Summary

Fittings such as elbows, tees and valves represent a significant component of the pressure loss in most pipe systems. This article details the calculation of pressure losses through pipe fittings and some minor equipment using the equivalent length method. The strength of the equivalent length method is that it is very simple to calculate. The weakness of the equivalent length method is that it is not as accurate as other methods unless very detailed tabulated data is available.

Definitions


$D$	:	Internal diameter of pipe
$(L/D)_{eq}$	:	Equivalent length of pipe
$R/D$	:	Ratio of elbow radius to pipe diameter

Introduction

The equivalent length method (L/D ratio) allows the user to describe the pressure drop through a fitting as a length of pipe. In theory the pressure drop through the fitting is equivalent to the pressure lost through a certain length of piping at that corresponding flow rate.

The most accurate way to use this method is when tabulated data is available for fittings at the given size, roughness and Reynolds Number for which the pressure drop is unknown. When using an equivalent length that was determined from a fitting of a different size the method relies on the assumption that as pipe size changes the fitting size retains the same relative proportions. This is rarely the case however, and as such some error is introduced in the pressure drop that results. Similarly the roughness and Reynolds Number are likely to be different from the conditions under which the fitting was characterised and error will be introduced.

Typically as the fittings size increase the flow coefficient (L/D ratio) decreases, thus at pipe sizes larger than those at which the fittings equivalent length was determined the pressure drop will be over-estimated. At smaller pipe sizes than those at which the equivalent length was estimated the pressure drop will be under-estimated.

The advantage of the equivalent length method is that it is very simple to calculate. All pipe runs and fittings can be summed up to make one total length, and the pressure loss calculated from this length.

There are several alternative methods for calculating pressure loss from fittings, such as:

For a discussion of which method is most appropriate see this summary of methods for estimating pressure loss from fittings.

Values for the Equivalent Length of Pipe for Various Fittings

Typical values for the equivalent length of pipe for various fittings are shown in the table below.

After summing these equivalent lengths as appropriate for your hydraulic system, you may simply calculate the pressure drop for the resulting length of pipe.

Category	Fitting	Types	$(L/D)_{eq}$
Elbow	90° Curved, Threaded	Standard Radius (R/D = 1)	30
Elbow	90° Curved, Threaded	Long Radius (R/D = 1.5)	16
Elbow	90° Curved, Flanged/Welded	Standard Radius (R/D = 1)	20
Elbow	90° Curved, Flanged/Welded	Long Radius (R/D = 2)	17
Elbow	90° Curved, Flanged/Welded	Long Radius (R/D = 4)	14
Elbow	90° Curved, Flanged/Welded	Long Radius (R/D = 6)	12
Elbow	90° Mitered	1 weld (90°)	60
Elbow	90° Mitered	2 welds (45°)	15
Elbow	90° Mitered	3 welds (30°)	8
Elbow	45° Curved, Threaded	Standard Radius (R/D = 1)	16
Elbow	45° Curved, Threaded	Long Radius (R/D = 1.5)
Elbow	45° Mitered	1 weld 45°	15
Elbow	45° Mitered	2 welds 22.5°	6
Elbow	180° Bend	Threaded, close-return (R/D = 1)	50
Elbow	180° Bend	Flanged (R/D = 1)
Elbow	180° Bend	All types (R/D = 1.5)
Tee	Through-branch as an Elbow	Threaded (r/D = 1)	60
Tee	Through-branch as an Elbow	Threaded (r/D = 1.5)
Tee	Through-branch as an Elbow	Flanged (r/D = 1)	20
Tee	Through-branch as an Elbow	Stub-in branch
Tee	Run-through	Threaded (r/D = 1)	20
Tee	Run-through	Flanged (r/D = 1)
Tee	Run-through	Stub-in branch
Valve	Angle valve	45°, full line size, $\beta = 1$	55
Valve	Angle valve	90° full line size, $\beta = 1$	150
Valve	Globe valve	Standard, $\beta = 1$	340
Valve	Plug valve	Branch flow	90
Valve	Plug valve	Straight through	18
Valve	Plug valve	Three-way (flow through)	30
Valve	Gate valve	Standard, $\beta = 1$	8
Valve	Ball valve	Standard, $\beta = 1$	3
Valve	Diaphragm	Dam type
Valve	Swing check valve	$V_{\min} = 35[\rho (\text{lb}_{\text{m}}/\text{ft}^{3})]^{-1/2}$	100
Valve	Lift check valve	$V_{\min} = 40[\rho (\text{lb}_{\text{m}}/\text{ft}^{3})]^{-1/2}$	600
Tee	Hose Coupling	Simple, Full Bore	5

Example Calculation of Pressure Loss using Equivalent Lengths

This example demonstrates how to use the equivalent length method to calculate the pressure loss through simple pipe and fitting arrangement. The example uses water in system of standard weight carbon steel pipe. Note that for this example we consider a flat system, with no elevation changes.

Equivalent Length Example

System details

Item	Value
Pipe Size	DN100 (4")
Pipe Diameter	102.3 mm
Pipe Length	50 m
Fittings	3 × 90° long radius (R/D = 2) elbows
Fluid Velocity	3 m/s
Fluid Density	1000 kg/m^{3}
Friction Factor	0.018

Calculation

Using the table of fittings and equivalent lengths above we find that the equivalent length for the 90° elbow is 17 pipe diameters.

$L_{eq} = 17 \times 102.3 \text{ mm} = 1.739 \text{ m}$

Taking the pipe length and number of elbows we calculated the equivalent length of the pipe work for pressure loss purposes.

$L_{eq} = 50 + 3 \times 1.739 = 55.217 \text{ m}$

Using the equation for pressure loss in pipe:

$\begin{aligned} \Delta p &= f \frac{L}{D} \frac{\rho V^2}{2} \\ \Delta p &= 0.018 \frac{55.217}{102.3/1000} \frac{1000 \times 3^2}{2} \\ \Delta p &= 43.7 \text{ kPa} \end{aligned}$

Pressure Loss from Fittings - Equivalent Length Method