A spherical particle falling at a terminal speed in a liquid must have the gravitational force balanced by the drag force and the buoyant force. The buoyant force is equal to the weight of the displaced fluid, while the drag force is assumed to be given by Stokes Law, Fs = 6πrηv. Show that the terminal speed is given by v = (2R2 g/9η) . (ρs − ρ1) , where R is the radius of the sphere, ρs is its density, and ρ1 is the density of the fluid, and η the coefficient of viscosity.
A spherical particle falling at a terminal speed in a liquid must have the gravitational force balanced by the drag force and the buoyant force. The buoyant force is equal to the weight of the displaced fluid, while the drag force is assumed to be given by Stokes Law, Fs = 6πrηv. Show that the terminal speed is given by v = (2R2 g/9η) . (ρs − ρ1) , where R is the radius of the sphere, ρs is its density, and ρ1 is the density of the fluid, and η the coefficient of viscosity.
Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter15: Fluid Mechanics
Section: Chapter Questions
Problem 35P
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A spherical particle falling at a terminal speed in a liquid must have the gravitational force balanced by the drag force and the buoyant force. The buoyant force is equal to the weight of the displaced fluid, while the drag force is assumed to be given by Stokes Law, Fs = 6πrηv. Show that the terminal speed is given by v = (2R2 g/9η) . (ρs − ρ1) , where R is the radius of the sphere, ρs is its density, and ρ1 is the density of the fluid, and η the coefficient of viscosity.
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