pipeline losess

8/11/2019 pipeline losess

1/23

Pipe Fitting Losses

Pipework fittingssuch as bends, tees, reducers etc., cause pressure loss or

resistance in a heating system.

When making approximatecalculations 10%, 15%, 20% or more may be added

to the pressure loss in straight pipe runs.

For accuratecalculations the fitting loss should be determined separately for

each fitting, as outlined below.

The concept of equivalent length is used and is defined as the length of straight

pipe which would give a friction pressure loss equivalent to one velocity head.

The DArcy equation is;

H = 4 . f . l . v2 / 2 . g . d

Where; H = head loss due to friction in a straight pipe (m)

f = friction coefficient

l = length of pipe (m)

d = diameter (m)

v = velocity of fluid (m/s)

g = acceleration due to gravity (m/s2)

The DArcy equation can be rewritten for pressure instead of head.

Pressure drop (pl) = ( 4 . f . l ) / d x ( v2. r . g ) / 2 . g

Where; pl = Pressure loss in a pipe section (Pa)

f = friction coefficient for pipe

l = length of pipe (m)

d = diameter of pipe (m)

v = water velocity (m/s)

r = density of water (kg/m3)

g = acceleration due to gravity (m/s2)

To simplify the above equation we get;

Pressure drop (pl) = ( 4 . f . l ) / d x ( v2. r ) / 2

or; Pressure drop (pl) = ( 4 . f . l ) / d x ( . r . v2)

For the friction pressure loss to equal one velocity head;

Velocity pressure = ( . . v2)


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Then 1.0 = ( 4 . f . l ) / d

The length (l) is now called equivalent length (le)and by rearranging theabove formula we get;

1.0 x d = 4 . f . le

le = d / 4 .f

Values of equivalent lengthare given in the FLOW of WATER in PIPESTABLE

for water at 75oC, see CIBSE guide C (2001) section 4 , Flow of Fluids in Pipes

and Ducts, Tables 4.9 to 4.33 for various types of pipes.

These values should be corrected for each particular type of fitting.

The correction factors of Velocity pressure loss factors are called(Zeta)

factors.

The resistance in a fitting is converted to equivalent straight lengths of pipe,

e.g. a bend may have a resistance equivalent to 1.2 metres of straight pipe.

The Total Equivalent Length of a Fitting = Equivalent Length x Pressure Loss

factor z(Zeta).

Total Equivalent Length of a Fitting (T.E.L.) (m) = (le) x (Zetafactor).

See CIBSE guide C (2007) section 4.4.1 and section 4.10 for more details of

fittings zeta factors.

Examples Of Zeta Factors

The following are some examples of pressure loss (zeta) factors for pipe

fittings:


3/23


4/23

Some Pipe Cross Sectional Areas

Area = .d2/4

Area (28mm) = .0.0282/ 4 = 0.0006158 m

2.

Area (22mm) = .0.0222/ 4 = 0.0003801 m2.

Area (15mm) = .0.0152/ 4 = 0.0001767 m

2.

Some Ratios of Pipe AreasFor 22mm x 15mm reduction

The ratio of area A2/A1= 0.0001767 / 0.0003801 = 0.465.

Therefore for reduction = 0.35approximately from the above table.

For 28mm x 22mm reduction

The ratio of area A2/A1= 0.0003801 / 0.0006158 = 0.617.

Therefore for reduction = 0.25approximately from the above table.


5/23

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Home Calculation Methods Pressure Drops in Pipe Fittings

Calculating Pressure Drops in Pipe Fittings

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Calculating Pressure

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Introduction
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Piping on a process plant

does more than run in a straight line. Piping consists of straight lengths of pipe punctuated by anynumber of fittings - including bends, valves and T-pieces. Line losses from pipe work fittings cannot be

discounted.

Pipe fittings impose a pressure drop as they:

Change the fluid flow direction

Change the size of the cross-sectional flow path, causing the f luid to either accelerate or de-accelerate.

Present an obstruction in the flow path.

