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

Answer:

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

Explanation:

Given:

Discharge $Q_{1} = 30000$ cfm

Pressure difference $\Delta P = 4$ inch

Efficiency $\eta = 50\%$

(A)

From the formula of fan power,

     $P _{1} = \frac{Q \Delta P}{6356 \eta}$

     $P_{1} = \frac{30000 \times 4}{6356 \times 0.5}$

     $P_{1} = 37.76$ Hp

(B)

Fan power and pressure is given by,

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

    $\frac{\Delta p_{2} }{\Delta P_{1} } = (\frac{Q_{2} }{Q_{1} } ) ^{2}$

   $\Delta P_{2} = (\frac{20000}{30000} ) \times 4$

   $\Delta P_{2} = 1.77$

Fan power proportional to the cube of discharge.

       $\frac{P_{2} }{P^{1} } = (\frac{Q_{2} }{Q_{1} } )^{3}$

       $P_{2} = \ (\frac{20000}{30000} ) ^{3} \times 37.76$

       $P_{2} = 11.18$ Hp

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