Air whose density is 0.078 lbm/ft3 enters the duct of an air-conditioning system at a volume flow rate of 450 ft3/min. If the diameter of the duct is 10 in, determine the velocity of the air at the duct inlet and the mass flow rate of air.

Velocity of the air in duct and the mass flow rate of air is 825 ft/min and 35.1 pound.

Density of material = 0.078 lbm / ft³

Volume flow rate = 450 ft³/min

Diameter of duct = 10 inch

Velocity of the air in duct and the mass flow rate of air

Velocity of the air in duct = 825 ft/min

Mass flow rate of air = (Density of material)(Velocity)

Mass flow rate of air = (0.078)(825)

Mass flow rate of air = 35.1 pound

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The velocity of air is approximately 825.059 meters per second.

The mass flow rate of air is 35.1 pounds per minute.

Explanation:

From Dimensional Analysis and under the consideration that air velocity is constant, we get that velocity (), measured in feet per minute, is:

(Eq. 1)

Where:

- Volume flow, measured in cubic feet per minute.

- Inner diameter of the air duct, measured in feet.

If we know that and , then air velocity is:

The velocity of air is approximately 825.059 meters per second.

And the mass flow (), measured in pounds per minute, is now calculated:

(Eq. 2)

Where is the density of air, measured in pounds per cubic feet.

If we know that and , then mass flow is:

The mass flow rate of air is 35.1 pounds per minute.