Fans of the same basic design and proportions operate theoretically in accordance with certain fan laws. In practise, these laws do not apply exactly because of design considerations and manufacturing tolerances, but they are useful in estimating approximate outputs of similar fans of different diameters and speeds as applied to normal ventilation work, and can be summarised as follows:
a
Volume of air flow varies as (fan diameter)3 and as rpm
b
Pressure developed varies as (fan diameter)2 and as (rpm)2
c
Power absorbed by the fan varies as (fan diameter)5 and as (rpm)3
It is important to note, however, that these Laws apply to the same point of operation on the fan characteristic. They cannot be used to predict other points on the fan's curve.
These laws are most often used to calculate change in flow rate, pressure, and power of a fan when the size, rotational speed or gas density is changed. Therefore, in the following Laws the suffice "I" has been used for initial known values and the suffice "2" for the changed values and the resulting calculated value when:
Q = volume flow rate
P = pressure (total, static or dynamic) p = gas density
n = fan rotational speed
D = impeller diameter
W = impeller power
1. VOLUME of air flow varies as the (fan diameter)3 and as the rpm
or:
New Volume = Old Volume ×
(
new impeller diameter
old impeller diameter
)
3
×
(
new rpm
old rpm
)
or:
Q2 = Q ×
(
D2
D1
)
3 ×
(
n2
n1
)
2. PRESSURE developed varies as the (fan diameter)2 and as the (rpm)2
or:
New Pressure = Old Pressure ×
(
new impeller diameter
old impeller diameter
)
2
×
(
new rpm
old rpm
)
or:
P2 = P1 ×
(
D2
D1
)
2
×
(
n2
n1
)
2
3. POWER ABSORBED by the fan varies (fan diameter)5 and as (rpm)3
or:
New Power = Old Power ×
(
new fan diameter
old fan diameter
)
5
×
(
new rpm3
old rpm
)
or:
W2 = W1 ×
(
D2
D1
)
5
×
(
n2
n1
)
3
Pressure and power calculation should also take gas density into account.
(new pressure) or p2
(old pressure) p1
But if this or any other variable is unchanged they can be omitted from the equation: for example if the fan diameter is constant, only speed variation applies:
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