QuestionMay 28, 2025

A heating plant for a large medical campus requires 22,000 MBH (1MBH=1,000,000btuh) of heating capacity. Which of the following pipe size and velocity in feet per second (fps)for the main would be needed if the plant is a 50 psig medium-pressure steam system? Select one: A. 8'' pipe at 130 fps B. 8'' pipe at 10 fps C. 4'' pipe at 6 fps D. 4'' pipe at 130 fps E. None of these

A heating plant for a large medical campus requires 22,000 MBH (1MBH=1,000,000btuh) of heating capacity. Which of the following pipe size and velocity in feet per second (fps)for the main would be needed if the plant is a 50 psig medium-pressure steam system? Select one: A. 8'' pipe at 130 fps B. 8'' pipe at 10 fps C. 4'' pipe at 6 fps D. 4'' pipe at 130 fps E. None of these
A heating plant for a large medical campus requires 22,000 MBH (1MBH=1,000,000btuh) of heating capacity. Which of the following pipe size and velocity in feet per second (fps)for the main would be needed if the plant is a 50 psig medium-pressure steam system? Select one: A. 8'' pipe at 130 fps B. 8'' pipe at 10 fps C. 4'' pipe at 6 fps D. 4'' pipe at 130 fps E. None of these

Solution
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Answer

E. None of these Explanation 1. Convert MBH to BTU/hr 22,000 \text{ MBH} = 22,000 \times 1,000,000 \text{ BTU/hr} = 22,000,000,000 \text{ BTU/hr} 2. Calculate Steam Flow Rate Use the formula for steam flow rate: **W = \frac{Q}{h_f - h_i}**, where Q is the heat load in BTU/hr, and h_f and h_i are the enthalpies of steam and water. For simplicity, assume typical values for medium pressure steam at 50 psig: h_f \approx 1190 \text{ BTU/lb}, h_i \approx 180 \text{ BTU/lb}. W = \frac{22,000,000,000}{1190 - 180} \approx 20,000,000 \text{ lb/hr} 3. Determine Pipe Size and Velocity Use the steam velocity formula: **V = \frac{W}{\rho \cdot A}**, where V is velocity, W is mass flow rate, \rho is density (approx. 0.05 \text{ lb/ft}^3 for steam), and A is cross-sectional area. For an 8'' pipe, A = \pi \left(\frac{8}{12}/2\right)^2 \approx 0.349 \text{ ft}^2. For a 4'' pipe, A = \pi \left(\frac{4}{12}/2\right)^2 \approx 0.087 \text{ ft}^2. Calculate velocity for each option: - 8'' pipe: V = \frac{20,000,000}{0.05 \times 0.349} \approx 1145 \text{ fps} - 4'' pipe: V = \frac{20,000,000}{0.05 \times 0.087} \approx 4598 \text{ fps} 4. Compare with Given Options None of the calculated velocities match the given options exactly.

Explanation

1. Convert MBH to BTU/hr<br /> $22,000 \text{ MBH} = 22,000 \times 1,000,000 \text{ BTU/hr} = 22,000,000,000 \text{ BTU/hr}$<br /><br />2. Calculate Steam Flow Rate<br /> Use the formula for steam flow rate: **$W = \frac{Q}{h_f - h_i}$**, where $Q$ is the heat load in BTU/hr, and $h_f$ and $h_i$ are the enthalpies of steam and water. For simplicity, assume typical values for medium pressure steam at 50 psig: $h_f \approx 1190 \text{ BTU/lb}$, $h_i \approx 180 \text{ BTU/lb}$.<br /> $W = \frac{22,000,000,000}{1190 - 180} \approx 20,000,000 \text{ lb/hr}$<br /><br />3. Determine Pipe Size and Velocity<br /> Use the steam velocity formula: **$V = \frac{W}{\rho \cdot A}$**, where $V$ is velocity, $W$ is mass flow rate, $\rho$ is density (approx. $0.05 \text{ lb/ft}^3$ for steam), and $A$ is cross-sectional area.<br /> For an $8''$ pipe, $A = \pi \left(\frac{8}{12}/2\right)^2 \approx 0.349 \text{ ft}^2$.<br /> For a $4''$ pipe, $A = \pi \left(\frac{4}{12}/2\right)^2 \approx 0.087 \text{ ft}^2$.<br /><br /> Calculate velocity for each option:<br />- $8''$ pipe: $V = \frac{20,000,000}{0.05 \times 0.349} \approx 1145 \text{ fps}$<br />- $4''$ pipe: $V = \frac{20,000,000}{0.05 \times 0.087} \approx 4598 \text{ fps}$<br /><br />4. Compare with Given Options<br /> None of the calculated velocities match the given options exactly.
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