(a) Determine the viscosity of this sample.

(b) How would you describe the viscosity of this material?

(c) What model would be the most appropriate to represent this viscosity?

(d) Determine the values of the parameters in the model that fit the model to the data.

27. Consider each of the fluids for which the viscosity is shown in Fig. 3-7, all of which exhibit a typical ''structural viscosity'' characteristic. Explain why this is a logical consequence of the composition or ''structural makeup'' for each of these fluids.

28. You are asked to measure the viscosity of an emulsion, so you use a tube flow viscometer similar to that illustrated in Fig. 3-4, with the container open to the atmosphere. The length of the tube is 10 cm, its diameter is 2mm, and the diameter of the container is 3 in. When the level of the sample is 10 cm above the bottom of the container the emulsion drains through the tube at a rate of 12 cm3/min, and when the level is 20 cm the flow rate is 30 cm3/min. The emulsion density is 1.3 g/cm3.

(a) What can you tell from the data about the viscous properties of the emulsion?

(b) Determine the viscosity of the emulsion.

(c) What would the sample viscosity be at a shear rate of 500 s-1?

29. 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) Determine the dimensionless groups that characterize this system. You want to use these to design a lab experiment from which you can scale up measurements to find the desired horsepower.

(b) Can you use the same slurry in the lab as in the pipeline?

(c) If you use a slurry in the lab that has a yield stress of 150 dyn/cm2, a limiting viscosity of 20 cP, and a density of 1.5 g/cm3, what size pipe and what flow rate (in gpm) should you use in the lab?

(d) If you run the lab system as designed and measure a pressure drop AP (psi) over a 100 ft length of pipe, show how you would use this information to determine the required horsepower for the pipeline.

30. You want to determine how fast a rock will settle in mud, which behaves like a Bingham plastic. The first step is to perform a dimensional analysis of the system.

(a) List the important variables that have an influence on this problem, with their dimensions (give careful attention to the factors that cause the rock to fall when listing these variables), and determine the appropriate dimension-less groups.

(b) Design an experiment in which you measure the velocity of a solid sphere falling in a Bingham plastic in the lab, and use the dimensionless variables to scale the answer to find the velocity of a 2 in. diameter rock, with a density of 3.5 g/cm3, falling in a mud with a yield stress of 300 dyn/cm2, a limiting viscosity of 80 cP, and a density of 1.6 g/cm3. Should you use this same mud in the lab, or can you use a different material that is also a Bingham plastic but with a different yield stress and limiting viscosity?

(c) If you use a suspension in the lab with a yield stress of 150 dyn/cm2, a limiting viscosity of 30 cP, and a density of 1.3 g/cm3 and a solid sphere, how big should the sphere be, and how much should it weigh?

(d) If the sphere in the lab falls at a rate of 4cm/s, how fast will the 2 in. diameter rock fall in the other mud?

31. 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.

(a) Perform a dimensional analysis of the system to determine an appropriate set of dimensionless groups to use (you may neglect the effect of wall roughness for this fluid).

(b) For the lab test fluid, you have available a sample of the above coal slurry and three different muds with the following properties:

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