Answer :
The smallest standpipe diameter required to carry 500 gallons per minute of ethylene glycol at a maximum velocity of 10.0 feet per second is approximately 3.076 feet, which is equivalent to around 11.9 inches. This calculation ensures that the flow rate and velocity requirements are met within the specified design parameters.
Let's break down the calculation step by step:
1. Convert Flow Rate from GPM to CFS:
Given: Flow rate (Q ) = 500 gallons per minute (GPM)
We know that
1 cubic foot = 7.4805 gallons.
So, to convert GPM to cubic feet per second (CFS):
[tex]\[ Q_{\text{CFS}} = \frac{500}{7.4805} \][/tex]
[tex]\[ Q_{\text{CFS}} \approx 66.81 \, \text{CFS} \][/tex]
2. Calculate Cross-sectional Area (A\):
Given:
Velocity (V) = 10.0 feet per second (FPS)
Using the formula [tex]A = \frac{Q}{V}\)[/tex]:
A = 66.81 \ 10.0
A = 6.681 square feet
3. Find the Radius (r):
Since the standpipe is circular, we can find the radius (r) using the formula for the area of a circle:
[tex]\[ A = \pi r^2 \][/tex]
[tex]\[ r^2 = \frac{A}{\pi} \][/tex]
[tex]\[ r = \sqrt{\frac{A}{\pi}} \][/tex]
[tex]\[ r = \sqrt{\frac{6.681}{\pi}} \][/tex]
[tex]\[ r \approx 1.538 \, \text{feet} \][/tex]
4. Calculate the Diameter ((d)):
The diameter (d) is twice the radius:
d = 2r
d ≈ 2 x 1.538
d ≈ 3.076 feet
Therefore, the diameter of the standpipe is approximately (3.076) feet, which is equivalent to approximately (11.9) inches.
