Friction gradient

Therefore, the solid frictional gradient is obtained from the calculated value 40.35 in the ratio of the friction factors. 

The friction gradient for two-phase flow is generally expressed similar to the single-phase flow as... 

The hydranlic friction gradient is defined as the head loss per unit length. It is defined as... 

Denomination (inch) Wall thickness (inch) Relative roughness for new pipe Speed of flow (m/s) Flow L/s Speed of flow (ft/s) Flow US gpm Darcy Reynolds Iriction number factor Friction gradient (tn/m) or (ft/ft)... 

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 2-7 Flydraulic friction gradient for water in a rubber-lined 4" pipe, Sell 40, Sell 80, and Sell 160. Rubber thickness = 0.25" (6.4 mm). Rubber roughness = 150 p,m (0.000492 ft). 2-FIDPE line 3" SDRl 1 roughness 1.5 p,m (0.00000492 ft). 

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

Pipe size Pipe inner diameter Relative Speed of flow Flow Speed of flow Flow US Reynolds Darcy friction Friction gradient (m/m)... 

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. 

A more advanced but less known method to estimate the friction gradient for saltation flows is the Graf-Acaroglu method that is presented in Chapter 6, which we will also discuss in the next section with a worked exampie. 

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