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Mean diameter of abrasive particles Formula

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Mean diameter of Abrasive Particles is the mean calculated from sampling method. Check FAQs

d mean = {(\frac{Z w}{A 0 \cdot N \cdot V^{\frac{3}{2}} \cdot {(\frac{ρ}{12 \cdot h b})}^{\frac{3}{4}}})}^{\frac{1}{3}}

d_mean - Mean Diameter of Abrasive Particles?Z_w - Metal Removal Rate?A₀ - Empirical Constant?N - Abrasive Particles Number Impacting Per Unit Time?V - Velocity?ρ - Density?h_b - Brinell Hardness?

Mean diameter of abrasive particles Example

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Here is how the Mean diameter of abrasive particles equation looks like with Values.

Here is how the Mean diameter of abrasive particles equation looks like with Units.

Here is how the Mean diameter of abrasive particles equation looks like.

4 = {(\frac{0.16}{100 \cdot 5 \cdot {1.4E+6}^{\frac{3}{2}} \cdot {(\frac{997}{12 \cdot 200})}^{\frac{3}{4}}})}^{\frac{1}{3}}

4mm = {(\frac{0.16m³/s}{100 \cdot 5 \cdot {1.4E+6m/s}^{\frac{3}{2}} \cdot {(\frac{997kg/m³}{12 \cdot 200kgf/mm²})}^{\frac{3}{4}}})}^{\frac{1}{3}}

4 = {(\frac{0.16}{100 \cdot 5 \cdot {1.4E+6}^{\frac{3}{2}} \cdot {(\frac{997}{12 \cdot 200})}^{\frac{3}{4}}})}^{\frac{1}{3}}

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Mean diameter of abrasive particles Solution

Follow our step by step solution on how to calculate Mean diameter of abrasive particles?

FIRST Step Consider the formula

d mean = {(\frac{Z w}{A 0 \cdot N \cdot V^{\frac{3}{2}} \cdot {(\frac{ρ}{12 \cdot h b})}^{\frac{3}{4}}})}^{\frac{1}{3}}

Next Step Substitute values of Variables

∴

d mean = {(\frac{0.16m³/s}{100 \cdot 5 \cdot {1.4E+6m/s}^{\frac{3}{2}} \cdot {(\frac{997kg/m³}{12 \cdot 200kgf/mm²})}^{\frac{3}{4}}})}^{\frac{1}{3}}

Next Step Convert Units

∴

d mean = {(\frac{0.16m³/s}{100 \cdot 5 \cdot {1.4E+6m/s}^{\frac{3}{2}} \cdot {(\frac{997kg/m³}{12 \cdot 2E+9Pa})}^{\frac{3}{4}}})}^{\frac{1}{3}}

Next Step Prepare to Evaluate

∴

d mean = {(\frac{0.16}{100 \cdot 5 \cdot {1.4E+6}^{\frac{3}{2}} \cdot {(\frac{997}{12 \cdot 2E+9})}^{\frac{3}{4}}})}^{\frac{1}{3}}

Next Step Evaluate

∴

d mean = 0.004m

LAST Step Convert to Output's Unit

∴

d mean = 4mm

Mean diameter of abrasive particles Formula Elements

Variables

Mean Diameter of Abrasive Particles

Mean diameter of Abrasive Particles is the mean calculated from sampling method.

Symbol: d_mean

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Mean Diameter of Abrasive Particles

Metal Removal Rate

Metal 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.

Symbol: Z_w

Measurement: Volumetric Flow RateUnit: m³/s

Note: Value should be greater than 0.

Formulas to find Metal Removal Rate

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.

Symbol: A₀

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Empirical Constant

Abrasive Particles Number Impacting Per Unit Time

Abrasive Particles Number Impacting Per Unit Time is defined as the average number of particles impacting work surface to cut it during Abrasive Jet Machining.

Symbol: N

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Abrasive Particles Number Impacting Per Unit Time

Velocity

Velocity is a vector quantity (it has both magnitude and direction) and is the rate of change of the position of an object with respect to time.

