Effective Particle Diameter by Ergun given Frication Factor Calculator

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Internal Flow

Basics of HMT

Conduction

Convection

Convective Mass Transfer

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Flow of Liquids inside Packed Beds

Flow inside tubes

✖The Friction factor or Moody chart is the plot of the relative roughness (e/D) of a pipe against Reynold's number.ⓘ Friction Factor [f]			+10% -10%
✖Length of Packaged Bed is the measurement or extent of something from end to end.ⓘ Length of Packaged Bed [L]			+10% -10%
✖Superficial Velocity is the volumetric flow rate divided by a cross sectional area.ⓘ Superficial Velocity [U_b]			+10% -10%
✖Void Fraction is the fraction of the channel volume that is occupied by the gas phase.ⓘ Void Fraction [∈]			+10% -10%
✖Acceleration due to Gravity is acceleration gained by an object because of gravitational force.ⓘ Acceleration due to Gravity [g]			+10% -10%
✖The Head of Fluid is the height of a vertical column of fluid and represents mechanical energy per pound of fluid.ⓘ Head of Fluid [H_f]			+10% -10%

✖Diameter(eff) is a chord that runs through the center point of the circle.ⓘ Effective Particle Diameter by Ergun given Frication Factor [D_eff]

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Formula

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Effective Particle Diameter by Ergun given Frication Factor

Formula

`"D"_{"eff"} = ("f"*"L"*"U"_{"b"}^2*(1-"∈"))/("g"*"H"_{"f"}*"∈"^3)`

Example

`"24.79214m"=("1.148"*"1100m"*("0.05m/s")^2*(1-"0.75"))/("9.8m/s²"*"0.0077m"*("0.75")^3)`

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Effective Particle Diameter by Ergun given Frication Factor Solution

STEP 0: Pre-Calculation Summary

Formula Used

Diameter(eff) = (Friction Factor*Length of Packaged Bed*Superficial Velocity^2*(1-Void Fraction))/(Acceleration due to Gravity*Head of Fluid*Void Fraction^3)
D_eff = (f*L*U_b^2*(1-∈))/(g*H_f*∈^3)
This formula uses 7 Variables

Variables Used

Diameter(eff) - (Measured in Meter) - Diameter(eff) is a chord that runs through the center point of the circle.
Friction Factor - The Friction factor or Moody chart is the plot of the relative roughness (e/D) of a pipe against Reynold's number.
Length of Packaged Bed - (Measured in Meter) - Length of Packaged Bed is the measurement or extent of something from end to end.
Superficial Velocity - (Measured in Meter per Second) - Superficial Velocity is the volumetric flow rate divided by a cross sectional area.
Void Fraction - Void Fraction is the fraction of the channel volume that is occupied by the gas phase.
Acceleration due to Gravity - (Measured in Meter per Square Second) - Acceleration due to Gravity is acceleration gained by an object because of gravitational force.
Head of Fluid - (Measured in Meter) - The Head of Fluid is the height of a vertical column of fluid and represents mechanical energy per pound of fluid.

STEP 1: Convert Input(s) to Base Unit

Friction Factor: 1.148 --> No Conversion Required
Length of Packaged Bed: 1100 Meter --> 1100 Meter No Conversion Required
Superficial Velocity: 0.05 Meter per Second --> 0.05 Meter per Second No Conversion Required
Void Fraction: 0.75 --> No Conversion Required
Acceleration due to Gravity: 9.8 Meter per Square Second --> 9.8 Meter per Square Second No Conversion Required
Head of Fluid: 0.0077 Meter --> 0.0077 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

D_eff = (f*L*U_b^2*(1-∈))/(g*H_f*∈^3) --> (1.148*1100*0.05^2*(1-0.75))/(9.8*0.0077*0.75^3)

Evaluating ... ...

D_eff = 24.7921390778534

STEP 3: Convert Result to Output's Unit

24.7921390778534 Meter --> No Conversion Required

FINAL ANSWER

24.7921390778534 ≈ 24.79214 Meter <-- Diameter(eff)

(Calculation completed in 00.004 seconds)

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< 12 Flow of Liquids inside Packed Beds Calculators

Effective Particle Diameter by Ergun given Frication Factor

Go Diameter(eff) = (Friction Factor*Length of Packaged Bed*Superficial Velocity^2*(1-Void Fraction))/(Acceleration due to Gravity*Head of Fluid*Void Fraction^3)

Head of Fluid Lost Due to Friction

Go Head of Fluid = (Friction Factor*Length of Packaged Bed*Superficial Velocity^2*(1-Void Fraction))/(Acceleration due to Gravity*Diameter(eff)*Void Fraction^3)

Friction Factor by Ergun

Go Friction Factor = (Acceleration due to Gravity*Diameter(eff)*Head of Fluid*Void Fraction^3)/(Length of Packaged Bed*Superficial Velocity^2*(1-Void Fraction))

Effective Particle Diameter by Ergun given Reynolds Number

Go Diameter(eff) = (Reynolds Number(pb)*Absolute Viscosity*(1-Void Fraction))/(Superficial Velocity*Density)

