Answer :
To solve this problem, let's break it down step by step.
1. Convert the diameter from inches to feet:
- The diameter of the pipeline is given as 8 inches.
- There are 12 inches in a foot, so the diameter in feet is:
[tex]\[
\text{diameter\_feet} = \frac{8 \text{ inches}}{12} = 0.6667 \text{ feet}
\][/tex]
2. Calculate the radius in feet:
- The radius is half of the diameter, so:
[tex]\[
\text{radius\_feet} = \frac{\text{diameter\_feet}}{2} = \frac{0.6667}{2} = 0.3333 \text{ feet}
\][/tex]
3. Calculate the cross-sectional area of the pipeline:
- The cross-sectional area of a circle is given by the formula [tex]\( A = \pi r^2 \)[/tex].
- Using the radius in feet:
[tex]\[
A = \pi \times (0.3333 \text{ feet})^2 \approx 0.3491 \text{ square feet}
\][/tex]
4. Calculate the flow rate in cubic feet per second (CFS):
- The flow rate in cubic feet per second is the cross-sectional area multiplied by the velocity:
[tex]\[
\text{flow\_rate\_cfs} = A \times \text{velocity\_fps} = 0.3491 \text{ square feet} \times 3.18 \text{ feet per second} \approx 1.1100 \text{ cubic feet per second}
\][/tex]
5. Convert the flow rate from CFS to GPM (gallons per minute):
- There are 7.48 gallons in a cubic foot, and 60 seconds in a minute.
- Therefore, to convert from cubic feet per second to gallons per minute:
[tex]\[
\text{flow\_rate\_gpm} = \text{flow\_rate\_cfs} \times 7.48 \times 60 = 1.1100 \text{ CFS} \times 7.48 \times 60 \approx 498.18 \text{ GPM}
\][/tex]
Based on these calculations, the flow rate from an 8-inch pipeline with a flow velocity of 3.18 feet per second is approximately 498.18 gallons per minute.
Thus, the closest choice is:
B. 500 GPM
1. Convert the diameter from inches to feet:
- The diameter of the pipeline is given as 8 inches.
- There are 12 inches in a foot, so the diameter in feet is:
[tex]\[
\text{diameter\_feet} = \frac{8 \text{ inches}}{12} = 0.6667 \text{ feet}
\][/tex]
2. Calculate the radius in feet:
- The radius is half of the diameter, so:
[tex]\[
\text{radius\_feet} = \frac{\text{diameter\_feet}}{2} = \frac{0.6667}{2} = 0.3333 \text{ feet}
\][/tex]
3. Calculate the cross-sectional area of the pipeline:
- The cross-sectional area of a circle is given by the formula [tex]\( A = \pi r^2 \)[/tex].
- Using the radius in feet:
[tex]\[
A = \pi \times (0.3333 \text{ feet})^2 \approx 0.3491 \text{ square feet}
\][/tex]
4. Calculate the flow rate in cubic feet per second (CFS):
- The flow rate in cubic feet per second is the cross-sectional area multiplied by the velocity:
[tex]\[
\text{flow\_rate\_cfs} = A \times \text{velocity\_fps} = 0.3491 \text{ square feet} \times 3.18 \text{ feet per second} \approx 1.1100 \text{ cubic feet per second}
\][/tex]
5. Convert the flow rate from CFS to GPM (gallons per minute):
- There are 7.48 gallons in a cubic foot, and 60 seconds in a minute.
- Therefore, to convert from cubic feet per second to gallons per minute:
[tex]\[
\text{flow\_rate\_gpm} = \text{flow\_rate\_cfs} \times 7.48 \times 60 = 1.1100 \text{ CFS} \times 7.48 \times 60 \approx 498.18 \text{ GPM}
\][/tex]
Based on these calculations, the flow rate from an 8-inch pipeline with a flow velocity of 3.18 feet per second is approximately 498.18 gallons per minute.
Thus, the closest choice is:
B. 500 GPM
