237 posts

### 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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537 posts

### 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

237 posts

### 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

79 posts

### 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*