✖Mass Fraction of a substance within a mixture is the ratio of the mass of that substance to the total mass of the mixture.ⓘ Mass Fraction [x_A]			+10% -10%
✖Size Of Particles Present In Fraction is the dimension of particles present in a certain fraction.ⓘ Size Of Particles Present In Fraction [D_pi]			+10% -10%

✖Mass Mean Diameter gives the average diameter of the sample space.ⓘ Mass Mean Diameter [D_W]

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Formula

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Mass Mean Diameter

Formula

`"D"_{"W"} = ("x"_{"A"}*"D"_{"pi"})`

Example

`"3m"=("0.6"*"5m")`

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Mass Mean Diameter Solution

STEP 0: Pre-Calculation Summary

Formula Used

Mass Mean Diameter = (Mass Fraction*Size Of Particles Present In Fraction)
D_W = (x_A*D_pi)
This formula uses 3 Variables

Variables Used

Mass Mean Diameter - (Measured in Meter) - Mass Mean Diameter gives the average diameter of the sample space.
Mass Fraction - Mass Fraction of a substance within a mixture is the ratio of the mass of that substance to the total mass of the mixture.
Size Of Particles Present In Fraction - (Measured in Meter) - Size Of Particles Present In Fraction is the dimension of particles present in a certain fraction.

STEP 1: Convert Input(s) to Base Unit

Mass Fraction: 0.6 --> No Conversion Required
Size Of Particles Present In Fraction: 5 Meter --> 5 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

D_W = (x_A*D_pi) --> (0.6*5)

Evaluating ... ...

D_W = 3

STEP 3: Convert Result to Output's Unit

3 Meter --> No Conversion Required

FINAL ANSWER

3 Meter <-- Mass Mean Diameter

(Calculation completed in 00.004 seconds)

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< 9 Basic Formulas Calculators

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

< 21 Basic Formulas of Mechanical Operations Calculators

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

Mass Mean Diameter Formula

Mass Mean Diameter = (Mass Fraction*Size Of Particles Present In Fraction)
D_W = (x_A*D_pi)

Why do you think that size separation is important?

Size separation is important in a number of ways like in order to determine particle size for the production of tablets and capsules, to improve mixing of powders, to improve the solubility and stability of particles during production, to optimize feed rate, agitation, screening during production.

How to Calculate Mass Mean Diameter?

Mass Mean Diameter calculator uses Mass Mean Diameter = (Mass Fraction*Size Of Particles Present In Fraction) to calculate the Mass Mean Diameter, Mass Mean Diameter gives the average diameter of the sample space. It is basically just a statistical formula that takes values of all the diameters and gives us a mean value . Mass Mean Diameter is denoted by D_W symbol.

How to calculate Mass Mean Diameter using this online calculator? To use this online calculator for Mass Mean Diameter, enter Mass Fraction (x_A) & Size Of Particles Present In Fraction (D_pi) and hit the calculate button. Here is how the Mass Mean Diameter calculation can be explained with given input values -> 3 = (0.6*5).

FAQ

What is Mass Mean Diameter?

Mass Mean Diameter gives the average diameter of the sample space. It is basically just a statistical formula that takes values of all the diameters and gives us a mean value and is represented as D_W = (x_A*D_pi) or Mass Mean Diameter = (Mass Fraction*Size Of Particles Present In Fraction). Mass Fraction of a substance within a mixture is the ratio of the mass of that substance to the total mass of the mixture & Size Of Particles Present In Fraction is the dimension of particles present in a certain fraction.

How to calculate Mass Mean Diameter?

Mass Mean Diameter gives the average diameter of the sample space. It is basically just a statistical formula that takes values of all the diameters and gives us a mean value is calculated using Mass Mean Diameter = (Mass Fraction*Size Of Particles Present In Fraction). To calculate Mass Mean Diameter, you need Mass Fraction (x_A) & Size Of Particles Present In Fraction (D_pi). With our tool, you need to enter the respective value for Mass Fraction & Size Of Particles Present In Fraction 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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