Pressure Loss in Pipe – Neutrium

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PRESSURE LOSS IN PIPE

SUMMARY

To determine the pressure loss or flowrate through pipe knowledge of the friction

between the fluid and the pipe is required. This article describes how to

incorporate friction into pressure loss or fluid flow calculations. It also outlines

several methods for determining the Darcy friction factor for rough and smooth

pipes in both he turbulent and laminar flow regime. Finally this article discusses

which correlation for pressure loss in pipe is the most appropriate.

1. DEFINITIONS

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: Absolute Roughness

: Hydraulic Diameter

: Hydraulic Radius

: Darcy Friction Factor: Fanning Friction Factor

: Pipe Diameter

: Relative Roughness

: Reynolds Number

: Length of Pipe

: Head loss due to friction

: Average Velocity

: Gravity

: Pressure: Density

2. INTRODUCTION

D

R

F

D

/ D

R

L

V

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Pressure loss in piping without any size changes or fittings occurs due to friction

between the fluid and the pipe walls. There have been a number of methods

developed to describe this relationship; generally a friction factor is used to

determine the pressure loss. The most important methods of determining this

friction factor are described in this article.

The key influences on the pressure drop as a fluid moves through a pipe are

Reynolds Number of the fluid and the roughness of the pipe.

2.1 Friction Factors: Fanning and Darcy

There are two common friction factors in use, the Darcy and Fanning friction

factors. The Darcy friction factor is also known as the DarcyWeisbach friction

factor or the Moody friction factor. It is important to understand which friction

factor is being described in an equation or chart to prevent error in pressure loss,

or fluid flow calculation results.

The difference between the two friction factors is that the value of the Darcy

friction factor is 4 times that of the Fanning friction factor. In all other aspects

they are identical, and by applying the conversion factor of 4 the friction factors

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may be used interchangeably.

Unless stated otherwise the Darcy friction factor is used in this article.

2.2 Head Loss and Pressure Loss Darcy Friction Factor

Head Loss:

Pressure Drop:

= 4

F

=

L

D

V

2

2

=

L

D

V

2

2

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3. METHODS OF DETERMINING THE DARCY FRICTION FACTOR

The Darcy friction factor may be determined by either using the appropriate

friction factor correlation, or by reading from a Moody Chart.

The Darcy friction factor is a dimensionless number; the pipe roughness and the

pipe diameter which are used to determine the friction factor should be

dimensionally consistent (e.g. use roughness and diameter both measured in mm,

or both measured in inches)

3.1 Moody Chart

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3.2 Which method should I use to calculate the Darcy Friction Factor?

There are many relationships available to determine the Darcy friction factor.

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Here we discuss the practicality and accuracy of applying these methods.

Different methods of determining the friction factor as used depending on the

flow regime of the fluid, as determined by the Reynolds Number .

3.3 Laminar Flow

In the laminar flow regime the Darcy Equation may be used to determine the

friction factor (see 2.2). (put links in here)

3.4 Transitional Flow

In the transitional flow regime the inconsistency of the flow patterns make the

prediction of friction factor impossible. No relationships are available to

adequately describe this flow regime.

3.5 Turbulent Flow Regime

In the turbulent flow regime the Colebrook equation (See 2.3) is widely accepted

for describing the Darcy friction factor. The only drawback to using this equation

is that it is implicit, and will require iteration to solve. Where iteration is possible

and there are no constraints on computation speed, calculation via the Colebrook

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equation is appropriate.

If calculating by hand calculator or by computer where iteration is difficult

Serghides equation (See 2.4) is most appropriate as it is explicit and has very low

error (less than 0.003%).

It should be noted that more accurate approximations of the Colebrook equation

have been proposed but generally the increased accuracy is not required. The

error introduced in approximating the Colebrook equation using Serghides

equation is likely to be many orders of magnitude less than error from other

sources (such as uncertainty in pipe roughness or the uncertainty in the original

data from which the Colebrook equation was produced).

4. FRICTION FACTOR EQUATIONS

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Here we detail some of the most common relationship for the Darcy friction

factor for reference. For a discussion of the most appropriate relationships to use

see above.

4.1 Darcy Equation

The Darcy equation describes the Darcy friction factor for laminar flow. If this

equation is substituted into the Pressure loss equation above it is also known as

Poiseuilles law or the HagenPoiseuille law.

