Friction Factor by Beek 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

✖Void Fraction is the fraction of the channel volume that is occupied by the gas phase.ⓘ Void Fraction [∈]			+10% -10%
✖Reynolds number(pb) is the ratio of inertial forces to viscous forces within a fluid which is subjected to relative internal movement due to different fluid velocities.ⓘ Reynolds Number(pb) [Re_pb]			+10% -10%

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

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Formula

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Friction Factor by Beek

Formula

`"f" = (1-"∈")/("∈"^3)*(1.75+150*((1-"∈")/"Re"_{"pb"}))`

Example

`"1.148148"=(1-"0.75")/(("0.75")^3)*(1.75+150*((1-"0.75")/"200"))`

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Friction Factor by Beek Solution

STEP 0: Pre-Calculation Summary

Formula Used

Friction Factor = (1-Void Fraction)/(Void Fraction^3)*(1.75+150*((1-Void Fraction)/Reynolds Number(pb)))
f = (1-∈)/(∈^3)*(1.75+150*((1-∈)/Re_pb))
This formula uses 3 Variables

Variables Used

Friction Factor - The Friction factor or Moody chart is the plot of the relative roughness (e/D) of a pipe against Reynold's number.
Void Fraction - Void Fraction is the fraction of the channel volume that is occupied by the gas phase.
Reynolds Number(pb) - Reynolds number(pb) is the ratio of inertial forces to viscous forces within a fluid which is subjected to relative internal movement due to different fluid velocities.

STEP 1: Convert Input(s) to Base Unit

Void Fraction: 0.75 --> No Conversion Required
Reynolds Number(pb): 200 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

f = (1-∈)/(∈^3)*(1.75+150*((1-∈)/Re_pb)) --> (1-0.75)/(0.75^3)*(1.75+150*((1-0.75)/200))

Evaluating ... ...

f = 1.14814814814815

STEP 3: Convert Result to Output's Unit

1.14814814814815 --> No Conversion Required

FINAL ANSWER

1.14814814814815 ≈ 1.148148 <-- Friction Factor

(Calculation completed in 00.008 seconds)

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Created by Nishan Poojary

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

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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

Friction Factor by Beek Formula

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

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 Beek?

Friction Factor by Beek calculator uses Friction Factor = (1-Void Fraction)/(Void Fraction^3)*(1.75+150*((1-Void Fraction)/Reynolds Number(pb))) to calculate the Friction Factor, The Friction factor by Beek formula is defined as the ratio of the absolute roughness ε of the pipe inside wall to the pipe inside diameter. Friction Factor is denoted by f symbol.

How to calculate Friction Factor by Beek using this online calculator? To use this online calculator for Friction Factor by Beek, enter Void Fraction (∈) & Reynolds Number(pb) (Re_pb) and hit the calculate button. Here is how the Friction Factor by Beek calculation can be explained with given input values -> 1.148148 = (1-0.75)/(0.75^3)*(1.75+150*((1-0.75)/200)).

FAQ

What is Friction Factor by Beek?

The Friction factor by Beek 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 = (1-∈)/(∈^3)*(1.75+150*((1-∈)/Re_pb)) or Friction Factor = (1-Void Fraction)/(Void Fraction^3)*(1.75+150*((1-Void Fraction)/Reynolds Number(pb))). Void Fraction is the fraction of the channel volume that is occupied by the gas phase & Reynolds number(pb) is the ratio of inertial forces to viscous forces within a fluid which is subjected to relative internal movement due to different fluid velocities.

How to calculate Friction Factor by Beek?

The Friction factor by Beek formula is defined as the ratio of the absolute roughness ε of the pipe inside wall to the pipe inside diameter is calculated using Friction Factor = (1-Void Fraction)/(Void Fraction^3)*(1.75+150*((1-Void Fraction)/Reynolds Number(pb))). To calculate Friction Factor by Beek, you need Void Fraction (∈) & Reynolds Number(pb) (Re_pb). With our tool, you need to enter the respective value for Void Fraction & Reynolds Number(pb) 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 Friction Factor?

In this formula, Friction Factor uses Void Fraction & Reynolds Number(pb). We can use 3 other way(s) to calculate the same, which is/are as follows -

Friction Factor = (Acceleration due to Gravity*Diameter(eff)*Head of Fluid*Void Fraction^3)/(Length of Packaged Bed*Superficial Velocity^2*(1-Void Fraction))
Friction Factor = 150/Reynolds Number(pb)
Friction Factor = 150/Reynolds Number(pb)+1.75

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