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

The image above represents velocity of fine particles. To calculate velocity of fine particles, four essential parameters are needed and these parameters are Constant for Fluid (k₁), 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 = k₁d²(ρ_s – ρ_f)

Where:

v = Velocity of Fine Particles
k₁ = 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;

k₁ = Constant for Fluid = 12
d = Particle Diameter = 8
ρ_s = Density of Solid Particle(s) = 4
ρ_f = Density of Fluid = 10

v = k₁d²(ρ_s – ρ_f)
v = 12(8)²(4 – 10)
So, 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 are Given

k₁ = ^v / _{d²(ρs – ρf)}

Where:

k₁ = 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

k₁ = ^v / _{d²(ρs – ρf)}
k₁ = ⁶⁸ / _{4²(10 – 6)}
That is, k₁ = ⁶⁸ / ₁₆₍₄₎
k₁ = ⁶⁸ / ₆₄
k₁ = 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 are Given

d = √(^v / _{k1 (ρs – ρf)})

Where:

d = Particle Diameter
v = Velocity of Fine Particles
k₁ = 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
k₁ = Constant for Fluid = 12
ρ_s = Density of Solid Particle(s) = 8
ρ_f = Density of Fluid = 5

d = √(^v / _{k1 (ρs – ρf)})
That is, d = √(⁸⁸ / _{12 (8 – 5)})
d = √(⁸⁸ / _{12 (3)})
d = √(⁸⁸ / ₃₆)
So, d = √2.44
d = 1.56

Therefore, the particle diameter is 1.56.

Read more: How to Calculate and Solve for Newton’s Drag Force for Turbulent Resistance | Mineral Processing

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

ρ_s = (^v / _k1d²) + ρ_f

Where:

ρ_s = Density of Solid Particle(s)
v = Velocity of Fine Particles
k₁ = Constant for Fluid
d = Particle Diameter
ρ_f = Density of Fluid

Let’s solve an example;
Find the density of solid particle when the velocity of fine particles is 24, the constant for fluid is 10, the particle diameter is 8, the density of fluid is 4.

This implies that;

v = Velocity of Fine Particles = 24
k₁ = Constant for Fluid = 10
d = Particle Diameter = 8
ρ_f = Density of Fluid = 4

ρ_s = (^v / _k1d²) + ρ_f
That is, ρ_s = (²⁴ / _10(8²)) + 4
ρ_s = (²⁴ / ₆₄₀) + 4
So, ρ_s = 0.0375 + 4
ρ_s = 4.0375

Therefore, the density of solid particle is 4.0375.

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

ρ_f = ρ_s – (^v / _k1d²)

Where:

ρ_f = Density of Fluid
v = Velocity of Fine Particles
k₁ = Constant for Fluid
d = Particle Diameter
ρ_s = Density of Solid Particle(s)

Let’s solve an example;
Find the density of fluid when the velocity of fine particles is 12, the constant for fluid is 2, the particle diameter is 5 and the density of solid particle is 6.

This implies that;

v = Velocity of Fine Particles = 12
k₁ = Constant for Fluid = 2
d = Particle Diameter = 5
ρ_s = Density of Solid Particle(s) = 6

ρ_f = ρ_s – (^v / _k1d²)
Then, ρ_f = 6 – (¹² / _2(5²))
ρ_f = 6 – (¹² / ₅₀)
So, ρ_f = 6 – 0.24
ρ_f = 5.76

Therefore, the density of fluid is 5.76.

Read more: How to Calculate and Solve for Velocity at Turbulent Flow | Mineral Processing

How to Calculate Velocity of Fine Particles With Nickzom Calculator

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the velocity of fine particles.

Now, Click on Mineral Processing under Materials and Metallurgical

Now, Click on Velocity of Fine Particles under Mineral Processing

The screenshot below displays the page or activity to enter your values, to get the answer for the velocity of fine particles according to the respective parameter which is the Constant for Fluid (k₁), Particle Diameter (d), Density of Solid Particle(s) (ρ_s) and Density of Fluid (ρ_f).

Now, enter the values appropriately and accordingly for the parameters as required by the Constant for Fluid (k₁) is 12, Particle Diameter (d) is 8, Density of Solid Particle(s) (ρ_s) is 4 and Density of Fluid (ρ_f) is 10.

Finally, Click on Calculate

As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia solves for the velocity of fine particles and presents the formula, workings and steps too.