Friction factor correlations, smooth pipes

Friction factor correlations, smooth pipes 67 - — Darcy and Fanning 67, 68 -- — Moody 65... 

In addition, there are several correlations for the friction factor. For smooth pipes, one of the simplest correlations is the Blasius equation ... 

A large number of experimental data on friction factors of smooth pipe and pipes of varying degrees of equivalent roughness have been obtained and the data correlated. For design purposes to predict the friction factor/and, hence, the frictional pressure drop of round pipe, the friction factor chart in Fig. 2.10-3 can be used. It is a log-log plot of/... 

Design a positive pressure dilute-phase pneumatic transport system to carry 500 kg/h of a powder of particle density 1800 kg/m and mean particle size 150 pm across a horizontal distance of 100 m and a vertical distance of 20 m using ambient air. Assume that the pipe is smooth, that four 90° bends are required and that the allowable pressure loss is 0.7 bar. See below for Blasius correlation for the gas-wall friction factor for smooth pipes. 

Blasius correlation for the gas-wall friction factor for smooth pipes fg = 0.079 Re ° ... 

The Beggs and Brill correlation significantly underpredicts pressure loss (34%) due to the assumption of smooth pipe friction factors. The smooth pipe friction factors in the original correlations were substituted with rough pipe friction factors to produce revised Beggs and Brill correlations. 

It should be noted that Equations 13.9 and 13.10 apply to smooth pipes, whereas the pipes used for transmission of fluids usually have some surface roughness, which increases the friction factor. However, for short fluid transmission pipes, the overall pressure drop is usually dominated by the pressure drop in the pipe fittings (valves, bends, etc). Thus, for short transmission pipes, there is little point in calculating the straight pipe pressure drop accurately. If the transmission pipe is long (>100 m) and straight, then the Fanning friction factor can be correlated as7 ... 

The friction factor plot is available in many handbooks, so that given a value of Re, one can find the corresponding value of /. In the context of numerical optimization, however, using a graph is a cumbersome procedure. Because all of the constraints should be expressed as mathematical relations, we select the Blasius correlation for a smooth pipe (Bird et al., 1964) ... 

Experimental results for the Fanning friction factor for turbulent flow of shear thinning fluids in smooth pipes have been correlated by Dodge and Metzner (1959) as a generalized form of the von Karman equation ... 

Many useful correlations have been published to determine the friction factor for fully developed turbulent flow of Newtonian fluids in smooth pipes. One of the earliest correlations was given by Blasius (8) as follows ... 

Figure ll.5.a-4 Correlation of data for porous media to friction factor plot for smooth pipe (from Brownell, et al. [13]). 

Urbina [58], Paraqueima [59], Norum [60], von Bernuth and Wilson [61] and Venkatesan et al. [62] have published friction factor data for the extruded plastic pipes and showed that these values were higher than those obtained using the smooth pipe equation. They all correlated their experimental friction factor data and the Reynolds number in the form of the following power function for individual pipe. 

Initially he conducted the experiment on water flow through horizontal pipe (same PVC pipe for both cases) to find the roughness values (Venkatesan et al. [62], He compared the experimental friction factor for coil with the values obtained from smooth coil equation and observed that the experimental friction factor was higher than that of smooth coil. He found that as coil diameter increased the friction factor decreased (Figure 2). He presented a generalized correlation for predicting the frictional pressure drop across the rough helical coils as... 

The friction-factor-Reynolds-number correlation can be expressed for smooth pipe as (Bird et al., 1960, p. 186)... 

For turbulent flow, numerous correlations exist for both smooth and rough-walled pipes. A number of charts have been prepared such as those by Moody, and by Stanton and Pannell, in which friction factor is correlated against Reynolds number for differing pipe surface roughness. Itisimportantto note thatthisFanningfrictionfactorhasavalueof one-quarter of the Darcy friction factor. 

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