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## Credits

University Institute of Technology RGPV (UIT - RGPV), Bhopal
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## Mean diameter of abrasive particles Solution

STEP 0: Pre-Calculation Summary
Formula Used
mean_diameter_of_abrasive_particles = (Material removal rate/(Empirical constant*No. of abrasive particles impacting per unit time*Velocity^(3/2)*(Density/(12*Brinell Hardness))^(3/4)))^(1/3)
d = (Zw/(A0*N*v^(3/2)*(ρ/(12*HB))^(3/4)))^(1/3)
This formula uses 6 Variables
Variables Used
Material removal rate - Material removal rate (MRR) is the amount of material removed per time unit (usually per minute) when performing machining operations such as using a lathe or milling machine. (Measured in Meter³ per Second)
Empirical constant- The Empirical constant is a self determined constant whose value is accessible from table of such constants. This constant is used to calculate the intrinsic carrier concentration.
No. of abrasive particles impacting per unit time- No. of abrasive particles impacting per unit time
Velocity - Velocity, in physics, is a vector quantity (it has both magnitude and direction), and is the time rate of change of position (of an object). (Measured in Meter per Second)
Density - The density of a material shows the denseness of that material in a specific given area. This is taken as mass per unit volume of a given object. (Measured in Kilogram per Meter³)
Brinell Hardness - Brinell Hardness uses a hard, spherical indenter which is forced into the surface of the metal to be tested. (Measured in Kilogram-Force per Square Millimeter)
STEP 1: Convert Input(s) to Base Unit
Material removal rate: 1 Meter³ per Second --> 1 Meter³ per Second No Conversion Required
Empirical constant: 100 --> No Conversion Required
No. of abrasive particles impacting per unit time: 5 --> No Conversion Required
Velocity: 60 Meter per Second --> 60 Meter per Second No Conversion Required
Density: 997 Kilogram per Meter³ --> 997 Kilogram per Meter³ No Conversion Required
Brinell Hardness: 200 Kilogram-Force per Square Millimeter --> 1961329999.99986 Pascal (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
d = (Zw/(A0*N*v^(3/2)*(ρ/(12*HB))^(3/4)))^(1/3) --> (1/(100*5*60^(3/2)*(997/(12*1961329999.99986))^(3/4)))^(1/3)
Evaluating ... ...
d = 1.13377505214266
STEP 3: Convert Result to Output's Unit
1.13377505214266 Meter -->1133.77505214266 Millimeter (Check conversion here)
1133.77505214266 Millimeter <-- Mean diameter of abrasive particles
(Calculation completed in 00.031 seconds)

## < 11 Other formulas that you can solve using the same Inputs

Stanton Number (using basic fluid properties)
stanton_number = External convection heat transfer coefficient/(Specific Heat Capacity*Fluid Velocity*Density) Go
Reynolds Number for Non-Circular Tubes
reynolds_number = Density*Fluid Velocity*Characteristic Length/Dynamic viscosity Go
Reynolds Number for Circular Tubes
reynolds_number = Density*Fluid Velocity*Diameter /Dynamic viscosity Go
Archimedes Principle
archimedes_principle = Density*Acceleration Due To Gravity*Velocity Go
Pressure when density and height are given
pressure = Density*Acceleration Due To Gravity*Height Go
Molar Volume
molar_volume = (Atomic Weight*Molar Mass)/Density Go
Centripetal Force
Air Resistance Force
air_resistance = Air Constant*Velocity^2 Go
Number of atomic sites
number_atomic_sites = Density/Atomic Mass Go
Kinetic Energy
kinetic_energy = (Mass*Velocity^2)/2 Go
Tensile strength from Brinell hardness
tensile_strength = (3.45/9.8067)*Brinell Hardness Go

### Mean diameter of abrasive particles Formula

mean_diameter_of_abrasive_particles = (Material removal rate/(Empirical constant*No. of abrasive particles impacting per unit time*Velocity^(3/2)*(Density/(12*Brinell Hardness))^(3/4)))^(1/3)
d = (Zw/(A0*N*v^(3/2)*(ρ/(12*HB))^(3/4)))^(1/3)

## What is Abrasive Jet Machining ?

Abrasive Jet Machining is a process that uses a very high speed (supersonic about 2.5 Mach number) water jet mixed with abrasives to cut any type of material without, in any way, affecting the work material or the environment. The AJM machines aim a highly focused, supersonic stream of water at the material such that it can cut composites smoothly by eroding them without generating any heat. Thus the AJM process eliminates all the thermal and mechanical distortion caused by conventional cutting methods. Also the water jet nozzle can be directed at any angle to the material thereby allowing for angled cuts. For cutting soft materials such as textiles and food stuffs, pure water without any abrasives is used.

## How to Calculate Mean diameter of abrasive particles?

Mean diameter of abrasive particles calculator uses mean_diameter_of_abrasive_particles = (Material removal rate/(Empirical constant*No. of abrasive particles impacting per unit time*Velocity^(3/2)*(Density/(12*Brinell Hardness))^(3/4)))^(1/3) to calculate the Mean diameter of abrasive particles, The Mean diameter of abrasive particles formula is defined as the average size of the impacting abrasive particles. Mean diameter of abrasive particles and is denoted by d symbol.

How to calculate Mean diameter of abrasive particles using this online calculator? To use this online calculator for Mean diameter of abrasive particles, enter Material removal rate (Zw), Empirical constant (A0), No. of abrasive particles impacting per unit time (N), Velocity (v), Density (ρ) and Brinell Hardness (HB) and hit the calculate button. Here is how the Mean diameter of abrasive particles calculation can be explained with given input values -> 1133.775 = (1/(100*5*60^(3/2)*(997/(12*1961329999.99986))^(3/4)))^(1/3).

### FAQ

What is Mean diameter of abrasive particles?
The Mean diameter of abrasive particles formula is defined as the average size of the impacting abrasive particles and is represented as d = (Zw/(A0*N*v^(3/2)*(ρ/(12*HB))^(3/4)))^(1/3) or mean_diameter_of_abrasive_particles = (Material removal rate/(Empirical constant*No. of abrasive particles impacting per unit time*Velocity^(3/2)*(Density/(12*Brinell Hardness))^(3/4)))^(1/3). Material removal rate (MRR) is the amount of material removed per time unit (usually per minute) when performing machining operations such as using a lathe or milling machine, The Empirical constant is a self determined constant whose value is accessible from table of such constants. This constant is used to calculate the intrinsic carrier concentration, No. of abrasive particles impacting per unit time, Velocity, in physics, is a vector quantity (it has both magnitude and direction), and is the time rate of change of position (of an object). , The density of a material shows the denseness of that material in a specific given area. This is taken as mass per unit volume of a given object. and Brinell Hardness uses a hard, spherical indenter which is forced into the surface of the metal to be tested.
How to calculate Mean diameter of abrasive particles?
The Mean diameter of abrasive particles formula is defined as the average size of the impacting abrasive particles is calculated using mean_diameter_of_abrasive_particles = (Material removal rate/(Empirical constant*No. of abrasive particles impacting per unit time*Velocity^(3/2)*(Density/(12*Brinell Hardness))^(3/4)))^(1/3). To calculate Mean diameter of abrasive particles, you need Material removal rate (Zw), Empirical constant (A0), No. of abrasive particles impacting per unit time (N), Velocity (v), Density (ρ) and Brinell Hardness (HB). With our tool, you need to enter the respective value for Material removal rate, Empirical constant, No. of abrasive particles impacting per unit time, Velocity, Density and Brinell Hardness 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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