Superficial Velocity by Ergun given Reynolds Number

Go Superficial Velocity = (Reynolds Number(pb)*Absolute Viscosity*(1-Void Fraction))/(Diameter(eff)*Density)

Reynolds Number of Packed Beds by Ergun

Go Reynolds Number(pb) = (Diameter(eff)*Superficial Velocity*Density)/(Absolute Viscosity*(1-Void Fraction))

Density of Fluid by Ergun

Go Density = (Reynolds Number(pb)*Absolute Viscosity*(1-Void Fraction))/(Diameter(eff)*Superficial Velocity)

Absolute Viscosity of Fluid by Ergun

Go Absolute Viscosity = (Diameter*Superficial Velocity*Density)/(Reynolds Number(pb)*(1-Void Fraction))

Friction Factor by Beek

Go Friction Factor = (1-Void Fraction)/(Void Fraction^3)*(1.75+150*((1-Void Fraction)/Reynolds Number(pb)))

Friction Factor by Ergun for Rep Value between 1 and 2500

Go Friction Factor = 150/Reynolds Number(pb)+1.75

Friction Factor by Kozeny-Carman

Go Friction Factor = 150/Reynolds Number(pb)

Mean Effective Diameter

Go Diameter = 6/Mean Specific Surface

Effective Particle Diameter by Ergun given Frication Factor Formula

Diameter(eff) = (Friction Factor*Length of Packaged Bed*Superficial Velocity^2*(1-Void Fraction))/(Acceleration due to Gravity*Head of Fluid*Void Fraction^3)
D_eff = (f*L*U_b^2*(1-∈))/(g*H_f*∈^3)

What is internal flow?

Internal flow is a flow for which the fluid is confined by a surface. Hence the boundary layer is unable to develop without eventually being constrained. The internal flow configuration represents a convenient geometry for heating and cooling fluids used in chemical processing, environmental control, and energy conversion technologies.
An example includes flow in a pipe.

How to Calculate Effective Particle Diameter by Ergun given Frication Factor?

Effective Particle Diameter by Ergun given Frication Factor calculator uses Diameter(eff) = (Friction Factor*Length of Packaged Bed*Superficial Velocity^2*(1-Void Fraction))/(Acceleration due to Gravity*Head of Fluid*Void Fraction^3) to calculate the Diameter(eff), The Effective particle diameter by Ergun given frication factor formula is defined as the diameter of the particle required for the given value pf friction factor. Diameter(eff) is denoted by D_eff symbol.

How to calculate Effective Particle Diameter by Ergun given Frication Factor using this online calculator? To use this online calculator for Effective Particle Diameter by Ergun given Frication Factor, enter Friction Factor (f), Length of Packaged Bed (L), Superficial Velocity (U_b), Void Fraction (∈), Acceleration due to Gravity (g) & Head of Fluid (H_f) and hit the calculate button. Here is how the Effective Particle Diameter by Ergun given Frication Factor calculation can be explained with given input values -> 24.79214 = (1.148*1100*0.05^2*(1-0.75))/(9.8*0.0077*0.75^3).

FAQ

What is Effective Particle Diameter by Ergun given Frication Factor?

The Effective particle diameter by Ergun given frication factor formula is defined as the diameter of the particle required for the given value pf friction factor and is represented as D_eff = (f*L*U_b^2*(1-∈))/(g*H_f*∈^3) or Diameter(eff) = (Friction Factor*Length of Packaged Bed*Superficial Velocity^2*(1-Void Fraction))/(Acceleration due to Gravity*Head of Fluid*Void Fraction^3). The Friction factor or Moody chart is the plot of the relative roughness (e/D) of a pipe against Reynold's number, Length of Packaged Bed is the measurement or extent of something from end to end, Superficial Velocity is the volumetric flow rate divided by a cross sectional area, Void Fraction is the fraction of the channel volume that is occupied by the gas phase, Acceleration due to Gravity is acceleration gained by an object because of gravitational force & The Head of Fluid is the height of a vertical column of fluid and represents mechanical energy per pound of fluid.

How to calculate Effective Particle Diameter by Ergun given Frication Factor?

The Effective particle diameter by Ergun given frication factor formula is defined as the diameter of the particle required for the given value pf friction factor is calculated using Diameter(eff) = (Friction Factor*Length of Packaged Bed*Superficial Velocity^2*(1-Void Fraction))/(Acceleration due to Gravity*Head of Fluid*Void Fraction^3). To calculate Effective Particle Diameter by Ergun given Frication Factor, you need Friction Factor (f), Length of Packaged Bed (L), Superficial Velocity (U_b), Void Fraction (∈), Acceleration due to Gravity (g) & Head of Fluid (H_f). With our tool, you need to enter the respective value for Friction Factor, Length of Packaged Bed, Superficial Velocity, Void Fraction, Acceleration due to Gravity & Head of Fluid and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Diameter(eff)?

In this formula, Diameter(eff) uses Friction Factor, Length of Packaged Bed, Superficial Velocity, Void Fraction, Acceleration due to Gravity & Head of Fluid. We can use 1 other way(s) to calculate the same, which is/are as follows -

Diameter(eff) = (Reynolds Number(pb)*Absolute Viscosity*(1-Void Fraction))/(Superficial Velocity*Density)

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