Often, pipe fitting pressure losses make up a sizable chunk of the total system pressure drop. Any estimate of the

hydraulics of a pipe line must consider the impact of the pipe work fittings.

Other articles of interest:

Pressure drop in pipe lines

Compressible flow pressure drops

Standard pipe sizes

Calculation Method

In anotherarticle,we introduced the Darcy Equation for calculating pressure drop in straight lengths of pipe:
http://www.mycheme.com/calculation-methods/calculating-pressure-drops-in-straight-pipe.htmlhttp://www.mycheme.com/calculation-methods/gas-pipeline-hydraulics.htmlhttp://www.mycheme.com/calculation-methods/gas-pipeline-hydraulics.htmlhttp://www.mycheme.com/technicaldata/standard-pipe-sizes.htmlhttp://www.mycheme.com/designguides/22-pressure-drop-straight-pipe.htmlhttp://www.mycheme.com/designguides/22-pressure-drop-straight-pipe.htmlhttp://www.mycheme.com/technicaldata/standard-pipe-sizes.htmlhttp://www.mycheme.com/calculation-methods/gas-pipeline-hydraulics.htmlhttp://www.mycheme.com/calculation-methods/calculating-pressure-drops-in-straight-pipe.html


7/23

The equivalent equation for pipe fittings is

Where:

PFittings - Pressure drop across fitting, Pa

- Fluid Density, kg/m3

u - Fluid velocity in the pipe, m/s

K - Resistance Coefficient (Dimensionless)

The Resistance Coefficient, K, is sometimes referred as the number of velocity heads and is specific to eachtype of fitting. Values of the resistance coefficient for various fitting types can be found in the literature, but typical

values are listed below.

Resistance

Cofficient, K

45oElbows 0.3

90oElbows (Standard Radius) 0.6-0.8

30oMitre Bends 0.2

45oMitre Bends 0.375


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60oMitre Bends 0.625

90oSquare Elbows 1.2

180oReturn Bend (Close Pattern) 1.25

T-Piece (Side Connection) 1.2-1.8

T-Piece (Flow through) 0.5

Globe Valves (Fully Open) 1.2-6.0

Gate Valves (Fully Open) 0.15

Gate Valves (3/4Open) 1



Plug Valves (Fully Open) 0.45

3-Way Valve (Straight Thru') 0.75

3-Way Valve (Side Connection) 2.25

Ball Valves 0.075

Butterfly Valves (less than 10" 250mm NB) 1.125


9/23

Butterfly Valves (10" 250mm NB - 14" 350mm

NB) 0.875

Butterfly Valves (Greater than 14" 350mm NB) 0.625

Check Valves (Swing Type) 2.5

Check Valves (Lift Type) 15

Pipe Exits 1

Pipe Entrances 0.78

Some textbooks use Equivalent Length instead of Resistance Coefficient to give a measure of resistance to fluid

flow in fittings (see box below).

Calculating Pressure Drops in Pipe Fittings - Page 2

Article Index

Calculating Pressure

Drops in Pipe Fittings

Page 2

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Limitations with this Calculation Method
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10/23

As with many engineering calculations, this

approach is only approximate and should be used with care. It is based on two important assumptions.

Firstly, it assumes that the Resistance Coefficient is constant for any given fitting type regardless of size. For

example, it assumes that a fully open gate valve has Resistance Coefficient of 0.15, regardless whether it is a

inch or 24 inch diameter. This would only be true if the valves were geometrically similar. In reality, this will not be

the case. Secondly, the Resistance Coefficients given above are for fully developed flowi.e. fully turbulent.

However, for many applications, this method produces acceptable results. For gases and low viscosity liquids

(e.g. water), pipelines are designed to produce fully turbulent flow. In addition, pipe sizes are selected before the

final pipe routing and actual number of pipe fittings is known. These uncertainties mean that this calculation

method should give results within the margin of error.

However, this calculation method breaks down at low Reynolds Numbers (espicially in laminar and transitional

flow). This will be an issue with high viscosity liquids where flow is typically at low Re numbers

There are refinements to this method which take into account these approximations. These are know as the 2K

and 3 K methods. However for most situations, the simplified approach outlined above is acceptable.


