Work required for Reduction of Particles Solution

STEP 0: Pre-Calculation Summary
Formula Used
Work Required for Reduction of Particles = Power Required by Machine/Feed Rate to Machine
WR = PM/
This formula uses 3 Variables
Variables Used
Work Required for Reduction of Particles - (Measured in Joule per Kilogram) - Work Required for Reduction of Particles is the amount of work the machine does to reduce the feed particles per unit mass.
Power Required by Machine - (Measured in Watt) - Power Required by Machine is the power that is required by the machine to reduce the feed particles into desired dimensions.
Feed Rate to Machine - (Measured in Kilogram per Second) - Feed Rate to Machine is the rate of flow of feed into the machine .
STEP 1: Convert Input(s) to Base Unit
Power Required by Machine: 23 Watt --> 23 Watt No Conversion Required
Feed Rate to Machine: 24 Kilogram per Second --> 24 Kilogram per Second No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
WR = PM/ṁ --> 23/24
Evaluating ... ...
WR = 0.958333333333333
STEP 3: Convert Result to Output's Unit
0.958333333333333 Joule per Kilogram --> No Conversion Required
FINAL ANSWER
0.958333333333333 0.958333 Joule per Kilogram <-- Work Required for Reduction of Particles
(Calculation completed in 00.004 seconds)

Credits

Created by Vaibhav Mishra
DJ Sanghvi College of Engineering (DJSCE), Mumbai
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Verified by Ayush gupta
University School of Chemical Technology-USCT (GGSIPU), New Delhi
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13 Formulas on Size Reduction Laws Calculators

Area of Product given Crushing Efficiency
Go Area of Product = ((Crushing Efficiency*Energy Absorbed by Material)/(Surface Energy per Unit Area*Length))+Area of Feed
Area of Feed given Crushing Efficiency
Go Area of Feed = Area of Product-((Crushing Efficiency*Energy Absorbed By Unit Mass Of Feed)/(Surface Energy per Unit Area))
Energy Absorbed by Material while Crushing
Go Energy Absorbed by Material = (Surface Energy per Unit Area*(Area of Product-Area of Feed))/(Crushing Efficiency)
Crushing Efficiency
Go Crushing Efficiency = (Surface Energy per Unit Area*(Area of Product-Area of Feed))/Energy Absorbed by Material
Power Consumption by Mill while Crushing
Go Power Consumption by Mill While Crushing = Power Consumption for Crushing Only+Power Consumption While Mill is Empty
Power Consumption for Crushing only
Go Power Consumption for Crushing Only = Power Consumption by Mill While Crushing-Power Consumption While Mill is Empty
Mechanical Efficiency given Energy fed to System
Go Mechanical Efficiency in Terms of Energy Fed = Energy Absorbed By Unit Mass Of Feed/Energy Fed to Machine
Radius of Crushing Rolls
Go Radius of Crushing Rolls = (Maximum Diameter of Particle Nipped by Rolls-Half of Gap between Rolls)/0.04
Maximum Diameter of Particle Nipped by Rolls
Go Maximum Diameter of Particle Nipped by Rolls = 0.04*Radius of Crushing Rolls+Half of Gap between Rolls
Power Required by Machine for Size Reduction of Particles
Go Power Required by Machine = Work Required for Reduction of Particles*Feed Rate to Machine
Feed Rate to Machine for Size Reduction of Particles
Go Feed Rate to Machine = Power Required by Machine/Work Required for Reduction of Particles
Work required for Reduction of Particles
Go Work Required for Reduction of Particles = Power Required by Machine/Feed Rate to Machine
Reduction Ratio
Go Reduction Ratio = Feed Diameter/Product Diameter

