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, F s = 6 π r η v . Show that the terminal speed is given by v = 2 R 2 g 9 η ( ρ s − ρ 1 ) , where R is the radius of the sphere, ρ s is its density, and ρ 1 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, F s = 6 π r η v . Show that the terminal speed is given by v = 2 R 2 g 9 η ( ρ s − ρ 1 ) , where R is the radius of the sphere, ρ s is its density, and ρ 1 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,
F
s
=
6
π
r
η
v
. Show that the terminal speed is given by
v
=
2
R
2
g
9
η
(
ρ
s
−
ρ
1
)
, where R is the radius of the sphere,
ρ
s
is its density, and
ρ
1
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: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, 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 small spherical bead of mass 3.00 g is released from rest at t =0 from a point under the surface of a viscous fluid. The terminal speed is observed to be vT = 2.00 cm/s.Find a) the value of the constant k that appears in F = -kv, b) the time t at which the bead reaches 0.632 vT and c) the value of the resistive force when the bead reaches terminal speed.
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