Bingham Limited

The power law model can be extended by including the yield value r — Tq = / 7 , which is called the Herschel-BulMey model, or by adding the Newtonian limiting viscosity,. The latter is done in the Sisko model, 77 +. These two models, along with the Newtonian, Bingham, and Casson... 

Because it is very difficult to measure the flow characteristics of a material at very low shear rates, behaviour at zero shear rate can often only be assessed by extrapolation of experimental data obtained over a limited range of shear rates. This extrapolation can be difficult, if not impossible. From Example 3.10 in Section 3.4.7, it can be seen that it is sometimes possible to approximate the behaviour of a fluid over the range of shear rates for which experimental results are available, either by a power-law or by a Bingham-plastic equation. 

Bingham number Nm N - T°° Moo / r0 = yield stress = limiting viscosity (Yield/viscous) stresses Flow of Bingham plastics... 

A film of paint, 3 mm thick, is applied to a flat surface that is inclined to the horizontal by an angle 9. If the paint is a Bingham plastic, with a yield stress of 150 dyn/cm2, a limiting viscosity of 65 cP, and an SG of 1.3, how large would the angle 9 have to be before the paint would start to run At this angle, what would the shear rate be if the paint follows the power law model instead, with a flow index of 0.6 and a consistency coefficient of 215 (in cgs units) ... 

The Bingham plastic model can describe acrylic latex paint, with a yield stress of 112 dyn/cm2, a limiting viscosity of 80 cP, and a density of 0.95 g/cm3. What is the maximum thickness of this paint that can be applied to a vertical wall without running ... 

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. 

A pipeline has been proposed to transport a coal slurry 1200 mi from Wyoming to Texas, at a rate of 50 million tons/yr, through a 36 in. diameter pipeline. The coal slurry has the properties of a Bingham plastic, with a yield stress of 150dyn/cm2, a limiting viscosity of 40 cP, and an SG of 1.5. You must conduct a lab experiment in which the measured pressure gradient can be used to determine the total pressure drop in the pipeline. 

You want to predict how fast a glacier that is 200 ft thick will flow down a slope inclined 25° to the horizontal. Assume that the glacier ice can be described by the Bingham plastic model with a yield stress of 50 psi, a limiting viscosity of 840 poise, and an SG of 0.98. The following materials are available to you in the lab, which also may be described by the Bingham plastic model ... 

Drilling mud has to be pumped down into an oil well that is 8000 ft deep. The mud is to be pumped at a rate of 50 gpm to the bottom of the well and back to the surface, through a pipe having an effective ID of 4 in. The pressure at the bottom of the well is 4500 psi. What pump head is required to do this The drilling mud has properties of a Bingham plastic, with a yield stress of 100 dyn/cm2, a limiting (plastic) viscosity of 35 cP, and a density of 1.2 g/cm3. 

A pipeline is installed to transport a red mud slurry from an open tank in an alumina plant to a disposal pond. The line is 5 in. sch 80 commercial steel, 12,000 ft long, and is designed to transport the slurry at a rate of 300 gpm. The slurry properties can be described by the Bingham plastic model, with a yield stress of 15 dyn/cm2, a limiting viscosity of 20 cP, and an SG of 1.3. You may neglect any fittings in this pipeline. 

Example 15-1 Determine the pressure gradient (in psi/ft) required to transport a slurry at 300 gpm through a 4 in. sch 40 pipeline. The slurry contains 50% (by weight) solids (SG = 2.5) in water. The slurry contains a bimodal particle size distribution, with half the particles below 100 pm and the other half about 2000 gm. The suspension of fines is stable and constitutes a pseudohomogeneous non-Newtonian vehicle in which the larger particles are suspended. The vehicle can be described as a Bingham plastic with a limiting viscosity of 30 cP and a yield stress of 55 dyn/cm2. 

An extrusion symposium (El) contains papers which deal extensively with the mathematics of viscous flow in screw extruders but which are limited to Newtonian materials. An extension of this work to materials which may be assumed to be Bingham plastic in behavior has been reported in Japan (M18, M19). The first of these papers deals with a screw extruder with a uniform channel the second with an extruder for which the depth of the channel decreases linearly with channel length. The mathematical results are shown graphically in terms of four dimensionless groups ... 

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