Summary

Fittings such as elbows, tees, valves and reducers 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 K-value method, also known as the Resistance Coefficient, Velocity Head, Excess Head or Crane method.

Definitions


$D$	:	Internal diameter of pipe
$f$	:	Pipe friction factor
$g$	:	Acceleration due to gravity
$h$	:	Head loss
$K$	:	Resistance Coefficient
$L$	:	Length as indicated
$V$	:	Average velocity

Introduction

The K-value, Resistance Coefficient, Velocity Head, Excess Head or Crane method allows the user to characterise the pressure loss through fittings in a pipe. The K-value represents the multiple of velocity heads that will be lost by fluid passing through the fitting.

It is more accurate than the Equivalent Length method, as it can be characterised against varying flow conditions (i.e. Reynold Number). However it is less accurate than other methods as it does not take into account the varying geometries of fittings at different sizes. For example a DN 50 (2") long radius 90° elbow is not geometrically similar to a DN 150 (6") long radius 90° elbow, thus the K-value is inaccurate at sizes other than that of the fitting used to determine the K-value. These K-values also generally assume fully developed turbulent flow, and thus are inaccurate at low Reynolds Numbers.

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

K-Value Method and Typical Values

The Velocity head method is named as such because it represents the pressure loss through a fitting as the equivalent number of “velocity heads”. It is in some ways similar to the equivalent length method, and the two may be equated by the formula below:

Formula for Calculating Head Loss from K Values

$K=f\frac{L}{D}$

where $L/D$ is the equivalent length.

$h_{L}=K\frac{V^{2}}{2g}$

Values of K for Various Fitting Types

There are many tabulations of K-values, as well as methods for calculating K-values. Below is table of typical K-values for various fitting types.

Category	Fitting	Types	K
Elbow	45°	Standard (R/D = 1)	0.35
Elbow	45°	Long Radius (R/D = 1.5)	0.2
Elbow	90° Curved	Standard (R/D = 1)	0.75
Elbow	90° Curved	Long Radius (R/D = 1.5)	0.45
Elbow	90° Square or Mitred		1.3
Elbow	180° Bend	Close Return	1.5
Tee	Run Through	Branch Blanked	0.4
Tee	Tee as Elbow	Entering in run	1
Tee	Tee as Elbow	Entering in branch	1
Tee	Tee Branching Flow		1
Joiner	Coupling	All	0.04
Joiner	Union	All	0.04
Valve	Gate valve	Fully Open	0.17
Valve	Gate valve	3/4 Open	0.9
Valve	Gate valve	1/2 Open	4.5
Valve	Gate valve	1/4 Open	24
Valve	Diaphragm valve	Fully Open	2.3
Valve	Diaphragm valve	3/4 Open	2.6
Valve	Diaphragm valve	1/2 Open	4.3
Valve	Diaphragm valve	1/4 Open	21
Valve	Globe valve, Bevel Seat	Fully Open	6
Valve	Globe valve, Bevel Seat	1/2 Open	9.5
Valve	Globe Valve, Composition Seat	Fully Open	6
Valve	Globe Valve, Composition Seat	1/2 Open	8.5
Valve	Plug disk valve	Fully Open	9
Valve	Plug disk valve	3/4 Open	13
Valve	Plug disk valve	1/2 Open	36
Valve	Plug disk valve	1/4 Open	112
Valve	Angle valve	Fully Open	2
Valve	Y valve or blowoff valve	Fully Open	3
Valve	Plug cock	$\theta = 5°$	0.05
Valve	Plug cock	$\theta = 10°$	0.29
Valve	Plug cock	$\theta = 20°$	1.56
Valve	Plug cock	$\theta = 40°$	17.3
Valve	Plug cock	$\theta = 60°$	206
Valve	Butterfly valve	$\theta = 5°$	0.24
Valve	Butterfly valve	$\theta = 10°$	0.52
Valve	Butterfly valve	$\theta = 20°$	1.54
Valve	Butterfly valve	$\theta = 40°$	10.8
Valve	Butterfly valve	$\theta = 60°$	118
Valve	Check valve	Swing	2
Valve	Check valve	Disk	10
Valve	Check valve	Ball	70
Valve	Foot valve		15
Meter	Water meter	Disk	7
Meter	Water meter	Piston	15
Meter	Water meter	Rotary (star-shaped disk)	10
Meter	Water meter	Turbine-wheel	6

Example Calculation of Pressure Loss using K-values

Overview

This example demonstrates how to use the excess head method to calculate the head 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 = 1.5) elbows
Fluid Velocity	3 m/s
Fluid Density	1000 kg/m^{3}
Friction Factor	0.018
Gravitational Acceleration	9.81 m/s^{2}

Calculation

Using the table of fittings and K-values above we find that the K-value for the 90° elbow is 0.45. With this we can calculate the head loss for a single elbow.

$\begin{aligned} h_{L} &= K \frac{V^{2}}{2g} \\ h_{L} &= 0.45 \frac {3^{2}}{2 \times 9.81} \\ h_{L} &= 0.206 \text{ m} \end{aligned}$

Using the equation for head loss in pipe, we can calculate the loss through the straight piping:

$\begin{aligned} h_{P} &= f \frac{L}{D} \frac{V^{2}}{2g} \\ h_{P} &= 0.018 \frac{50}{102.3/1000} \frac{3^{2}}{2 \times 9.81} \\ h_{P} &= 4.03 \text{ m} \end{aligned}$

The total head loss for the system is the addition of the head loss from the pipe and the fittings.

$\begin{aligned} h_{T} &= h_{P} + 3 \times h_{L} \\ h_{T} &= 4.03 + 3 \times 0.206 \\ h_{T} &= 4.648 \text{ m} \end{aligned}$

In the above example we first calculated the head loss for a single fitting and then multiplied by the number of fittings. It is also correct to add or multiply the K-values of fittings and then convert to a pressure or head loss. This is useful when there are many fittings of several types.

Pressure Loss from Fittings - Excess Head (K) Method