How to Calculate and Solve for Velocity of Fine Particles | Mineral Processing
Last Updated on November 23, 2021
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 (k1), Particle Diameter (d), Density of Solid Particle(s) (ρs) and Density of Fluid (ρf).
The formula for calculating the velocity of fine particles:
v = k1d²(ρs – ρf)
Where:
v = Velocity of Fine Particles
k1 = Constant for Fluid
d = Particle Diameter
ρs = Density of Solid Particle(s)
ρf = 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
ρs = Density of Solid Particle(s) = 4
ρf = Density of Fluid = 10
v = k1d²(ρs – ρf)
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.
k1 = v / d²(ρs – ρf)
Where:
k1 = Constant for Fluid
v = Velocity of Fine Particles
d = Particle Diameter
ρs = Density of Solid Particle(s)
ρf = 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
ρs = Density of Solid Particle(s) = 10
ρf = Density of Fluid = 6
k1 = v / d²(ρs – ρf)
k1 = 68 / 4²(10 – 6)
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 is Given.
d = √(v / k1 (ρs – ρf))
Where:
d = Particle Diameter
v = Velocity of Fine Particles
k1 = Constant for Fluid
ρs = Density of Solid Particle(s)
ρf = 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
ρs = Density of Solid Particle(s) = 8
ρf = Density of Fluid = 5
d = √(v / k1 (ρs – ρf))
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.
Calculating the Density of Solid Particle when the Velocity of Fine Particles, the Constant for Fluid, the Particle Diameter and the Density of Fluid is Given.
ρs = (v / k1d²) + ρf
Where:
ρs = Density of Solid Particle(s)
v = Velocity of Fine Particles
k1 = Constant for Fluid
d = Particle Diameter
ρf = 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
ρf = Density of Fluid = 4
ρs = (v / k1d²) + ρf
ρs = (24 / 10(8²)) + 4
ρs = (24 / 640) + 4
ρs = 0.0375 + 4
ρs = 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 is Given.
ρf = ρs – (v / k1d²)
Where:
ρf = Density of Fluid
v = Velocity of Fine Particles
k1 = Constant for Fluid
d = Particle Diameter
ρs = 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
ρs = Density of Solid Particle(s) = 6
ρf = ρs – (v / k1d²)
ρf = 6 – (12 / 2(5²))
ρf = 6 – (12 / 50)
ρf = 6 – 0.24
ρf = 5.76
Therefore, the density of fluid is 5.76.
Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the velocity of fine particles.
To get the answer and workings of the velocity of fine particles using the Nickzom Calculator – The Calculator Encyclopedia. First, you need to obtain the app.
You can get this app via any of these means:
Web – https://www.nickzom.org/calculator-plus
To get access to the professional version via web, you need to register and subscribe to have utter access to all functionalities.
You can also try the demo version via https://www.nickzom.org/calculator
Android (Paid) – https://play.google.com/store/apps/details?id=org.nickzom.nickzomcalculator
Android (Free) – https://play.google.com/store/apps/details?id=com.nickzom.nickzomcalculator
Apple (Paid) – https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8
Once, you have obtained the calculator encyclopedia app, proceed to the Calculator Map, then click on Materials and Metallurgical under Engineering.
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) (ρs) and Density of Fluid (ρf).
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) (ρs) is 4 and Density of Fluid (ρf) 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.