11/23

Pipe Friction Loss Calculations

Flow of fluid through a pipe is resisted by viscous shear stresses within the fluid and

the turbulence that occurs along the internal pipe wall, which is dependent on the roughness of the

pipe material.

This resistance is termed pipe friction and is usually measured in feet or metres head of the fluid,

which is why it is also refered to as the head loss due to pipe friction.

Head Loss in a PipeA large amount of research has been carried out over many years to establish various

formulae that can calculate head loss in a pipe. Most of this work has been developed based

on experimental data.

Overall head loss in a pipe is affected by a number of factors which include the viscosity of

the fluid, the size of the internal pipe diameter, the internal roughness of the inner surface of

the pipe, the change in elevation between the ends of the pipe and the length of the pipe along

which the fluid travels.

Valves and fittings on a pipe also contribute to the overall head loss that occurs, however

these must be calculated separately to the pipe wall friction loss, using a method ofmodeling

pipe fitting losses with k factors.

Darcy Weisbach Formula

The Darcy formula or the Darcy-Weisbach equation as it tends to be referred to, is now

accepted as the most accurate pipe friction loss formula, and although more difficult to

calculate and use than other friction loss formula, with the introduction of computers, it has

now become the standard equation for hydraulic engineers.

Weisbach first proposed the relationship that we now know as the Darcy-Weisbach equation

or the Darcy-Weisbach formula, for calculating friction loss in a pipe.

Darcy-Weisbach equation:

hf = f (L/D) x (v2/2g)

where:

hf = head loss (m)

f = friction factorL = length of pipe work (m)
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12/23

d = inner diameter of pipe work (m)

v = velocity of fluid (m/s)

g = acceleration due to gravity (m/s)

or:

hf = head loss (ft)

f = friction factor

L = length of pipe work (ft)

d = inner diameter of pipe work (ft)

v = velocity of fluid (ft/s)

g = acceleration due to gravity (ft/s)

The establishment of the friction factors was however still unresolved, and indeed was an

issue that needed further work to develop a solution such as that produced by theColebrook-

White formulaand the data presented in the Moody chart.

The Moody Chart

The Moody Chartfinally provided a method of finding an accurate friction factor and this

encouraged use of the Darcy-Weisbach equation, which quickly became the method of choice

for hydraulic engineers.

The introduction of the personnel computer from the 1980's onwards reduced the time

required to calculate the friction factor and pipe head loss. This itself has widened the use of

the Darcy-Weisbach formula to the point that most other equations are no longer used.

Hazen-Williams Formula

Before the advent of personal computers the Hazen-Williams formula was extremely popular

with piping engineers because of its relatively simple calculation properties.

However the Hazen-Williams results rely upon the value of the friction factor, C hw, which is

used in the formula, and the C value can vary significantly, from around 80 up to 130 and

higher, depending on the pipe material, pipe size and the fluid velocity.

Also the Hazen-Williams equation only really gives good results when the fluid is Water andcan produce large inaccuracies when this is not the case.

The imperial form of the Hazen-Williams formula is:

hf = 0.002083 x L x (100/C)^1.85 x (gpm^1.85 / d^4.8655)

where:

hf = head loss in feet of water

L = length of pipe in feet

C = friction coefficient
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13/23

gpm = gallons per minute (USA gallons not imperial gallons)

d = inside diameter of the pipe in inches

The empirical nature of the friction factor C hw means that the Hazen-Williams formula is

not suitable for accurate prediction of head loss. The friction loss results are only valid for

fluids with a kinematic viscosity of 1.13 centistokes, where the velocity of flow is less than10 feet per sec, and where the pipe diameter has a size greater than 2 inches.

Notes: Water at 60 F (15.5 C) has a kinematic viscosity of 1.13 centistokes.

