FAN EFFICIENCY FORMULA DERIVATION

DEAR EXPERTS 

CAN ANYBODY SHARE THE HOW TO DERIVE FAN EFFICIENCY FORMULA.

I TRIED A LOT BUT HOW 102 IS COMING IN DENOMINATOR ?

PLEASE EXPLAIN

SIDHANT

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re FAN EFFICIENCY FORMULA DERIVATION

Hello Sidhant,

The factor of 102 is used to convert mmWC into pascals because the formula for the static fan efficiency in SI units is;-

Static Fan Efficiency =  Volume (m3/s) * Pressure gain (Pa) /  Power input (W) * 100

But, if the pressure is measured in mmWC instead of Pascals and Power is expressed in kW, the formula can be derived as follows;-

1 mmWC = 9.81Pa

Therefore 1Pa = 1/9.81 = 0.102 mmWC  (or, divide mmWC by 0.102 to get Pa)

So, Static Fan Efficiency =  [Volume (m3/s) * Pressure gain (mmWC) / 0.102] /  [Power input (kW) * 1000] * 100

or  Static Fan Efficiency = [Volume (m3/s) * Pressure gain (mmWC)]  /  [Power input (kW) * 1000 * 0.102] *100

or  Static Fan Efficiency = [Volume (m3/s) * Pressure gain (mmWC)] *100 /  [Power input (kW) * 102]  

Regards,

Ted

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re FAN EFFICIENCY FORMULA DERIVATION

Dear Ted

thanks a lot but

eff. = m3/s * Pa divided by motor kw

Now 

1mmwc = 9.8 Pa

so put 1Pa = 0.102 mmwc

efficiency = m3/s X 0.102 mmwc *100/( motor kw x motoe eff.)

so 102 value comes in numerator instead of denomenator.

Still it is not clear.

Please do reply

Sidhant

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re FAN EFFICIENCY FORMULA DERIVATION

Dear Sidhant,

You are getting confusions for change in unit from mmH2O to Pascal. As explained by Ted ,I am only showing you an example for calculation in both the units and I hope you doubt will be clear.

1 mmH2O = 9.80 Pascals

Let us assume a fan having a flow of volume 16m3/sec and devlops a total pressure of 500 mmH2O.

1. Using the formula given in books using mmH2O as pressure

Kw = (m3/sec x Pressure mmH2O)  /102  = 16 x 500 /102 = 78.4 Kw

2. Using the formula given by Ted as Watt = m3/sec x pressure (pa)

500 mmH2O = 500 x 9.8 = 4900 pascal

so Watt = 16 x 4900 = 78400

= 78400/1000 = 78.4Kw

In both the cases the power is same , I dont think there is any confusions now,

Both the formulas are used in SI units and in general the work done theory the amount of air handle by a fan against a pressure is called work done and dividing workdone by time will give you the power.

regards

vdchari

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