Answer:
The pressure and power of fan is 1.77 and 11.18 Hp respectively.
Explanation:
Given:
Discharge [tex]Q_{1} = 30000[/tex] cfm
Pressure difference [tex]\Delta P = 4[/tex] inch
Efficiency [tex]\eta = 50\%[/tex]
(A)
From the formula of fan power,
[tex]P _{1} = \frac{Q \Delta P}{6356 \eta}[/tex]
[tex]P_{1} = \frac{30000 \times 4}{6356 \times 0.5}[/tex]
[tex]P_{1} = 37.76[/tex] Hp
(B)
Fan power and pressure is given by,
We know that pressure difference is proportional to the square of discharge.
[tex]\frac{\Delta p_{2} }{\Delta P_{1} } = (\frac{Q_{2} }{Q_{1} } ) ^{2}[/tex]
[tex]\Delta P_{2} = (\frac{20000}{30000} ) \times 4[/tex]
[tex]\Delta P_{2} = 1.77[/tex]
Fan power proportional to the cube of discharge.
[tex]\frac{P_{2} }{P^{1} } = (\frac{Q_{2} }{Q_{1} } )^{3}[/tex]
[tex]P_{2} = \ (\frac{20000}{30000} ) ^{3} \times 37.76[/tex]
[tex]P_{2} = 11.18[/tex] Hp
Therefore, the pressure and power of fan is 1.77 and 11.18 Hp respectively.
