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Answer:
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 ([tex]v[/tex]), measured in feet per minute, is:
[tex]v = \frac{4\cdot \dot V}{\pi\cdot D^{2}}[/tex] (Eq. 1)
Where:
[tex]\dot V[/tex] - Volume flow, measured in cubic feet per minute.
[tex]D[/tex] - Inner diameter of the air duct, measured in feet.
If we know that [tex]\dot V = 450\,\frac{ft^{3}}{min}[/tex] and [tex]D = \frac{5}{6}\,ft[/tex], then air velocity is:
[tex]v = \frac{4\cdot \left(450\,\frac{ft^{3}}{min} \right)}{\pi\cdot \left(\frac{10}{12}\,ft \right)^{2}}[/tex]
[tex]v \approx 825.059\,\frac{m}{s}[/tex]
The velocity of air is approximately 825.059 meters per second.
And the mass flow ([tex]\dot m[/tex]), measured in pounds per minute, is now calculated:
[tex]\dot m = \rho \cdot \dot V[/tex] (Eq. 2)
Where [tex]\rho[/tex] is the density of air, measured in pounds per cubic feet.
If we know that [tex]\rho = 0.078\,\frac{lbm}{ft^{3}}[/tex] and [tex]\dot V = 450\,\frac{ft^{3}}{min}[/tex], then mass flow is:
[tex]\dot m = \left(0.078\,\frac{lbm}{ft^{3}}\right)\cdot \left(450\,\frac{ft^{3}}{min} \right)[/tex]
[tex]\dot m = 35.1\,\frac{lbm}{min}[/tex]
The mass flow rate of air is 35.1 pounds per minute.
Velocity of the air in duct and the mass flow rate of air is 825 ft/min and 35.1 pound.
Given that;
Density of material = 0.078 lbm / ft³
Volume flow rate = 450 ft³/min
Diameter of duct = 10 inch
Find:
Velocity of the air in duct and the mass flow rate of air
Computation:
[tex]V = \frac{v}{\pi D^2/4 } \\\\V = \frac{450}{(3.14) 10^2/4 } \\\\V = \frac{450}{(3.14) 100/4 } \\\\V = 825 ft/min[/tex]
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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