Laminar flow Bingham slurries

The rheological behaviour of a coal slurry (1160kg/m ) can be approximated by the Bingham plastic model with Tq = 0.5 Pa and /ng = 14mPa-s. It is to be pumped through a 400 mm diameter pipe at the rate of 188kg/s. Ascertain the nature of the flow by calculating the maximum permissible velocity for laminar flow conditions. 

A mud slurry is draining in laminar flow from the bottom of a large tank through a 5 m long horizontal pipe with a 1 cm inside diameter. The open end of the pipe is 5 m below the level in the tank. The mud is a Bingham plastic with a yield stress of 15 N/m, an apparent viscosity of 0.06 kg/m/s, and a density of 2000 kg/m. At what velocity will the mud slurry drain from the hose ... 

A Bingham slurry with a concentration of 50% by weight is tested in a plastic-lined pipe with an inner diameter of 2.5 in. The tests indicate a yield stress of 1.5 Pa, a slurry mixture specific gravity of 1.54, and a coefficient of rigidity of 0.4 Pa s. Assuming a flow speed of 4 ft/s in a laminar regime, determine the friction factor by Buckingham s equation. 

Bingham slurries. In some respects, it is a useful tool for hand calculations. A more widely accepted method since the mid 1980s is to compute the transition velocity that was proposed by Wilson and Thomas, to be discussed in Section 5-4-3. It is then assumed that the transition from laminar to turbulent flow occurs when the Wilson-Thomas and the Buckingham equations intersect. 

Bingham slurries do not exhibit a sudden change from laminar to turbulent flow. Darby et al. (1992) reviewed the work of previous authors and proposed to combine the laminar and turbulent fanning friction factors into the following equation ... 

A behaviour of the dense fine grained slurries in laminar flow regime can be described by Bingham fluid model or the yield pseudoplastic rheological model, respectively... 

Figure 6.6. Critical Reynolds number for transition from laminar to turbulent flow of Bingham fluids. The data also are represented by Eqs. (6.56) and (6.5T) (O) cement rock slurry (A) river mud slurries ( ) clay slurry (B) sewage sludge (A) Th02 slurries ( ) lime slurry. [Hanks and Prall, SPE Journal, 342-346 (Dec. 1967)].

As with slurries following a power-law flow model, it is necessary to reliably predict the pressure drop in a horizontal pipe of diameter D under laminar, fully developed flow conditions. A fundamental analysis of the Bingham plastic model yields the following expression for the mean velocity in terms of the yield stress Ty and the wall shear stress tq. 

For a Bingham plastic slurry, the transition from laminar to turbulent flow depends on the Hedstrom number. The critical Reynolds number, which allows... 

Although there has been little systematic study of deposition in tm-bulent flow of non-Newtonian slurries, the existing evidence for aqueous slurries suggests that the correlations in Equation 3 may be used for estimation purposes if the viscosity p is replaced by the high shear rate asymptotic quotient of shear stress and shear rate. Thus for example, a Bingham carrier fluid would be represented by its plastic viscosity. It must be emphasized that this recommendation is a tentative one and is restricted to turbulent slurry flows. The situation for laminar slurry flows will be quite different. 

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