Energy Required to Crush Coarse Materials according to Bond's Law Calculator

✖Work Index always means the equivalent amount of energy to reduce one ton of the ore from a very large size to 100 um. Just as the meter is used to measure and compare distances.ⓘ Work Index [W_i]			+10% -10%
✖Product Diameter is the diameter of the sieve aperture that allows 80% of the mass of the ground material to pass.ⓘ Product Diameter [d₂]			+10% -10%
✖Feed Diameter is the diameter of the sieve aperture that allows 80% of the mass of the feed to pass.ⓘ Feed Diameter [d₁]			+10% -10%

✖Energy per Unit Mass of Feed is the energy required to process one unit mass of feed for given operation.ⓘ Energy Required to Crush Coarse Materials according to Bond's Law [E]

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Formula

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Energy Required to Crush Coarse Materials according to Bond's Law

Formula

`"E" = "W"_{"i"}*((100/"d"_{"2"})^0.5-(100/"d"_{"1"})^0.5)`

Example

`"22.15064J/kg"="11.6J/kg"*((100/"1.9m")^0.5-(100/"3.5m")^0.5)`

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Energy Required to Crush Coarse Materials according to Bond's Law Solution

STEP 0: Pre-Calculation Summary

Formula Used

Energy per Unit Mass of Feed = Work Index*((100/Product Diameter)^0.5-(100/Feed Diameter)^0.5)
E = W_i*((100/d₂)^0.5-(100/d₁)^0.5)
This formula uses 4 Variables

Variables Used

Energy per Unit Mass of Feed - (Measured in Joule per Kilogram) - Energy per Unit Mass of Feed is the energy required to process one unit mass of feed for given operation.
Work Index - (Measured in Joule per Kilogram) - Work Index always means the equivalent amount of energy to reduce one ton of the ore from a very large size to 100 um. Just as the meter is used to measure and compare distances.
Product Diameter - (Measured in Meter) - Product Diameter is the diameter of the sieve aperture that allows 80% of the mass of the ground material to pass.
Feed Diameter - (Measured in Meter) - Feed Diameter is the diameter of the sieve aperture that allows 80% of the mass of the feed to pass.

STEP 1: Convert Input(s) to Base Unit

Work Index: 11.6 Joule per Kilogram --> 11.6 Joule per Kilogram No Conversion Required
Product Diameter: 1.9 Meter --> 1.9 Meter No Conversion Required
Feed Diameter: 3.5 Meter --> 3.5 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

E = W_i*((100/d₂)^0.5-(100/d₁)^0.5) --> 11.6*((100/1.9)^0.5-(100/3.5)^0.5)

Evaluating ... ...

E = 22.1506368890789

STEP 3: Convert Result to Output's Unit

22.1506368890789 Joule per Kilogram --> No Conversion Required

FINAL ANSWER

22.1506368890789 ≈ 22.15064 Joule per Kilogram <-- Energy per Unit Mass of Feed

(Calculation completed in 00.004 seconds)

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Created by Ishan Gupta

Birla Institute of Technology & Science (BITS), Pilani

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Total Surface Area of Particle using Spericity

Go Total Surface Area of Particles = Mass*6/(Sphericity of Particle*Density Of Particle*Arithmetic Mean Diameter)

Total Number of Particles in Mixture

Go Total Number of Particles in Mixture = Total Mass of Mixture/(Density Of Particle*Volume Of One Particle)

Energy Required to Crush Coarse Materials according to Bond's Law

Go Energy per Unit Mass of Feed = Work Index*((100/Product Diameter)^0.5-(100/Feed Diameter)^0.5)

Number of Particles

Go Number of Particles = Mixture Mass/(Density of One Particle*Volume of Spherical Particle)

Total Number of Particles given Total Surface Area

Go Total Number of Particles in Mixture = Total Surface Area of Particles/Surface Area of One Particle

Specific Surface Area of Mixture

Go Specific Surface Area of Mixture = Total Surface Area/Total Mass of Mixture

Mass Mean Diameter

Go Mass Mean Diameter = (Mass Fraction*Size Of Particles Present In Fraction)

Sauter Mean Diameter

Go Sauter Mean Diameter = (6*Volume of Particle)/(Surface Area of Particle)

Total Surface Area of Particles

Go Surface Area = Surface Area of One Particle*Number of Particles

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Sphericity of Cuboidal Particle

Go Sphericity of Cuboidal Particle = ((((Length*Breadth*Height)*(0.75/pi))^(1/3)^2)*4*pi)/(2*(Length*Breadth+Breadth*Height+Height*Length))

Sphericity of Cylindrical Particle

Go Sphericity of Cylindrical Particle = (((((Cylinder Radius)^2*Cylinder Height*3/4)^(1/3))^2)*4*pi)/(2*pi*Cylinder Radius*(Cylinder Radius+Cylinder Height))

Pressure Gradient using Kozeny Carman Equation

Go Pressure Gradient = (150*Dynamic Viscosity*(1-Porosity)^2*Velocity)/((Sphericity of Particle)^2*(Equivalent Diameter)^2*(Porosity)^3)

Projected Area of Solid Body

Go Projected Area of Solid Particle Body = 2*(Drag Force)/(Drag Coefficient*Density of Liquid*(Velocity of Liquid)^(2))

Total Surface Area of Particle using Spericity

Go Total Surface Area of Particles = Mass*6/(Sphericity of Particle*Density Of Particle*Arithmetic Mean Diameter)