Common Friction Factor Values of C hw used for design purposes are:

Asbestos Cement 140

Brass tube 130

Cast-Iron tube 100

Concrete tube 110

Copper tube 130Corrugated steel tube 60

Galvanized tubing 120

Glass tube 130

Lead piping 130

Plastic pipe 140

PVC pipe 150

General smooth pipes 140

Steel pipe 120

Steel riveted pipes 100

Tar coated cast iron tube 100

Tin tubing130

Wood Stave 110

These C hw values provide some allowance for changes to the roughness of internal pipe

surface, due to pitting of the pipe wall during long periods of use and the build up of other

deposits.


14/23

Friction Factor Calculations

The Darcy-Weisbach equation, for calculating the friction loss in a pipe, uses a dimensionless value

known as the friction factor (also known as the Darcy-Weisbach friction factor or the Moody friction

factor) and it is four times larger than the Fanning friction factor.

Friction Factor Chart / Moody Chart

The friction factor or Moody chart is the plot of the relative roughness (e/D) of a pipe against

theReynold's number.The blue lines plot the friction factor for flow in the wholly turbulent

region of the chart, while the straight black line plots the friction factor for flow in the wholly

laminar region of the chart.

In 1944, LF Moody plotted the data from the Colebrook equation and the resulting chart

became known as The Moody Chartor sometimes the Friction Factor Chart. It was this chart

which first enabled the user to obtain a reasonably accurate friction factor for turbulent flowconditions, based on the Reynolds number and the Relative Roughness of the pipe.

Friction Factor for Laminar Flow

The friction factor for laminar flow is calculated by dividing 64 by theReynold's number.

Friction factor (for laminar flow) = 64 / Re

Critical Flow Condition
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15/23

When flow occurs between the Laminar and Turbulent flow conditions (Re 2300 to Re 4000)

the flow condition is known as critical and is difficult to predict. Here the flow is neither

wholly laminar nor wholly turbulent. It is a combination of the two flow conditions.

Friction Factor for Turbulent FlowThe friction factor for turbulent flow is calculated using the Colebrook-White equation:

Colebrook-White Equation

Due to the implicit formation of the Colebrook-White equation, calculation of the friction

factor requires an iterative solution via numerical methods.

The friction factor is then used in theDarcy-Weisbach formulato calculate the fluid frictional

loss in a pipe.

Reynold's Numbers

Fluid flow in a pipe encounters frictional resistance due to the internal roughness (e)

of the pipe wall, which can create local eddy currents within the fluid. Calculation of the Reynold's

Number helps to determine if the flow in the pipe is Laminar Flow or Turbulent Flow.

Pipes that have a smooth wall such as glass, copper, brass and polyethylene cause less fritional

resistance and hence they produce a smaller frictional loss than those pipes with a greater internal

roughness, such as concrete, cast iron and steel.

The velocity profile of fluid flow in a pipe shows that the fluid at the centre of the stream movesmore quickly than the fluid flow towards the edge of the stream. Therefore friction occurs between

layers within the fluid.

Fluids with a high viscosity flow more slowly and generally not produce eddy currents, thus the

internal roughness of the pipe has little or no effect on the frictional resistance to flow in the pipe.

This condition is known as laminar flow.

Reynold's Number Calculation
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16/23

The Reynolds number (Re) of a flowing fluid is calculated by multiplying the fluid velocity

by the internal pipe diameter (to obtain the inertia force of the fluid) and then dividing the

result by the kinematic viscosity (viscous force per unit length).

Kinematic viscosity = dynamic viscosity/fluid density

Reynolds number = (Fluid velocity x Internal pipe diameter) / Kinematic viscosity

Laminar Flow in a Pipe

Laminar flow occurs when the calculated Reynolds number is less than 2300 and in this case

the resistance to flow is independent of the pipe wall roughness.

Turbulent Flow in a Pipe

Turbulent flow occurs when the Reynolds number calculation exceeds 4000.

When Eddy currents occur within the flow, the ratio of the pipe's internal roughness to the

internal diameter of the pipe needs to be considered to calculate the friction factor, which in

turn is used to calculate the friction loss that occurs.

