presented in Figures 2-5 to 2-13. Rubber thickness of 6.4 mm (0.25") was assumed for 2", 3", 4", and 6" (up to 150 mm) pipes. Rubber thickness of 9.5 mm (0.375") was assumed for 8" to 24" (200 to 610 mm NB) pipes. HDPE friction head was plotted for similar sizes at SDRll (suitable for 100 psi pressure), to mark the advantages of reduced friction at these sizes using HDPE instead of rubber-lined pipes, wherever it may be appropriate. The design engineer must take in account the pressure limitations of HDPE pipes versus rubber-lined steel pipes. 

These curves and tables allow an easier and accurate determination of the hydraulic friction gradient of water than the Moody diagram. 

FIGURE 2-6 Hydraulic friction gradient for water in a rubber lined 3" pipe, Sch 40, Sch 80,... 

FIGURE 2-11 Hydraulic friction gradient of water in 10" and 12" SDRll HOPE pipes. Roughness 1.5 pm (0.00000492 ft). 

In this chapter, some very important principles regarding water flows were introduced. Since water is the principal carrier of slurry mixtures, the tools developed in this chapter such as hydraulic friction gradients and methods to correlate the friction velocity with the friction factor will be extensively used for pipe flow and open channel flow of heterogeneous mixtures (Chapters 4 and 6). 

HYDRAULIC FRICTION GRADIENT OF HORIZONTAL HETEROGENEOUS FLOWS... 

FIGURE 4-9 Concepts of the hydraulic friction gradients and /y for slurry mixture and for water. 

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. 

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. 

Based on the above mentioned, the programme of theoretical and experimental investigation of the main parameters of coal-methanol (or its water solution) mixture pipeline transport should be opened. As the first step of the programme the comparison of power consumption (dependency of hydraulic gradient I on slurry flow velocity V and solid concentration Cs) for the pipeline transport of coal-water mixture and coal-methanol solution mixture was realised. The special laboratory measurements were made to define unknown input data of semi-empirical relationships, i.e. the limit volumetric concentration Cm and the coefficient of mechanical friction of coal in the water or water-methanol solution ka. The resultant comparison of the hydraulic gradient I of the coal-water and coal-methanol solution mixture flow is presented in Figure 2, where density of coal was pc = 1480 kg/m3, diameter of the pipe was D = 0.103 mm, the maximal grain size of coal dmax was less than 0.25 mm, volumetric concentration - C = 20 %. 

Consider now conditions at the valve as affected by both pipe friction and damping. When the pressure wave from N has reached a midpoint B in the pipe length L, the water in BN will be at rest and for zero flow the hydraulic gradient should be a horizontal line. There is thus a tendency for the gradient to flatten out for the portion BN. Hence, instead of the transient gradient having the slope imposed by friction, it will approach a horizontal line starting from the transient value at B. Thus... 

Figure 12-8 Friction factor used in the calculation of the hydraulic gradient, hg, for sieve trays with crossflow. [B. D. Smith, Design of Equilibrium Stage Processes, McGraw-Hill Book Company, New York, 1963, by courtesy McGraw-Hill Book Company.]...

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