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

The image above represents velocity at turbulent flow.

To compute for velocity at turbulent flow, four essential parameters are needed and these parameters are Acceleration due to Gravity (g), Particle Diameter (d), Density of Solid Particle (ρs) and Density of Fluid (ρf).

The formula for calculating velocity at turbulent flow:

v = [3gd(ρs – ρf)/ρf]0.5

Where:

v = Velocity at Turbulent Flow
g = Acceleration due to Gravity
d = Particle Diameter
ρs = Density of Solid Particle
ρf = Density of Fluid

Let’s solve an example;
Find the velocity at turbulent flow when the acceleration due to gravity is 14, the particle diameter is 10, the density of solid particle is 24 and the density of fluid is 12.

This implies that;

g = Acceleration due to Gravity = 14
d = Particle Diameter = 10
ρs = Density of Solid Particle = 24
ρf = Density of Fluid = 12

v = [3gd(ρs – ρf)/ρf]0.5
v = [3(14)(10)(24 – 12)/12]0.5
v = [3(14)(10)(12)/12]0.5
v = [5040/12]0.5
v = (420)0.5
v = 20.49

Therefore, the velocity at turbulent flow is 20.49 m/s.

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How to Calculate and Solve for Constant for Fluid | Mineral Processing

The image above represents constant for fluid.

To compute for constant for fluid, two essential parameters are needed and these parameters are Acceleration due to Gravity (g) and Fluid Viscosity (μ).

The formula for calculating constant for fluid:

k1 = g / 18μ

Where:

k1 = Constant for Fluid
g = Acceleration due to Gravity
μ = Fluid Viscosity

Let’s solve an example;
Find the constant for fluid when the acceleration due to gravity is 24 and the fluid viscosity is 6.

This implies that;

g = Acceleration due to Gravity = 24
μ = Fluid Viscosity = 6

k1 = g / 18μ
k1 = 24 / 18(6)
k1 = 24 / 108
k1 = 0.22

Therefore, the constant for fluid is 0.22.

Calculating the Acceleration due to Gravity when the Constant for Fluid and the Fluid Viscosity is Given.

g = k1 x 18μ

Where:

g = Acceleration due to Gravity
k1 = Constant for Fluid
μ = Fluid Viscosity

Let’s solve an example;
Find the acceleration due to gravity when the constant for fluid is 10 and the fluid viscosity is 2.

This implies that;

k1 = Constant for Fluid = 10
μ = Fluid Viscosity = 2

g = k1 x 18μ
g = 10 x 18 (2)
g = 10 x 36
g = 360

Therefore, the acceleration due to gravity is 360.

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How to Calculate and Solve for Drag Force with Respect to Velocity and Density | Mineral Processing

The image above represents drag force with respect to velocity and density.

To compute for drag force with respect to velocity and density, four essential parameters are needed and these parameters are Particle Diameter (d), Acceleration due to Gravity (g), Density of Solid Particle (ρs) and Density of Fluid (ρf).

The formula for calculating the drag force with respect to velocity and density:

D = πd³g(ρs – ρf) / 6

Where:

D = Drag Force with Respect to Velocity and Density
d = Particle Diameter
g = Acceleration due to Gravity
ρs = Density of Solid Particle
ρf = Density of Fluid

Let’s solve an example;
Find the drag force with respect to velocity and density when the particle diameter is 6, the acceleration due to gravity is 3, the density of solid particle is 8 and density of fluid is 2.

This implies that;

d = Particle Diameter = 6
g = Acceleration due to Gravity = 3
ρs = Density of Solid Particle = 8
ρf = Density of Fluid = 2

D = πd³g(ρs – ρf) / 6
D = π(6)³(3)(8 – 2) / 6
D = π(216)(3)(6) / 6
D = 12214.5 / 6
D = 2035.75

Therefore, the drag force with respect to velocity and density is 2035.75 N.

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How to Calculate and Solve for Drag Force for Moving Particle | Mineral Processing

The image above represents drag force for moving particle.

To compute for drag force for moving particle, three essential parameters are needed and these parameters are Mass of Solid (ms), Mass of Fluid (mf) and Acceleration due to Gravity (g).

The formula for calculating drag force for moving particle:

D = (ms – mf)g

Where:

D = Drag Force for Moving Particles
ms = Mass of Solid
mf = Mass of Fluid
g = Acceleration due to Gravity

Let’s solve an example;
Find the drag force for moving particles when the mass of solid is 14, the mass of fluid is 12 and the acceleration due to gravity is 10.

This implies that;

ms = Mass of Solid = 14
mf = Mass of Fluid = 12
g = Acceleration due to Gravity = 10

D = (ms – mf)g
D = (14 – 12)10
D = (2)10
D = 20

Therefore, the drag force for moving particles is 20 N.

Calculating the Mass of Solid when the Drag Force for Moving Particles, the Mass of Fluid and the Acceleration due to Gravity is Given.

ms = (D / g) + mf

Where:

ms = Mass of Solid
D = Drag Force for Moving Particles
mf = Mass of Fluid
g = Acceleration due to Gravity

Let’s solve an example;
Find the mass of solid when the drag force for moving particles is 10, the mass of fluid is 4 and the acceleration due to gravity is 5.

This implies that;

D = Drag Force for Moving Particles = 10
mf = Mass of Fluid = 4
g = Acceleration due to Gravity = 5

ms = (D / g) + mf
ms = (10 / 5) + 4
ms = 2 + 4
ms = 6

Therefore, the mass of solid is 6.

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