Symbol: V

Measurement: SpeedUnit: m/s

Note: Value can be positive or negative.

Formulas to find Velocity

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.

Symbol: ρ

Measurement: DensityUnit: kg/m³

Note: Value should be greater than 0.

Formulas to find Density

Brinell Hardness

Brinell Hardness uses a hard, spherical indenter which is forced into the surface of the metal to be tested.

Symbol: h_b

Measurement: PressureUnit: kgf/mm²

Note: Value should be greater than 0.

Formulas to find Brinell Hardness

Other formulas in Abrasive Jet Machining (AJM) category

Go Material removal rate

Z w = A 0 \cdot N \cdot {d mean}^{3} \cdot V^{\frac{3}{2}} \cdot {(\frac{ρ}{12 \cdot h b})}^{\frac{3}{4}}

Go Empirical constant for AJM

A 0 = \frac{Z w}{N \cdot {d mean}^{3} \cdot V^{\frac{3}{2}} \cdot {(\frac{ρ}{12 \cdot h b})}^{\frac{3}{4}}}

How to Evaluate Mean diameter of abrasive particles?

Mean diameter of abrasive particles evaluator uses Mean Diameter of Abrasive Particles = (Metal Removal Rate/(Empirical Constant*Abrasive Particles Number Impacting Per Unit Time*Velocity^(3/2)*(Density/(12*Brinell Hardness))^(3/4)))^(1/3) to evaluate the Mean Diameter of Abrasive Particles, The mean diameter of abrasive particles refers to the average size of the abrasive particles used in processes like Abrasive Jet Machining (AJM) or abrasive grinding. It's a crucial parameter because it affects the material removal rate, surface finish, and overall efficiency of the machining operation. Mean Diameter of Abrasive Particles is denoted by d_mean symbol.

How to evaluate Mean diameter of abrasive particles using this online evaluator? To use this online evaluator for Mean diameter of abrasive particles, enter Metal Removal Rate (Z_w), Empirical Constant (A₀), Abrasive Particles Number Impacting Per Unit Time (N), Velocity (V), Density (ρ) & Brinell Hardness (h_b) and hit the calculate button.

FAQs on Mean diameter of abrasive particles

What is the formula to find Mean diameter of abrasive particles?

The formula of Mean diameter of abrasive particles is expressed as Mean Diameter of Abrasive Particles = (Metal Removal Rate/(Empirical Constant*Abrasive Particles Number Impacting Per Unit Time*Velocity^(3/2)*(Density/(12*Brinell Hardness))^(3/4)))^(1/3). Here is an example- 4000 = (0.16/(100*5*1420686.92120444^(3/2)*(997/(12*1961329999.99986))^(3/4)))^(1/3).

How to calculate Mean diameter of abrasive particles?

With Metal Removal Rate (Z_w), Empirical Constant (A₀), Abrasive Particles Number Impacting Per Unit Time (N), Velocity (V), Density (ρ) & Brinell Hardness (h_b) we can find Mean diameter of abrasive particles using the formula - Mean Diameter of Abrasive Particles = (Metal Removal Rate/(Empirical Constant*Abrasive Particles Number Impacting Per Unit Time*Velocity^(3/2)*(Density/(12*Brinell Hardness))^(3/4)))^(1/3).

Can the Mean diameter of abrasive particles be negative?

No, the Mean diameter of abrasive particles, measured in Length cannot be negative.

Which unit is used to measure Mean diameter of abrasive particles?

Mean diameter of abrasive particles is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Mean diameter of abrasive particles can be measured.

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Mean diameter of abrasive particles Formula

Mean diameter of abrasive particles Example

Mean diameter of abrasive particles Solution

Mean diameter of abrasive particles Formula Elements

Other formulas in Abrasive Jet Machining (AJM) category

How to Evaluate Mean diameter of abrasive particles?

FAQs on Mean diameter of abrasive particles

Variable Name