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Answer :
To find out how many pounds of air would be moved per minute through an 18-inch round duct with a velocity of 1100 feet per minute (FPM), we can follow these steps:
1. Convert the duct diameter from inches to feet:
[tex]\[
\text{Diameter in feet} = \frac{18 \text{ inches}}{12} = 1.5 \text{ feet}
\][/tex]
2. Calculate the radius of the duct in feet:
[tex]\[
\text{Radius} = \frac{\text{Diameter in feet}}{2} = \frac{1.5}{2} = 0.75 \text{ feet}
\][/tex]
3. Calculate the cross-sectional area of the duct:
The area [tex]\( A \)[/tex] of a circle is given by the formula:
[tex]\[
A = \pi \times (\text{radius})^2
\][/tex]
[tex]\[
A = \pi \times (0.75)^2 \approx 1.767 \text{ square feet}
\][/tex]
4. Calculate the volume of air moved per minute:
The volume of air moved is the cross-sectional area of the duct multiplied by the velocity of the air:
[tex]\[
\text{Air volume per minute} = 1.767 \text{ square feet} \times 1100 \text{ FPM} \approx 1943.86 \text{ cubic feet per minute}
\][/tex]
5. Calculate the weight of the air moved per minute:
Given that 1 pound of air occupies 14 cubic feet, we can find the number of pounds of air moved as follows:
[tex]\[
\text{Pounds of air per minute} = \frac{\text{Air volume per minute}}{\text{Air volume per pound}}
\][/tex]
[tex]\[
\text{Pounds of air per minute} = \frac{1943.86}{14} \approx 138.85 \text{ pounds}
\][/tex]
Based on this calculation, approximately 139 pounds of air are moved per minute through the duct. Therefore, the correct answer is:
D. 139 pounds
1. Convert the duct diameter from inches to feet:
[tex]\[
\text{Diameter in feet} = \frac{18 \text{ inches}}{12} = 1.5 \text{ feet}
\][/tex]
2. Calculate the radius of the duct in feet:
[tex]\[
\text{Radius} = \frac{\text{Diameter in feet}}{2} = \frac{1.5}{2} = 0.75 \text{ feet}
\][/tex]
3. Calculate the cross-sectional area of the duct:
The area [tex]\( A \)[/tex] of a circle is given by the formula:
[tex]\[
A = \pi \times (\text{radius})^2
\][/tex]
[tex]\[
A = \pi \times (0.75)^2 \approx 1.767 \text{ square feet}
\][/tex]
4. Calculate the volume of air moved per minute:
The volume of air moved is the cross-sectional area of the duct multiplied by the velocity of the air:
[tex]\[
\text{Air volume per minute} = 1.767 \text{ square feet} \times 1100 \text{ FPM} \approx 1943.86 \text{ cubic feet per minute}
\][/tex]
5. Calculate the weight of the air moved per minute:
Given that 1 pound of air occupies 14 cubic feet, we can find the number of pounds of air moved as follows:
[tex]\[
\text{Pounds of air per minute} = \frac{\text{Air volume per minute}}{\text{Air volume per pound}}
\][/tex]
[tex]\[
\text{Pounds of air per minute} = \frac{1943.86}{14} \approx 138.85 \text{ pounds}
\][/tex]
Based on this calculation, approximately 139 pounds of air are moved per minute through the duct. Therefore, the correct answer is:
D. 139 pounds
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