Dodge-Metzner equation

Experimental measurements [13] for aqueous solutions of Carbopol and slurries of Attagel are in good agreement with the predictions of the Dodge-Metzner equation, as shown in Fig. 10.21. 

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] ... 

Hartnett and Kostic [12] studied a number of correlations for predicting the turbulent friction factor of purely viscous non-Newtonian fluids flowing in circular and non-circular geometries. They concluded that the Dodge-Metzner Equation 7 was the best over the entire range of power law value. 

Applying the Dodge-Metzner model Want et al. (1982) applied Equation 5-20 to express the consumed power under turbulent conditions as ... 

HARTNETT and KOSTIC 26 have recently examined the published correlations for turbulent flow of shear-thinning power-law fluids in pipes and in non-circular ducts, and have concluded that, for smooth pipes, Dodge and Metzner S(27) modification of equation 3.11 (to which it reduces for Newtonian fluids) is the most satisfactory. 

Dodge and Metzner (1959) modified the von Karman equation to apply to power law fluids, with the following result ... 

This correlation is shown in Figure 3.8. The broken lines represent extrapolation of equation 3.36 for values of n and Re beyond those of the measurements made by Dodge and Metzner. More recent studies tend to... 

Dodge and Metzner (1959) deduced the velocity profile from their measurements of flow rate and pressure gradient for turbulent flow of power law fluids in pipes. For the turbulent core, the appropriate equation is... 

The constants of such equations must be found experimentally over a range of conditions for each particular case, and related to the friction factor with which pressure drops and power requirements can be evaluated. The topic of nonsettling slurries is treated by Bain and Bonnington (1970) and Clift (1980). Friction factors of power-law systems are treated by Dodge and Metzner (1959) and of fiber suspensions by Bobkowitz and Gauvin (1967). 

Turbulent Flow. Correlations have been achieved for all four models, Eqs. (6.45)-(6.48). For power-law flow the correlation of Dodge and Metzner (1959) is shown in Figure 6.5(a) and is represented by the equation... 

Dodge and Metzner (16) obtained excellent agreement between calculated (with equation 15) and experimental friction factors over values of n from 0.36 to 1 and Re from 2900 to 36,000. 

Metzner and Reed (89) and Dodge and Metzner (90) derived a generalized Reynolds number from the Rabinowitsch-Mooney equation... 

Keck et al. (19) proposed the following Dodge and Metzner (36) type equation for the clean fluids ... 

A more detailed derivation of equation (3.37) is available in their original paper and elsewhere [Skelland, 1967. For Newtonian fluids n = 1), equation (3.37) reduces to the well-known Nikuiadse equation. Dodge and Metzner [1959] also demonstrated that their data for elay suspensions which did not conform to power-law behaviour, were consistent with equation (3.37) provided that the slope of log — log(8V/D) plots was evaluated at the... 

In turbulent flow of time-independent fluids the Reynolds number at which turbulent flow occurs varies with the flow properties of the non-Newtonian fluid. Dodge and Metzner (D2) in a comprehensive study derived a theoretical equation for turbulent flow of non-Newtonian fluids through smooth round tubes. The final equation is plotted in Fig. 3.5-3, where the Fanning friction factor is plotted versus the generalized Reynolds... 

For turbulent flows. Dodge and Metzner (1959) developed the following equation for the power-law fluids in smooth pipes based on a semitheoretical analysis ... 

Although Equation 5-29 has been extensively used, it has its own limitations. Measur ing the power exponent " n" in laminar flow tests and then trying to apply it to turbulent flows is asking for trouble, particularly for cases when / < 0.5. Hey wood and Richardson (1978) showed that pumping flocculated clays yielded higher experimental values of friction coefficient than those predicted by Dodge and Metzner (1959), particularly when the value of n had been obtained at low shear stress. 

Slatter et al. (1996) reported that Kemblowski and Kolodziejski (1973) found that the Dodge and Metzner model did not well represent the flow of kaolin slurries. They derived the following empirical equation ... 

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