Question

A supply fan is operating at 30000 cfm and 4 inch of water with an efficiency of 50%. (a) Calculate the fan power at the current operating condition. (b) Calculate the pressure and power if the supply fan reduces its speed to deliver 20000 cfm.

Answer 1

The pressure and power of fan is 1.77 and 11.18 Hp respectively.

Step-by-step explanation:

Given:

Discharge
`Q_(1) = 30000` cfm

Pressure difference
`\Delta P = 4` inch

Efficiency
`\eta = 50\%`

(A)

From the formula of fan power,

`P _(1) = (Q \Delta P)/(6356 \eta)`

`P_(1) = (30000 * 4)/(6356 * 0.5)`

`P_(1) = 37.76` Hp

(B)

Fan power and pressure is given by,

We know that pressure difference is proportional to the square of discharge.

`(\Delta p_(2) )/(\Delta P_(1) ) = ((Q_(2) )/(Q_(1) ) ) ^(2)`

`\Delta P_(2) = ((20000)/(30000) ) * 4`

`\Delta P_(2) = 1.77`

Fan power proportional to the cube of discharge.

`(P_(2) )/(P^(1) ) = ((Q_(2) )/(Q_(1) ) )^(3)`

`P_(2) = \ ((20000)/(30000) ) ^(3) * 37.76`

`P_(2) = 11.18` Hp

Therefore, the pressure and power of fan is 1.77 and 11.18 Hp respectively.