For pipes with a small diameter, the internal roughness can have a major influence on the

friction factor. For pipes with a large diameter the overall effect of the eddy currents are less

significant.

You can use this link to view information on theinternal roughness for various pipe materials.
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17/23

Therelative roughnessof the pipe and the Reynold's number can be used to plot the friction

factor chart.

When flow occurs between the Laminar and Turbulent flow conditions (Re 2300 to Re 4000)

the flow condition is known as critical and is difficult to predict. Here the flow is neither

wholly laminar nor wholly turbulent. It is a combination of the two flow conditions.

TheColebrook-White equationis used to calculate the friction factor for turbulent flow.

The friction factor is then used in the Darcy-Weisbach formula to calculate the fluid frictional

loss in a pipe.

Pipe Fittings Loss Calculations with K

Factors

Pipe fittings, valves and bends usually have some associated K factor or local loss coefficient, whichallows the calculation of the pressure loss through the fitting for a particular fluid flowing at a

specified velocity. Manufacturers of pipe work fittings and valves often publish a fitting's associated

'K' factor.

Pipe Fitting Loss Formula
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18/23

Fluid head loss through a fitting can be calculated by the following equation:

h = K x v / 2g

where

h = pressure loss in terms of fluid head, i.e. fluid head lossK = manufacturer's published 'K' factor for the fitting

v = velocity of fluid

g = acceleration due to gravity

Where the length of the pipe is relatively long, the effect of the fitting losses are usually

considered as minor losses, and are often ignored during initial analysis of the pipe system.

If the piping design contains a partially open valve then the effect and head loss through the

valve should always be included since the valve head loss may turn out to be significant.

Pipe Fittings and K factors database

Our Pipe Flow Expert software has a database that contains the K factors for many different

types of valves and fittings. It also has special wizard helpers that can calculate the K factor

for special types of fittings such as:

gradual enlargements

gradual contractions

sudden enlargements

sudden contractions

rounded entrances long pipe bends

Addition information about losses through pipe fittings is published in 'Flow of Fluids

through valves, fittings and pipe' - Crane Technical Paper No. 410.


19/23

Chapter 11 : Applications of Viscous Flows Through Pipes

Lecture 37 :

Losses In Pipe Fittings

An additional loss of head takes place in the course of flow through pipe fittings likevalves, couplings and so on. In-general, more restricted the passage is, greater isthe loss of head.

For turbulent flow, the losses are proportional to the square of the average flow

velocity and are usually expressed by , where V is the average velocity offlow. The value of Kdepends on the exact shape of the flow passages. Typicalvalues of K are

Approximate Loss Coefficients, Kfor Commercial Pipe Fittings .

Type and position of fittings Values of K

Globe valve,wide open 10

Gate valve, wide open 0.2

Gate valve, three-quarters open 1.15

Gate valve, half open 5.6

Gate valve, quarter open 24

Pump foot valve 1.5

90elbow(threaded) 0.9

45elbow(threaded) 0.4

Side outlet of T junction 1.8

Since the eddies generated by fittings persist for some distance downstream, thetotal loss of head caused by two fittings close together is not necessarily the sameas the sum of the losses which,each alone would cause.These losses are sometimes expressed in terms of an equivalent length of anunobstructed straight pipe in which an equal loss would occur for the same averageflow velocity. That is

(37.5)

where, represents the equivalent length which is usually expressed in terms of

the pipe diameter as given by Eq. (37.5). Thus depends upon the frictionfactor f , and therefore on the Reynolds number and roughness of the pipe.

.
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Chapter 11 : Applications of Viscous Flows Through Pipes

Lecture 37 :

Power Transmission By A Pipeline

In certain occasions, hydraulic power is transmitted by conveying fluidthrough a pipeline. For example, water from a reservoir at a high altitude isoften conveyed by a pipeline to an impulse hydraulic turbine in anhydroelectric power station. The hydrostatic head of water is thustransmitted by a pipeline. Let us analyse the efficiency of power transmissionunder this situation.