Terminal Settling Velocity of Single Particle

Go Terminal Velocity of Single Particle = Settling Velocity of Group of Particles/(Void fraction)^Richardsonb Zaki Index

Material Characteristic using Angle of Friction

Go Material Characteristic = (1-sin(Angle of Friction))/(1+sin(Angle of Friction))

Sphericity of Particle

Go Sphericity of Particle = (6*Volume of One Spherical Particle)/(Surface Area of Particle*Equivalent Diameter)

Total Number of Particles in Mixture

Go Total Number of Particles in Mixture = Total Mass of Mixture/(Density Of Particle*Volume Of One Particle)

Energy Required to Crush Coarse Materials according to Bond's Law

Go Energy per Unit Mass of Feed = Work Index*((100/Product Diameter)^0.5-(100/Feed Diameter)^0.5)

Number of Particles

Go Number of Particles = Mixture Mass/(Density of One Particle*Volume of Spherical Particle)

Fraction of Cycle Time used for Cake Formation

Go Fraction of Cycle Time Used For Cake Formation = Time Required For Cake Formation/Total Cycle Time

Time Required for Cake Formation

Go Time Required For Cake Formation = Fraction of Cycle Time Used For Cake Formation*Total Cycle Time

Specific Surface Area of Mixture

Go Specific Surface Area of Mixture = Total Surface Area/Total Mass of Mixture

Mass Mean Diameter

Go Mass Mean Diameter = (Mass Fraction*Size Of Particles Present In Fraction)

Sauter Mean Diameter

Go Sauter Mean Diameter = (6*Volume of Particle)/(Surface Area of Particle)

Porosity or Void Fraction

Go Porosity or Void Fraction = Volume of Voids in Bed/Total Volume of Bed

Total Surface Area of Particles

Go Surface Area = Surface Area of One Particle*Number of Particles

Applied Pressure in Terms of Coefficient of Flowability for Solids

Go Applied Pressure = Normal Pressure/Coefficient of Flowability

Coefficient of Flowability of Solids

Go Coefficient of Flowability = Normal Pressure/Applied Pressure

Surface Shape Factor

Go Surface Shape Factor = 1/Sphericity of Particle

Energy Required to Crush Coarse Materials according to Bond's Law Formula

Energy per Unit Mass of Feed = Work Index*((100/Product Diameter)^0.5-(100/Feed Diameter)^0.5)
E = W_i*((100/d₂)^0.5-(100/d₁)^0.5)

Energy Required to Crush Coarse Materials according to Bond's Law

Energy Required to Crush Coarse Materials according to Bond's Law calculates the energy needed to crush raw materials such that 80% of the product pass through a sieve aperture of product diameter.

Bond’s theory states that the energy used in crack
propagation is proportional to the new crack length produced.

Application: This law is useful in rough mill sizing. The work
index is useful in comparing the efficiency of milling
operations.

How to Calculate Energy Required to Crush Coarse Materials according to Bond's Law?

Energy Required to Crush Coarse Materials according to Bond's Law calculator uses Energy per Unit Mass of Feed = Work Index*((100/Product Diameter)^0.5-(100/Feed Diameter)^0.5) to calculate the Energy per Unit Mass of Feed, Energy Required to Crush Coarse Materials according to Bond's Law calculates the energy needed to crush raw materials such that 80% of the product pass through a sieve aperture of product diameter. Energy per Unit Mass of Feed is denoted by E symbol.

How to calculate Energy Required to Crush Coarse Materials according to Bond's Law using this online calculator? To use this online calculator for Energy Required to Crush Coarse Materials according to Bond's Law, enter Work Index (W_i), Product Diameter (d₂) & Feed Diameter (d₁) and hit the calculate button. Here is how the Energy Required to Crush Coarse Materials according to Bond's Law calculation can be explained with given input values -> 22.15064 = 11.6*((100/1.9)^0.5-(100/3.5)^0.5).

FAQ

What is Energy Required to Crush Coarse Materials according to Bond's Law?

Energy Required to Crush Coarse Materials according to Bond's Law calculates the energy needed to crush raw materials such that 80% of the product pass through a sieve aperture of product diameter and is represented as E = W_i*((100/d₂)^0.5-(100/d₁)^0.5) or Energy per Unit Mass of Feed = Work Index*((100/Product Diameter)^0.5-(100/Feed Diameter)^0.5). Work Index always means the equivalent amount of energy to reduce one ton of the ore from a very large size to 100 um. Just as the meter is used to measure and compare distances, Product Diameter is the diameter of the sieve aperture that allows 80% of the mass of the ground material to pass & Feed Diameter is the diameter of the sieve aperture that allows 80% of the mass of the feed to pass.

How to calculate Energy Required to Crush Coarse Materials according to Bond's Law?

Energy Required to Crush Coarse Materials according to Bond's Law calculates the energy needed to crush raw materials such that 80% of the product pass through a sieve aperture of product diameter is calculated using Energy per Unit Mass of Feed = Work Index*((100/Product Diameter)^0.5-(100/Feed Diameter)^0.5). To calculate Energy Required to Crush Coarse Materials according to Bond's Law, you need Work Index (W_i), Product Diameter (d₂) & Feed Diameter (d₁). With our tool, you need to enter the respective value for Work Index, Product Diameter & Feed Diameter and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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