4.2 Colebrooks Equation

Also known as the Colebrook-White Equation. This equation was developed

taking into account experimental results for the flow through both smooth and

rough pipe. It is valid only in the turbulent regime for fluid filled pipes. It is

widely accepted and most of the relationships discussed in this article are merely

f o r R < 2 1 0 0

=

6 4

R

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explicit approximations for this relationship. Due to the implicit nature of this

equation it must be solved iteratively. A result of suitable accuracy for almost all

industrial applications will be achieved in less than 10 iterations.

The Colebrook equation may be calculated as follows:

4.3 Serghides Equation

The Serghides equation is an approximation of the Colebrook equation use to

solve for the Darcy friction factor explicitly. It is applied to fluid flowing in a

filled circular pipe. The equation is presented using 3 intermediate values for

simplicity. It provides and explicit approximation for the Colebrook equation that

is highly accurate over a wide range of values for both surface roughness and

Reynolds number. This method will result in errors of less than 0.003% in the

ranges: Reynolds number 4000-1x1010, relative roughness 1x10-7 1.

f o r R < 2 3 0 0 a n d R > 4 0 0 0

= 2 (

+)

1

1 0

/

D

3 . 7

2 . 5 1

R

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The friction factor from the Serghide's approximation may be calculated from

following set of equations:

4.4 Chens Equation

Chens equation is an approximation of the Colebrook equation used to solve for

the Darcy friction factor explicitly. It is applied to fluid flowing in a filled circular

pipe.

f o r R < 2 3 0 0 a n d R > 4 0 0 0

A

B

C

= 2 (

+)

1 0

/

D

3 . 7

1 2

R

= 2 (

+)

1 0

/

D

3 . 7

2 . 5 1 A

R

= 2 (

+)

1 0

/

D

3 . 7

2 . 5 1 B

R

=( A

)

(B

A

)

2

C 2

B+

A

2

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The friction factor from Chen's approximation may be calculated as follows:

4.5 Zigrang & Sylvesters Equation

Zigrang & Sylvesters equation is an approximation of the Colebrook equation use

to solve for the Darcy friction factor explicitly. It is applied to fluid flowing in a

filled circular pipe.

4.6 Haaland Equation

= 2 ( ( + ) )

1

1 0

/

D

3 . 7 0 6 5

5 . 0 4 5 2

R

1 0

(

/D

)

1 . 1 0 9 8

2 . 8 2 5 7

5 . 5 8 0 6

R

0 . 8 9 8 1

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= 2

(

(

+) )

1

1 0

/

D

3 . 7

5 . 0 2

R

1 0

/

D

3 . 7

1 2

R

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The Haaland equation is an approximation of the Colebrook equation use to solve

for the Darcy friction factor explicitly. It is applied to fluid flowing in a filled

circular pipe and may be calculated as follows:

4.7 Swamee-Jain Equation

The Swamee-Jain equation is an approximation of the Colebrook equation used to

solve for the Darcy friction factor explicitly. It is applied to fluid flowing in a

filled circular pipe and may be calculated as follows:

f o r R < 2 3 0 0 a n d R > 4 0 0 0

= 1 . 8 (

+)

1

1 0

/

D

3 . 7

6 . 9

R

f o r R < 2 3 0 0 a n d R > 4 0 0 0

=

0 . 2 5

1 0

(

)

/

D

3 . 7

5 . 7 4

R

0 . 9

2

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4.8 Churchill Equation

The Churchill equation combines both the expressions for friction factor in both

the laminar and turbulent flow regimes. It is accurate to within the error of the

data used to construct the Moody diagram. This model also provides an estimate

for the intermediate (transition) region, however this should be used with

caution.

The Churchill equation shows very good agreement with the Darcy equation for

laminar flow, accuracy through the transitional flow regime is unknown, in the

turbulent regime a difference of around 0.5-2% is observed between the Churchillequation and the Colebrook equation.

f o r R < 2 1 0 0 a n d R > 4 0 0 0

1 / 1 2

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ARTICLE TAGS

Flow Regime Fluid Flow Friction Factor Laminar Flow Pipe

Pipe Diameter Pressure Drop Pressure Loss Reynolds Number Roughness

Transitional Flow Turbulent Flow

A

B

= 8

+

8

R

1 2

1

(A

+B

)

1 . 5

1 / 1 2

= 2 . 4 5 7

1

+ 0 . 2 7 ( )

7

R

0 . 9

D

1 6

=

3 7 , 5 3 0

R

1 6

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Article Created: April 29, 2012Back

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