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Ve A river bed is covered with a layer of small stones as shown in the figure. The diameters of stones vary between 3.7 mm and 3.7 cm. It is observed that at some critical flow velocity some stones will rise and be transported along the river. A model is to be used to determine this critical velocity. Assume that the river bed is horizontal and the critical velocity, Ve, is a function of the particle diameter, d, the fluid density, p, and viscosity, u, the density of the particles, Pp, and the acceleration of gravity, g. a) Determine a suitable set of dimensionless variables for this problem and clearly mark them on your solution sheet. How many pi terms are required to describe the problem?

Ve A river bed is covered with a layer of small stones as shown in the figure. The diameters of stones vary between 3.7 mm and 3.7 cm. It is observed that at some critical flow velocity some stones will rise and be transported along the river. A model is to be used to determine this critical velocity. Assume that the river bed is horizontal and the critical velocity, Ve, is a function of the particle diameter, d, the fluid density, p, and viscosity, u, the density of the particles, Pp, and the acceleration of gravity, g. a) Determine a suitable set of dimensionless variables for this problem and clearly mark them on your solution sheet. How many pi terms are required to describe the problem?

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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b) For a length scale of 0.29 and a fluid density scale of 2.6, what will be the ratio of the critical velocity of the model to the critical velocity of the river (assuming all similarity requirements are satisfied)? Answer:
Transcribed Image Text:b) For a length scale of 0.29 and a fluid density scale of 2.6, what will be the ratio of the critical velocity of the model to the critical velocity of the river (assuming all similarity requirements are satisfied)? Answer:
Ve A river bed is covered with a layer of small stones as shown in the figure. The diameters of stones vary between 3.7 mm and 3.7 cm. It is observed that at some critical flow velocity some stones will rise and be transported along the river. A model is to be used to determine this critical velocity. Assume that the river bed is horizontal and the critical velocity, Ve, is a function of the particle diameter, d, the fluid density, p, and viscosity, u, the density of the particles, Pp, and the acceleration of gravity, g. a) Determine a suitable set of dimensionless variables for this problem and clearly mark them on your solution sheet. How many pi terms are required to describe the problem?
Transcribed Image Text:Ve A river bed is covered with a layer of small stones as shown in the figure. The diameters of stones vary between 3.7 mm and 3.7 cm. It is observed that at some critical flow velocity some stones will rise and be transported along the river. A model is to be used to determine this critical velocity. Assume that the river bed is horizontal and the critical velocity, Ve, is a function of the particle diameter, d, the fluid density, p, and viscosity, u, the density of the particles, Pp, and the acceleration of gravity, g. a) Determine a suitable set of dimensionless variables for this problem and clearly mark them on your solution sheet. How many pi terms are required to describe the problem?
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