Multi-Wing Australia P/L

17.03.2009

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This is our first article of a series that we are hoping our customers will find useful. The series will contain information relating to our product field and other facets of air moving applications.

The Fan Laws

We will start of with the basic fan laws. The laws show the relationships between Diameter, Flow, Speed, Pressure(Head), and Power for incompressible flow. There are more elaborate forms of these equations to allow for such things as compression, but we will leave those out for now.

The laws help to create the system resistance curve in our Optimiser program, if you like you can have a quick try to check the fan laws as we go, simply double click a point on the curve and the resistnace curve will appear, you may then follow this up to your your second curve with either increased/decreased diameter, or increased/decreased rotational speed.

Something to remember when working with the Fan Laws: They are all linked, you can not use these laws to trace a constant pressure with varying rotational speeds.

Law 1. The first law holds the Diameter (D) constant, lets look at how things change:

Law 1a. The flow-rate is directly proportional to the rotational speed, so double the speed, gives double the flow:

${ Q_1 \over \ Q_2} = { \left ( {N_1 \over N_2} \right )}$

Law 1b. The pressure is proportional to the square of the rotational speed. Double the speed, and you get four times the pressure:

${H_1 \over H_2} = { \left ( {N_1 \over N_2} \right )^2 }$

Law 1c. The power is proportional to the cube of the rotational speed. Double the speed, and you will be absorbing eight times the power:

: ${P_1 \over P_2} = { \left ( {N_1 \over N_2} \right )^3 }$

Law 2. The second law holds the shaft speed (N) constant:

Law 2a. The flow is proportional to impeller diameter:

${ Q_1 \over \ Q_2} = { \left ( {D_1 \over D_2} \right )}$

Law 2b. The pressure is proportional to the square of impeller diameter:

${H_1 \over H_2} = { \left ( {D_1 \over D_2} \right )^2 }$

Law 2c. The power is proportional to the cube of impeller diameter :

${P_1 \over P_2} = { \left ( {D_1 \over D_2} \right )^3 }$

Definitions of common terms and units

Just as a quick reference for those who do not have a simple list handy. Here is a list of the most commonly used flow measures based around 1 metre cubed per second of air at the density of 1.225kg/m³ (15 Degrees Celsius).

Volume Flow-Rate Conversions

cubic metre per second	m³ s^-1	1
cubic metres per minute	m³ min^-1	60
cubic metre per hour	m³ h^-1	3600
litre per second	l s^-1	1000
litre per minute	l min^-1	60000
litre per hour	l h^-1	3600000
cubic foot per second	ft³ s^-1	35.3
cubic foot per minute	ft³ min^-1	2120
cubic foot per hour	ft³ h^-1	127200
Kilograms per second	kg s^-1	1.225
Kilograms per minute	kg min^-1	73.5
Kilograms per hour	kg h^-1	4410

Pressure Measurement Conversions

Pascals	N m^-2	100
mmWg (Water Gauge)	mm	10.2
inWg (Inches)	inches	0.402
MilliBar	mBar	1

Please note that these conversion factors are for constant temperature, pressure and density only. Air density used = 1.225kg/m³

The difference between Static and Dynamic Pressure

Static Pressure
In an air distribution system, Static pressure is the pressure which the fan must supply to overcome the resistance to airflow through the system ductwork and system components.

Dynamic Pressure
Dynamic pressure is related to the fluid velocity. The following equation is the basic form for incompressible flow.

q

= dynamic pressure in pascals

ρ

= fluid density in kg/m³ (e.g. density of air)

v

= fluid velocity in m/s

Total Pressure
Total pressure is the sum of the Dynamic pressure and the Static pressure.

General fan characteristics

The impeller characteristic

The main tool when selecting air-moving applications is the impeller characteristic curve. In fig. 1.1, the curve illustrates the performance in terms of the relationship between airflow and static pressures. The graph also shows the absorbed power for the impeller, where the scale for the power curve is set to the default location on the top right in our Multi-Wing Optimiser.

The traditional approach is to select an impeller, where the curve matches a working point in terms of flow and pressure. By knowing, or estimating, the working point it will be possible to complete the system curve since the pressure drop is proportional to the square of the airflow. If the impeller characteristic does not match the duty point exactly, the true working point will balance at the intersection between the fan characteristic and the system characteristic.

Apart from selecting the impeller according to the required performance, the curve is useful to judge the stability of the working point. The dip of the curve indicates the stalling area of the characteristic, and for higher pitch angles, this area is extremely unsuitable. The gradient of the curve near the working point marks how much the flow changes whenever there is a change in pressure.

The impeller characteristic can also contain the efficiency curve. This curve is given by the performance and power consumption, and is normally defined as:

In the Multi-Wing Optimiser software the efficiency is also specified as a colour code when monitoring the performance curve. As indicated on the curve below the highest efficiency point is located in the lower part of the curve in terms of pressure. This is typical for all axial impellers while centrifugal fans generally have a higher efficiency point in the high-pressure area. As shown below the efficiency curve can be added to the view in the Multi-Wing Optimiser.

Fig. 1.1. The impeller characteristic

The method used to measure the Multi-Wing impellers is according to AMCA 210 in a configuration refered to as Amca-A . This configuration is a short piece of tube duct with a rounded inlet.