Afan draws air from the atmosphere through a 0.30‐m‐diameter round duct that has a smoothly rounded entrance. a differential manometer connected to an opening in the wall of the duct shows a vacuum pressure of 2.5 cm of water. the density of air is 1.22 kg/m3. determine the volume rate of air flow in the duct in cubic feet per second. what is the horsepower output of the fan?

The volume air flow rate is

The output of the fan is 0.446 hp

Solution:

As per the question:

Diameter of the round duct, d = 0.30 m

Radius of the duct, R =

Pressure of the opening, P = 2.5 cm of water = 0.025 m of water

P =

Density of air,

Now, the velocity, v can be calculated as:

Now,

Volume rate of air flow is given by:

Now,

1 ft = 3.2808 m

Now, the output of the fan in horsepower (hp):

Power output, P' =

Now,

1 hp = 746 W

P' (in hp) =