Flow rate Bingham plastic slurries

You must determine the horsepower required to pump a coal slurry through an 18 in. diameter pipeline, 300 mi long, at a rate of 5 million tons/yr. The slurry can be described by the Bingham plastic model, with a yield stress of 75 dyn/cm2, a limiting viscosity of 40 cP, and a density of 1.4 g/cm3. For non-Newtonian fluids, the flow is not sensitive to the wall roughness. 

The Bingham plastic model usually provides a good representation for the viscosity of concentrated slurries, suspensions, emulsions, foams, etc. Such materials often exhibit a yield stress that must be exceeded before the material will flow at a significant rate. Other examples include paint, shaving cream, and mayonnaise. There are also many fluids, such as blood, that may have a yield stress that is not as pronounced. 

Fig. 1 Classes of rheological behavior that can be shown by coal slurries, as they appear when plotted on a shear rate/ shear stress graph. It is desirable for coal slurries to be Bingham plastic or pseudoplastic with yield, as such slurries flow readily at high shear rates (such as during pumping or atomization), while remaining stable against settling at low shear rates because of their yield stress. Dilatant slurries are completely unsuitable for coal slurry applications because they are extremely difficult to pump.

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 18% iron oxide slurry (density 1170kg/m ) behaves as a Bingham plastic fluid with Tq = 0.78 Pa and yu-s = 4.5 mPa s. Estimate the wall shear stress as a function of the nominal wall shear rate (8F/D) in the range 0.4 < V < 1.75 m/s for flow in a 79 mm diameter pipeline. 

At high particle concentrations, slurries are often non-Newtonian. For non-Newtonian fluids, the relationship between the shear stress and shear rate, which describes the rheology of the slurry, is not linear and/or a certain minimum stress is required before flow begins. The power-law, Bingham plastic and Herschel-Bulkley models are various models used to describe the flow behaviour of slurries in which these other types of relationships between the shear stress and shear rate exist. Although less common, some slurries also display time-dependent flow behaviour. In these cases, the shear stress can decrease with time when the shear rate is maintained constant (thixotropic fluid) or can increase with time when the shear rate is maintained constant (rheopectic fluid). Milk is an example of a non-settling slurry which behaves as a thixotropic liquid. 

Certain slurries require a minimum level of stress before they can flow. An example is fresh concrete that does not flow unless the angle of the chute exceeds a certain minimum. Such a mixture is said to posses a yield stress magnitude that must be exceeded before that flow can commence. A number of flows such as Bingham plastics, pseudoplastics, yield pseudoplastics, and dilatant are classified as time independent non Newtonian flu ids. The relationship of wall shear stress versus shear rate is of the type shown in Figure 3 9 (a), and the relationship between the apparent viscosity and the shear rate is shown in Figtne 3-9 (b). The apparent viscosity is defined as... 

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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