The image above represents velocity of fine particles.

To compute for velocity of fine particles, four essential parameters are needed and these parameters are **Constant for Fluid (k**_{1}), Particle Diameter (d), Density of Solid Particle(s) (ρ_{s}) and **Density of Fluid (ρ**_{f}).

The formula for calculating the velocity of fine particles:

v = k_{1}d²(ρ_{s} – ρ_{f})

Where:

v = Velocity of Fine Particles

k_{1} = Constant for Fluid

d = Particle Diameter

ρ_{s} = Density of Solid Particle(s)

ρ_{f} = Density of Fluid

Let’s solve an example;

Find the velocity of fine particles when the constant for fluid is 12, the particle diameter is 8, the density of solid particle is 4 and the density of fluid is 10.

This implies that;

k_{1} = Constant for Fluid = 12

d = Particle Diameter = 8

ρ_{s} = Density of Solid Particle(s) = 4

ρ_{f} = Density of Fluid = 10

v = k_{1}d²(ρ_{s} – ρ_{f})

v = 12(8)²(4 – 10)

v = 12(64)(-6)

v = -4608

Therefore, the **velocity of fine particles **is **-4608 m/s.**

**Calculating the Constant for Fluid when the Velocity of Fine Particles, the Particle Diameter, the Density of Solid Particle and the Density of Fluid is Given.**

k_{1} = ^{v} / _{d²(ρ}_{s} – ρ_{f})

Where:

k_{1} = Constant for Fluid

v = Velocity of Fine Particles

d = Particle Diameter

ρ_{s} = Density of Solid Particle(s)

ρ_{f} = Density of Fluid

Let’s solve an example;

Find the constant for fluid when the velocity of fine particles is 68, the particle diameter is 4, the density of solid particle is 10 and the density of fluid is 6.

This implies that;

v = Velocity of Fine Particles = 68

d = Particle Diameter = 4

ρ_{s} = Density of Solid Particle(s) = 10

ρ_{f} = Density of Fluid = 6

k_{1} = ^{v} / _{d²(ρ}_{s} – ρ_{f})

k_{1} = ^{68} / _{4²(10 – 6)}

k_{1} = ^{68} / _{16(4)}

k_{1} = ^{68} / _{64}

k_{1} = 1.06

Therefore, the **constant for fluid **is **1.06.**

**Calculating the Particle Diameter when the Velocity of Fine Particles, the Constant for Fluid, the Density of Solid Particle and the Density of Fluid is Given.**

d = √(^{v} / _{k}_{1} (ρ_{s} – ρ_{f}))

Where:

d = Particle Diameter

v = Velocity of Fine Particles

k_{1} = Constant for Fluid

ρ_{s} = Density of Solid Particle(s)

ρ_{f} = Density of Fluid

Let’s solve an example;

Find the particle diameter when the velocity of fine particles is 88, the constant for fluid is 12, the density of solid particle is 8 and the density of fluid is 5.

This implies that;

v = Velocity of Fine Particles = 88

k_{1} = Constant for Fluid = 12

ρ_{s} = Density of Solid Particle(s) = 8

ρ_{f} = Density of Fluid = 5

d = √(^{v} / _{k}_{1} (ρ_{s} – ρ_{f}))

d = √(^{88} / _{12 (8 – 5)})

d = √(^{88} / _{12 (3)})

d = √(^{88} / _{36})

d = √2.44

d = 1.56

Therefore, the **particle diameter **is **1.56.**

Continue reading How to Calculate and Solve for Velocity of Fine Particles | Mineral Processing