Friction Factor by Ergun Calculator

✖Acceleration due to Gravity is acceleration gained by an object because of gravitational force.ⓘ Acceleration due to Gravity [g]			+10% -10%
✖Diameter(eff) is a chord that runs through the center point of the circle.ⓘ Diameter(eff) [D_eff]			+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%
✖Void Fraction is the fraction of the channel volume that is occupied by the gas phase.ⓘ Void Fraction [∈]			+10% -10%
✖Length of Packaged Bed is the measurement or extent of something from end to end.ⓘ Length of Packaged Bed [L_b]			+10% -10%
✖Superficial Velocity is the volumetric flow rate divided by a cross sectional area.ⓘ Superficial Velocity [U_b]			+10% -10%

✖Factor of Friction or Moody chart is the plot of the relative roughness (e/D) of a pipe against Reynold's number.ⓘ Friction Factor by Ergun [f_f]

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Formula

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Friction Factor by Ergun

Formula

f f = \frac{g \cdot D eff \cdot H f \cdot ∈^{3}}{L b \cdot {U b}^{2} \cdot (1 - ∈)}

Example

1.157162 = \frac{9.8 m/s² \cdot 24.99 m \cdot 0.0077 m \cdot {0.75}^{3}}{1100 m \cdot {0.05 m/s}^{2} \cdot (1 - 0.75)}

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Friction Factor by Ergun Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

Factor of Friction - Factor of Friction or Moody chart is the plot of the relative roughness (e/D) of a pipe against Reynold's number.
Acceleration due to Gravity - (Measured in Meter per Square Second) - Acceleration due to Gravity is acceleration gained by an object because of gravitational force.
Diameter(eff) - (Measured in Meter) - Diameter(eff) is a chord that runs through the center point of the circle.
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.
Void Fraction - Void Fraction is the fraction of the channel volume that is occupied by the gas phase.
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.

STEP 1: Convert Input(s) to Base Unit

Acceleration due to Gravity: 9.8 Meter per Square Second --> 9.8 Meter per Square Second No Conversion Required
Diameter(eff): 24.99 Meter --> 24.99 Meter No Conversion Required
Head of Fluid: 0.0077 Meter --> 0.0077 Meter No Conversion Required
Void Fraction: 0.75 --> 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

STEP 2: Evaluate Formula

Substituting Input Values in Formula

f_f = (g*D_eff*H_f*∈^3)/(L_b*U_b^2*(1-∈)) --> (9.8*24.99*0.0077*0.75^3)/(1100*0.05^2*(1-0.75))

Evaluating ... ...

f_f = 1.15716195

STEP 3: Convert Result to Output's Unit

1.15716195 --> No Conversion Required

FINAL ANSWER

1.15716195 ≈ 1.157162 <-- Factor of Friction

(Calculation completed in 00.020 seconds)

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Home » Physics » Heat and Mass Transfer » Internal Flow » Mechanical » Flow of Liquids inside Packed Beds » Friction Factor by Ergun

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Shri Madhwa Vadiraja Institute of Technology and Management (SMVITM), Udupi

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< Flow of Liquids inside Packed Beds Calculators

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)

Friction Factor by Ergun Formula

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 Friction Factor by Ergun?

Friction Factor by Ergun calculator uses Factor of Friction = (Acceleration due to Gravity*Diameter(eff)*Head of Fluid*Void Fraction^3)/(Length of Packaged Bed*Superficial Velocity^2*(1-Void Fraction)) to calculate the Factor of Friction, The Friction factor by Ergun formula is defined as the ratio of the absolute roughness ε of the pipe inside wall to the pipe inside diameter. Factor of Friction is denoted by f_f symbol.

How to calculate Friction Factor by Ergun using this online calculator? To use this online calculator for Friction Factor by Ergun, enter Acceleration due to Gravity (g), Diameter(eff) (D_eff), Head of Fluid (H_f), Void Fraction (∈), Length of Packaged Bed (L_b) & Superficial Velocity (U_b) and hit the calculate button. Here is how the Friction Factor by Ergun calculation can be explained with given input values -> 0.000463 = (9.8*24.99*0.0077*0.75^3)/(1100*0.05^2*(1-0.75)).

FAQ

What is Friction Factor by Ergun?

The Friction factor by Ergun formula is defined as the ratio of the absolute roughness ε of the pipe inside wall to the pipe inside diameter and is represented as f_f = (g*D_eff*H_f*∈^3)/(L_b*U_b^2*(1-∈)) or Factor of Friction = (Acceleration due to Gravity*Diameter(eff)*Head of Fluid*Void Fraction^3)/(Length of Packaged Bed*Superficial Velocity^2*(1-Void Fraction)). Acceleration due to Gravity is acceleration gained by an object because of gravitational force, Diameter(eff) is a chord that runs through the center point of the circle, The Head of Fluid is the height of a vertical column of fluid and represents mechanical energy per pound of fluid, Void Fraction is the fraction of the channel volume that is occupied by the gas phase, 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.

How to calculate Friction Factor by Ergun?

The Friction factor by Ergun formula is defined as the ratio of the absolute roughness ε of the pipe inside wall to the pipe inside diameter is calculated using Factor of Friction = (Acceleration due to Gravity*Diameter(eff)*Head of Fluid*Void Fraction^3)/(Length of Packaged Bed*Superficial Velocity^2*(1-Void Fraction)). To calculate Friction Factor by Ergun, you need Acceleration due to Gravity (g), Diameter(eff) (D_eff), Head of Fluid (H_f), Void Fraction (∈), Length of Packaged Bed (L_b) & Superficial Velocity (U_b). With our tool, you need to enter the respective value for Acceleration due to Gravity, Diameter(eff), Head of Fluid, Void Fraction, Length of Packaged Bed & Superficial Velocity 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 Factor of Friction?

In this formula, Factor of Friction uses Acceleration due to Gravity, Diameter(eff), Head of Fluid, Void Fraction, Length of Packaged Bed & Superficial Velocity. We can use 3 other way(s) to calculate the same, which is/are as follows -

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

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