Pressure Gradient using Kozeny Carman Equation Calculator

✖Dynamic Viscosity of a fluid is the measure of its resistance to flow when an external force is applied.ⓘ Dynamic Viscosity [μ]			+10% -10%
✖Porosity is the ratio of volume of voids to volume of soil.ⓘ Porosity [η]			+10% -10%
✖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.ⓘ Velocity [v]			+10% -10%
✖Sphericity of Particle is a measure of how closely the shape of an object resembles that of a perfect sphere.ⓘ Sphericity of Particle [Φ_p]			+10% -10%
✖Equivalent diameter is the diameter equivalent to the given value.ⓘ Equivalent Diameter [De]			+10% -10%

✖Pressure Gradient is the change in pressure with respect to radial distance of element.ⓘ Pressure Gradient using Kozeny Carman Equation [dPbydr]

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Formula

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Pressure Gradient using Kozeny Carman Equation

Formula

`"dPbydr" = (150*"μ"*(1-"η")^2*"v")/(("Φ"_{"p"})^2*("De")^2*("η")^3)`

Example

`"10.30234N/m³"=(150*"0.59P"*(1-"0.5")^2*"60m/s")/(("18.46")^2*("0.55m")^2*("0.5")^3)`

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Pressure Gradient using Kozeny Carman Equation Solution

STEP 0: Pre-Calculation Summary

Formula Used

Pressure Gradient = (150*Dynamic Viscosity*(1-Porosity)^2*Velocity)/((Sphericity of Particle)^2*(Equivalent Diameter)^2*(Porosity)^3)
dPbydr = (150*μ*(1-η)^2*v)/((Φ_p)^2*(De)^2*(η)^3)
This formula uses 6 Variables

Variables Used

Pressure Gradient - (Measured in Newton per Cubic Meter) - Pressure Gradient is the change in pressure with respect to radial distance of element.
Dynamic Viscosity - (Measured in Pascal Second) - Dynamic Viscosity of a fluid is the measure of its resistance to flow when an external force is applied.
Porosity - Porosity is the ratio of volume of voids to volume of soil.
Velocity - (Measured in Meter per Second) - 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.
Sphericity of Particle - Sphericity of Particle is a measure of how closely the shape of an object resembles that of a perfect sphere.
Equivalent Diameter - (Measured in Meter) - Equivalent diameter is the diameter equivalent to the given value.

STEP 1: Convert Input(s) to Base Unit

Dynamic Viscosity: 0.59 Poise --> 0.059 Pascal Second (Check conversion here)
Porosity: 0.5 --> No Conversion Required
Velocity: 60 Meter per Second --> 60 Meter per Second No Conversion Required
Sphericity of Particle: 18.46 --> No Conversion Required
Equivalent Diameter: 0.55 Meter --> 0.55 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

dPbydr = (150*μ*(1-η)^2*v)/((Φ_p)^2*(De)^2*(η)^3) --> (150*0.059*(1-0.5)^2*60)/((18.46)^2*(0.55)^2*(0.5)^3)

Evaluating ... ...

dPbydr = 10.3023368193033

STEP 3: Convert Result to Output's Unit

10.3023368193033 Newton per Cubic Meter --> No Conversion Required

FINAL ANSWER

10.3023368193033 ≈ 10.30234 Newton per Cubic Meter <-- Pressure Gradient

(Calculation completed in 00.004 seconds)

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DJ Sanghvi College of Engineering (DJSCE), Mumbai

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< 5 Fluidisation Calculators

Dynamic Viscosity based on Kozeny Carman Equation

Go Dynamic Viscosity = (Pressure Gradient*(Sphericity of Particle)^2*(Equivalent Diameter)^2*(Porosity)^3)/(150*(1-Porosity)^2*Velocity)

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)

Volume of Voids in Bed Based on Porosity

Go Volume of Voids in Bed = Porosity or Void Fraction*Total Volume of Bed

Total Volume of Bed Based on Porosity

Go Total Volume of Bed = Volume of Voids in Bed/Porosity or Void Fraction

Porosity or Void Fraction

Go Porosity or Void Fraction = Volume of Voids in Bed/Total Volume of Bed

< 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

Pressure Gradient using Kozeny Carman Equation Formula

Pressure Gradient = (150*Dynamic Viscosity*(1-Porosity)^2*Velocity)/((Sphericity of Particle)^2*(Equivalent Diameter)^2*(Porosity)^3)
dPbydr = (150*μ*(1-η)^2*v)/((Φ_p)^2*(De)^2*(η)^3)

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How to Calculate Pressure Gradient using Kozeny Carman Equation?

Pressure Gradient using Kozeny Carman Equation calculator uses Pressure Gradient = (150*Dynamic Viscosity*(1-Porosity)^2*Velocity)/((Sphericity of Particle)^2*(Equivalent Diameter)^2*(Porosity)^3) to calculate the Pressure Gradient, The Pressure Gradient using Kozeny Carman Equation is a relation used in the field of fluid dynamics to calculate the pressure drop of a fluid flowing through a packed bed of solids. Pressure Gradient is denoted by dPbydr symbol.

How to calculate Pressure Gradient using Kozeny Carman Equation using this online calculator? To use this online calculator for Pressure Gradient using Kozeny Carman Equation, enter Dynamic Viscosity (μ), Porosity (η), Velocity (v), Sphericity of Particle (Φ_p) & Equivalent Diameter (De) and hit the calculate button. Here is how the Pressure Gradient using Kozeny Carman Equation calculation can be explained with given input values -> 10.47695 = (150*0.059*(1-0.5)^2*60)/((18.46)^2*(0.55)^2*(0.5)^3).

FAQ

What is Pressure Gradient using Kozeny Carman Equation?

The Pressure Gradient using Kozeny Carman Equation is a relation used in the field of fluid dynamics to calculate the pressure drop of a fluid flowing through a packed bed of solids and is represented as dPbydr = (150*μ*(1-η)^2*v)/((Φ_p)^2*(De)^2*(η)^3) or Pressure Gradient = (150*Dynamic Viscosity*(1-Porosity)^2*Velocity)/((Sphericity of Particle)^2*(Equivalent Diameter)^2*(Porosity)^3). Dynamic Viscosity of a fluid is the measure of its resistance to flow when an external force is applied, Porosity is the ratio of volume of voids to volume of soil, 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, Sphericity of Particle is a measure of how closely the shape of an object resembles that of a perfect sphere & Equivalent diameter is the diameter equivalent to the given value.

How to calculate Pressure Gradient using Kozeny Carman Equation?

The Pressure Gradient using Kozeny Carman Equation is a relation used in the field of fluid dynamics to calculate the pressure drop of a fluid flowing through a packed bed of solids is calculated using Pressure Gradient = (150*Dynamic Viscosity*(1-Porosity)^2*Velocity)/((Sphericity of Particle)^2*(Equivalent Diameter)^2*(Porosity)^3). To calculate Pressure Gradient using Kozeny Carman Equation, you need Dynamic Viscosity (μ), Porosity (η), Velocity (v), Sphericity of Particle (Φ_p) & Equivalent Diameter (De). With our tool, you need to enter the respective value for Dynamic Viscosity, Porosity, Velocity, Sphericity of Particle & Equivalent Diameter 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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