Sauter Mean Diameter Calculator

✖Volume of Particle is the amount of space that particular particle occupies.ⓘ Volume of Particle [V_{particle_1}]			+10% -10%
✖Surface Area of Particle is a measure of the total area that the surface of the object occupies.ⓘ Surface Area of Particle [S_particle]			+10% -10%

✖Sauter Mean Diameter is defined as the diameter of a sphere that has the same volume/surface area ratio as a particle of interest.ⓘ Sauter Mean Diameter [d_sauter]

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Formula

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Sauter Mean Diameter

Formula

`"d"_{"sauter"} = (6*"V"_{"particle_1"})/("S"_{"particle"})`

Example

`"8.942308m"=(6*"15.5m³")/("10.4m²")`

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Sauter Mean Diameter Solution

STEP 0: Pre-Calculation Summary

Formula Used

Sauter Mean Diameter = (6*Volume of Particle)/(Surface Area of Particle)
d_sauter = (6*V_{particle_1})/(S_particle)
This formula uses 3 Variables

Variables Used

Sauter Mean Diameter - (Measured in Meter) - Sauter Mean Diameter is defined as the diameter of a sphere that has the same volume/surface area ratio as a particle of interest.
Volume of Particle - (Measured in Cubic Meter) - Volume of Particle is the amount of space that particular particle occupies.
Surface Area of Particle - (Measured in Square Meter) - Surface Area of Particle is a measure of the total area that the surface of the object occupies.

STEP 1: Convert Input(s) to Base Unit

Volume of Particle: 15.5 Cubic Meter --> 15.5 Cubic Meter No Conversion Required
Surface Area of Particle: 10.4 Square Meter --> 10.4 Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d_sauter = (6*V_{particle_1})/(S_particle) --> (6*15.5)/(10.4)

Evaluating ... ...

d_sauter = 8.94230769230769

STEP 3: Convert Result to Output's Unit

8.94230769230769 Meter --> No Conversion Required

FINAL ANSWER

8.94230769230769 ≈ 8.942308 Meter <-- Sauter Mean Diameter

(Calculation completed in 00.020 seconds)

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NIT Srinagar (NIT SRI), Srinagar, Kashmir

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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

Sauter Mean Diameter Formula

Sauter Mean Diameter = (6*Volume of Particle)/(Surface Area of Particle)
d_sauter = (6*V_{particle_1})/(S_particle)

What is a sieving?

Sieving is a process by which fine particles are separated from bigger particles by using a sieve. It is used in flour mill or at construction sites. In flour mill, impurities like husks and stones are removed from wheat. Pebbles and stones are removed from sand by sieving.

How to Calculate Sauter Mean Diameter?

Sauter Mean Diameter calculator uses Sauter Mean Diameter = (6*Volume of Particle)/(Surface Area of Particle) to calculate the Sauter Mean Diameter, Sauter mean diameter is an average of particle size. It is defined as the diameter of a sphere that has the same volume/surface area ratio as a particle of interest. SMD is typically defined in terms of the surface diameter and volume diameter. Sauter Mean Diameter is denoted by d_sauter symbol.

How to calculate Sauter Mean Diameter using this online calculator? To use this online calculator for Sauter Mean Diameter, enter Volume of Particle (V_{particle_1}) & Surface Area of Particle (S_particle) and hit the calculate button. Here is how the Sauter Mean Diameter calculation can be explained with given input values -> 8.942308 = (6*15.5)/(10.4).

FAQ

What is Sauter Mean Diameter?

Sauter mean diameter is an average of particle size. It is defined as the diameter of a sphere that has the same volume/surface area ratio as a particle of interest. SMD is typically defined in terms of the surface diameter and volume diameter and is represented as d_sauter = (6*V_{particle_1})/(S_particle) or Sauter Mean Diameter = (6*Volume of Particle)/(Surface Area of Particle). Volume of Particle is the amount of space that particular particle occupies & Surface Area of Particle is a measure of the total area that the surface of the object occupies.

How to calculate Sauter Mean Diameter?

Sauter mean diameter is an average of particle size. It is defined as the diameter of a sphere that has the same volume/surface area ratio as a particle of interest. SMD is typically defined in terms of the surface diameter and volume diameter is calculated using Sauter Mean Diameter = (6*Volume of Particle)/(Surface Area of Particle). To calculate Sauter Mean Diameter, you need Volume of Particle (V_{particle_1}) & Surface Area of Particle (S_particle). With our tool, you need to enter the respective value for Volume of Particle & Surface Area of Particle 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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