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: Fd = 6πRηv, where R is the radius of the object, η is the coefficient of viscosity in the fluid, and v is the terminal speed. a) Give the equation for terminal speed in the variables from Stokes law, and the densities of the sphere ρs and the fluid ρ1. b) Using the equation of the previous step, find the viscosity of motor oil (in kg/m/s) in which a steel ball of radius 0.95 mm falls with a terminal speed of 4.34 cm/s. The densities of the ball and the oil are 7.7 and 0.72 g/mL, respectively.
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:
Fd = 6πRηv,
where R is the radius of the object, η is the coefficient of viscosity in the fluid, and v is the terminal speed.
a) Give the equation for terminal speed in the variables from Stokes law, and the densities of the sphere ρs and the fluid ρ1.
b) Using the equation of the previous step, find the viscosity of motor oil (in kg/m/s) in which a steel ball of radius 0.95 mm falls with a terminal speed of 4.34 cm/s. The densities of the ball and the oil are 7.7 and 0.72 g/mL, respectively.
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