Terminal Velocity of Falling Particles
Terminal Velocity of Falling Particles
This Demonstration calculates the terminal velocity of a spherical solid particle falling in a fluid under the force of gravity.
Three forces act on the particle: the downward force of gravity, an upward force of buoyancy, and a drag force that acts opposite to the direction of motion of the particle. The equation relating these forces to the particle acceleration is:
4
3
3
r
ρ
p
dV
dt
4
3
3
r
ρ
p
1
2
2
r
C
d
2
V
where is the radius of the sphere; and are the densities of the fluid and the particle, respectively; is the gravitational constant; is the particle velocity; and is the drag coefficient that varies with the Reynolds number, , as follows [1]:
r
ρ
ρ
p
g
V
C
d
Re=Vρ
D
p
μ
C
d
24
Re
2.6
Re
5.0
1+
1.52
Re
5.0
0.411
-7.94
Re
263000
1+
-8.00
Re
263000
0.8
Re
461000
where is the viscosity in and is the particle diameter; CGS units are used throughout. The equation for is valid over the entire range of the available experimental data; use beyond is not reliable. For the equation follows the creeping flow result =24/Re. You can calculate the terminal velocity, the Reynolds number, and the drag coefficient over a wide range of the variables , , , , and . The artificial values of gravity included in the calculation can be achieved particularly in space, but also on Earth.
μ
g/cms
D
p
C
d
Re=
6
10
Re<0.1
C
d
ρ
ρ
p
D
p
μ
g