Fig. 37.3 Transmission of hydraulic power by a pipeline to a turbine

The potential head of water in the reservoir = H ( the difference in the water level inthe reservoir and the turbine center)

The head available at the pipe exit (or at the turbine entry)

Where is the loss of head in the pipeline due to friction.

Assuming that the friction coefficient and other loss coefficients are constant,we can write

Where Q is the volume flow rate and R is the hydraulic resistance of the pipeline.Therefore, the power available P at the exit of the pipeline becomes

For P to be maximum, for a given head H, dP/dQshould be zero. This gives

(37.6)


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or,

is always negative which shows that Phas only a maximum value (not

a minimum) with Q.

From Eq. (37.6), we can say that maximum power is obtained when onethird of the head available at the source (reservoir) is lost due to friction inthe flow.

The efficiency of power transmission is defined as

(37.7)

1. The efficiency equals to unity for the trivial case of Q = 0.

2. For flow to commence and hence is a monotonically decreasingfunction of Q from a maximum value of unity to zero.

3. The zero value of corresponds to the situation given by

when the head H available at thereservoir is totally lost to overcome friction in the flow through thepipe.

The efficiency of transmission at the condition of maximum power deliveredis obtained by substituting RQ

2from Eq. (37.6) in Eq. (37.7) as

Therefore the maximum power transmission efficiency through a pipeline is 67%.

Exercise Problems - Chapter 11

1. Calculate the force F required on the piston to discharge of water through a syringe(see Fig. 37.4), taking into account the frictional loss in the syringe needle only. Assume fully

developed laminar flow in the syringe needle. Take the dynamic viscosity of water .
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Figure 37.4

2. A hydrocarbon oil (viscosity 0.025 pa-s and density 900 kg/m3 ) is transported using a 0.6 m

diameter, 10 km long pipe. The maximum allowable pressure drop across the pipe length is 1 MPa.Due to a maintenance schedule on this pipeline, it is required to use a 0.4 m diameter, 10 km longpipe to pump the oil at the same volumetric flow rate as in the earlier case. Estimate the pressure

drop for the 0.4 m diameter pipe. Assume both pipes to be hydrodynamically smooth and in the rangeof operating conditions, the Fanning friction factor is given by:

3. Two reservoirs 1 and 2 are connected as shown in the Fig 37.5 through a turbine T. Given thefriction factor relation

for the connecting pipes, the turbine characteristics of water [ Qin m3/s] and anideal draft tube at the discharge end, find (a) the volume flow rate between the two reservoirs

and (b) the power developed by the turbine. Note:

Use an initial guess for power developed by the turbine as 1 MW. Show only two iterations. Also H

is head available at the turbine.


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figure 37.5

Recap

In this course you have learnt the following

The Fannings friction coefficient for a flow through a closed duct,in terms of wall shear stress, and Cf = ( )(Dh/L)P*/(1/2) V

2in terms of piezometric

pressure drop Darcys friction factor is defined as f = 4Cf

Loss of head in a pipe flow is expressed in terms of Darcys friction factor as h f =f(L/D)(V

2/2g)

Friction factor in case of laminar fully developed flow is found by N-S equation and isgiven by f = 64/Re. Friction factor for turbulent flow depends both on Re and theroughness at pipe surface.

Flows, in practice, takes place through several pipes together either in series or parallelor in combination of both of them. The relationship between the head causing the flow

H and flow rate Q can be expressed asH= RQ2, where R is the flow resistance in

the hydraulic path.

The loss of head due to friction over a length L of a pipe. Where the entire flow isdrained off uniformly from the side tappings, becomes 1/3 of that in a pipe of samelength and diameter, but without side tappings.

An additional head loss over that due to pipe friction takes place in a flow through pipebends and pipe fittings like valves, couplings and so on.

The hydraulic power can be transmitted by a pipeline. For a maximum powertransmission, the head due to friction in the flow equals to one third of the head atsource to be transmitted. The maximum power transmitted efficiency is 67%.

pipeline losess

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