19 Important Formulas in Size Reduction Laws Calculators

Half of Gaps between Rolls
Go Half of Gap between Rolls = ((cos(Half Angle of Nip))*(Radius of Feed+Radius of Crushing Rolls))-Radius of Crushing Rolls
Area of Product given Crushing Efficiency
Go Area of Product = ((Crushing Efficiency*Energy Absorbed by Material)/(Surface Energy per Unit Area*Length))+Area of Feed
Radius of Feed in Smooth Roll Crusher
Go Radius of Feed = (Radius of Crushing Rolls+Half of Gap between Rolls)/cos(Half Angle of Nip)-Radius of Crushing Rolls
Critical Speed of Conical Ball Mill
Go Critical Speed of Conical Ball Mill = 1/(2*pi)*sqrt( [g]/(Radius of Ball Mill-Radius of Ball))
Area of Feed given Crushing Efficiency
Go Area of Feed = Area of Product-((Crushing Efficiency*Energy Absorbed By Unit Mass Of Feed)/(Surface Energy per Unit Area))
Projected Area of Solid Body
Go Projected Area of Solid Particle Body = 2*(Drag Force)/(Drag Coefficient*Density of Liquid*(Velocity of Liquid)^(2))
Energy Absorbed by Material while Crushing
Go Energy Absorbed by Material = (Surface Energy per Unit Area*(Area of Product-Area of Feed))/(Crushing Efficiency)
Crushing Efficiency
Go Crushing Efficiency = (Surface Energy per Unit Area*(Area of Product-Area of Feed))/Energy Absorbed by Material
Radius of Ball Mill
Go Radius of Ball Mill = ([g]/(2*pi*Critical Speed of Conical Ball Mill)^2)+Radius of Ball
Terminal Settling Velocity of Single Particle
Go Terminal Velocity of Single Particle = Settling Velocity of Group of Particles/(Void fraction)^Richardsonb Zaki Index
Power Consumption while Mill is Empty
Go Power Consumption While Mill is Empty = Power Consumption by Mill While Crushing-Power Consumption for Crushing Only
Power Consumption for Crushing only
Go Power Consumption for Crushing Only = Power Consumption by Mill While Crushing-Power Consumption While Mill is Empty
Mechanical Efficiency given Energy fed to System
Go Mechanical Efficiency in Terms of Energy Fed = Energy Absorbed By Unit Mass Of Feed/Energy Fed to Machine
Radius of Crushing Rolls
Go Radius of Crushing Rolls = (Maximum Diameter of Particle Nipped by Rolls-Half of Gap between Rolls)/0.04
Maximum Diameter of Particle Nipped by Rolls
Go Maximum Diameter of Particle Nipped by Rolls = 0.04*Radius of Crushing Rolls+Half of Gap between Rolls
Work required for Reduction of Particles
Go Work Required for Reduction of Particles = Power Required by Machine/Feed Rate to Machine
Product Diameter Based on Reduction Ratio
Go Product Diameter = Feed Diameter/Reduction Ratio
Feed Diameter based on Reduction Law
Go Feed Diameter = Reduction Ratio*Product Diameter
Reduction Ratio
Go Reduction Ratio = Feed Diameter/Product Diameter

Work required for Reduction of Particles Formula

Work Required for Reduction of Particles = Power Required by Machine/Feed Rate to Machine
WR = PM/

What is Kick's theory of size reduction?

The Kick's law states that the energy required to reduce the size of particles is proportional to the ratio of the initial size of a typical dimension (for example the diameter of the particles) to the final size of that dimension. This relation is derived directly form the elasticity theory of ideal brittle solids.

What is Size reduction?

Size reduction is a process in which the particle size of a solid is made smaller. The term size reduction is applied to ways in which particles of solids are cut or broken into smaller pieces. Size reduction is necessary if the starting material is too coarse, and the final product needs to be a fine powder.

How to Calculate Work required for Reduction of Particles?

Work required for Reduction of Particles calculator uses Work Required for Reduction of Particles = Power Required by Machine/Feed Rate to Machine to calculate the Work Required for Reduction of Particles, The Work required for Reduction of Particles is the amount of work the machine does to reduce the feed particles per unit mass, it is really useful while operating mills. Work Required for Reduction of Particles is denoted by WR symbol.

How to calculate Work required for Reduction of Particles using this online calculator? To use this online calculator for Work required for Reduction of Particles, enter Power Required by Machine (PM) & Feed Rate to Machine (ṁ) and hit the calculate button. Here is how the Work required for Reduction of Particles calculation can be explained with given input values -> 0.958333 = 23/24.

FAQ

What is Work required for Reduction of Particles?
The Work required for Reduction of Particles is the amount of work the machine does to reduce the feed particles per unit mass, it is really useful while operating mills and is represented as WR = PM/ṁ or Work Required for Reduction of Particles = Power Required by Machine/Feed Rate to Machine. Power Required by Machine is the power that is required by the machine to reduce the feed particles into desired dimensions & Feed Rate to Machine is the rate of flow of feed into the machine .
How to calculate Work required for Reduction of Particles?
The Work required for Reduction of Particles is the amount of work the machine does to reduce the feed particles per unit mass, it is really useful while operating mills is calculated using Work Required for Reduction of Particles = Power Required by Machine/Feed Rate to Machine. To calculate Work required for Reduction of Particles, you need Power Required by Machine (PM) & Feed Rate to Machine (ṁ). With our tool, you need to enter the respective value for Power Required by Machine & Feed Rate to Machine 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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