Friction Factor in Turbulent Flow

The Moody diagram illustrates the effect of roughness on the friction factor in turbulent flow but indicates no effect of roughness in laminar flow. Explain why this is so. Are there any restrictions or limitations that should be placed on this conclusion Explain. 

Check the assumed friction factor in Example 6.17. For the value of relative roughness shown, the range of possible friction factors in turbulent flow is 0.004 to 0.01. How much would the economic diameter differ at/= 0.01 ... 

C Pressure Drop and Friction Factor in Turbulent Flow... 

In the turbulent flow region, it is not possible to obtain an analytical solution for the friction factor as we do for laminar flow. Most of the data available for evaluating the friction factor in turbulent flow have been derived from experiments. For turbulent flow (Reynolds number above 4(X)0), the friction factor is dependent upon the pipe wall roughness as well as the Reynolds number. For turbulent flow, Colebrook (1939) found an implicit correlation for the friction factor in round pipes. This correlation converges well in a few iterations. 

For laminar flow (Re < 2000), generally found only in circuits handling heavy oils or other viscous fluids, / = 16/Re. For turbulent flow, the friction factor is dependent on the relative roughness of the pipe and on the Reynolds number. An approximation of the Fanning friction factor for turbulent flow in smooth pipes, reasonably good up to Re = 150,000, is given by / = (0.079)/(4i e ). 

For flow in a smooth pipe, the friction factor for turbulent flow is given approximately by the Blasius equation and is proportional to the Reynolds number (and hence the velocity) raised to a power of -2. From equations 12.102 and 12.103, therefore, the heat and mass transfer coefficients are both proportional to w 75. 

Barna, P.S., Fluid Mechanics for Engineers, London, Butterworths, p. 85, (1969). Haaland, S.E., Simple and explicit formulas for the friction factor in turbulent pipe flow, Transactions of ASME, Journal of Fluids Engineering, Series 1105, pp. 89-90 (1983). 

Friction factors for turbulent flow in smooth pipes... 

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 ... 

Laminar and Turbulent Flow Below a critical Reynolds number of about 2,100, the flow is laminar over the range 2,100 < Re < 5,000 there is a transition to turbulent flow. Reliable correlations for the friction factor in transitional flow are not available. For laminar flow, the Hagen-Poiseuille equation... 

In Ref. 11 the friction factor for turbulent flow in channels with smooth circular or noncircular cross sections is related to the geometry parameter for laminar flow. The... 

Based on the observation that the friction factors for turbulent flow in rod bundles differ only little from those of circular tubes, a very simple empirical correlation was proposed [12] ... 

K. Rehme, Simple method of predicting friction factors of turbulent flow in non-circular channels, Int. J. Heat Mass Transfer 16 933 (1973). 

The friction factor correlations for fully developed turbulent flow in a rough circular duct are summarized in Table 5.9. The friction factor for turbulent flow in an artificially roughed circular duct can be found in Rao [59]. 

FIGURE 5.17 Normalized apparent friction factors for turbulent flow in the hydro-dynamic entrance region of a smooth concentric annular duct (r = 0.5168) [114]. 

FIGURE 5.31 Fully developed friction factor for turbulent flow in smooth right-angled and equilateral triangular ducts [45]. 

Ito [214] has proposed the following correlation to calculate the friction factor for turbulent flow in helicoidal coils ... 

S. E. Haaland, Simple and Explicit Formulas for the Friction Factor in Turbulent Pipe Flow, J. Fluids Eng., (105) 89-90,1983. 

The fully established friction factor for turbulent flow of purely viscous nonnewtonian fluids in rectangular channels may be determined by the modified Dodge-Metzner equation [72,110] ... 

The fully established friction factor for turbulent flow of a viscoelastic fluid in a rectangular channel is dependent on the aspect ratio, the Reynolds number, and the Weissenberg number. As in the case of the circular tube, at small values of Ws, the friction factor decreases from the newtonian value. It continues to decrease with increasing values of Ws, ultimately reaching a lower asymptotic limit. This limiting friction factor may be calculated from the following equation ... 

Several studies have been reported to determine friction losses in turbulent flow of slurries. Hannah et al. (29) presented an approach in which they compared expressions for the friction pressure of the slurry and clean fluid. In their analysis, they assumed Blasius (30) turbulent Fanning friction factor versus Reynolds number equation for Newtonian fluids. The following expression for estimating slurry friction pressure knowing the clean fluid friction pressure is proposed. 

Hetsroni et al. [6] also reexamined previous studies of friction factor in microchannels and drew the same conclusions that they did for transition in microchannels. They found that the anomalous results reported in some studies could be explained by the same factors that contributed to the observation of anomalous transitional behavior. Indeed, in the only study performed to date combining both microPIV and extensive pressure drop measurements. Sharp and Adrian [8] found that transition as measured by microPIV agreed well transition as inferred from friction factor data and also found that their measured friction factors agreed well with macroscale results. As with transition to turbulence, the experimental evidence on friction factors in turbulent microchannel flow shows that microscale flow exhibits the same behavior as macroscale flows. 

For evaluation of pressure drop for flow through a pipe one needs to know the friction factor. In laminar flow regime the friction factor is a function of Reynolds number only, and in the case of turbulent flow the friction factor is a function of Reynolds number and also the relative roughness factor. Blasius showed analytically... 

Ito, H., Friction Factors for Turbulent Flow in Curved Pipes, Trans. ASME J. Basic Engg., 81, 123-134 (1959). 

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