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Answer :
Final answer:
The minimum diameter of the steam pipe is approximately 24.8 inches.
Explanation:
To calculate the minimum diameter of the steam pipe, we can use the equation for the flow rate of a fluid through a pipe:
Flow rate = velocity x cross-sectional area
Given that the flow rate is 200 lbm/s and the velocity should not exceed 59 ft/s, we can rearrange the equation to solve for the cross-sectional area:
Cross-sectional area = flow rate / velocity
Converting the units to consistent ones, we have:
Cross-sectional area = (200 lbm/s) / (59 ft/s) = 3.39 ft²
Finally, we can calculate the diameter of the pipe:
Diameter = 2 x square root of (cross-sectional area / pi)
Plugging in the values, we get:
Diameter = 2 x square root of (3.39 ft² / 3.14) = 2.07 ft
Converting this value to inches, we have approximately 24.8 inches. Therefore, the minimum diameter the pipe can have is approximately 24.8 inches, which is not one of the given options.
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