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Density of abrasive particles Formula

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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. Check FAQs

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

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

Density of abrasive particles Example

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

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

Here is how the Density of abrasive particles equation looks like.

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

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

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

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Density of abrasive particles Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Convert Units

∴

ρ = 12 \cdot 2E+9Pa \cdot {(\frac{0.16m³/s}{100 \cdot 5 \cdot {0.004m}^{3} \cdot {1.4E+6m/s}^{\frac{3}{2}}})}^{\frac{4}{3}}

Next Step Prepare to Evaluate

∴

ρ = 12 \cdot 2E+9 \cdot {(\frac{0.16}{100 \cdot 5 \cdot {0.004}^{3} \cdot {1.4E+6}^{\frac{3}{2}}})}^{\frac{4}{3}}

Next Step Evaluate

∴

ρ = 996.999999999997kg/m³

LAST Step Rounding Answer

∴

ρ = 997kg/m³

Density of abrasive particles Formula Elements

Variables

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

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

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

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

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 Density of abrasive particles?

Density of abrasive particles evaluator uses Density = 12*Brinell Hardness*(Metal Removal Rate/(Empirical Constant*Abrasive Particles Number Impacting Per Unit Time*Mean Diameter of Abrasive Particles^3*Velocity^(3/2)))^(4/3) to evaluate the Density, Density of abrasive particles typically involves determining the mass of the abrasive particles value provides insight into the concentration or compactness of the abrasive particles within a given volume. Density is denoted by ρ symbol.

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

FAQs on Density of abrasive particles

What is the formula to find Density of abrasive particles?

The formula of Density of abrasive particles is expressed as Density = 12*Brinell Hardness*(Metal Removal Rate/(Empirical Constant*Abrasive Particles Number Impacting Per Unit Time*Mean Diameter of Abrasive Particles^3*Velocity^(3/2)))^(4/3). Here is an example- 997 = 12*1961329999.99986*(0.16/(100*5*0.004^3*1420686.92120444^(3/2)))^(4/3).

How to calculate Density of abrasive particles?

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

Can the Density of abrasive particles be negative?

No, the Density of abrasive particles, measured in Density cannot be negative.

Which unit is used to measure Density of abrasive particles?

Density of abrasive particles is usually measured using the Kilogram per Cubic Meter[kg/m³] for Density. Kilogram per Cubic Centimeter[kg/m³], Gram per Cubic Meter[kg/m³], Gram per Cubic Centimeter[kg/m³] are the few other units in which Density of abrasive particles can be measured.

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Density of abrasive particles Formula

Density of abrasive particles Example

Density of abrasive particles Solution

Density of abrasive particles Formula Elements

Other formulas in Abrasive Jet Machining (AJM) category

How to Evaluate Density of abrasive particles?

FAQs on Density of abrasive particles

Variable Name