Calculate the capacity (in m³/hour) of the vacuum pump that is required for the hospital based on the given departments and room specifications.
Understand the Problem
The question is asking to calculate the vacuum capacity required for patient rooms and operating rooms in a hospital, based on the provided information regarding the number of rooms, types of vacuum terminals, and the specifications of the hospital departments. The focus is on the total vacuum pump capacity in cubic meters per hour that is required for the renovation of the hospital's vacuum system.
Answer
The vacuum capacity required is approximately $23.578 \text{ m³/h}$.
Answer for screen readers
The vacuum capacity required for the renovation of the hospital's vacuum system is approximately $23.578 \text{ m³/h}$.
Steps to Solve
- Calculate vacuum capacity for patient rooms
Each patient room has a Type B vacuum terminal with a capacity factor of $UF_B = 0.5$. The formula for vacuum capacity is:
$$ \text{Vacuum Capacity for Patient Rooms} = N \times 0.25 \times UF_B $$
where ( N ) is the number of patient rooms.
Given that there are 75 patient rooms:
$$ \text{Vacuum Capacity for Patient Rooms} = 75 \times 0.25 \times 0.5 = 9.375 \text{ SCFM} $$
- Calculate vacuum capacity for operating rooms
Each operating room has 3 vacuum terminals with a mix of type B and a different type (let's call it Type A). Given the values provided, the formula is:
$$ \text{Vacuum Capacity for OR} = N_A \times 0.25 \times UF_A + (N_B \times 1.5 \times UF_B) $$
With ( N_A = 6 ) operating rooms and ( UF_B = 0.5 ):
$$ \text{Vacuum Capacity for OR} = (6 \times 1.5 \times 0.5) = 4.5 \text{ SCFM} $$
- Total vacuum capacity calculation
Now, we combine the vacuum capacities for both patient rooms and operating rooms:
$$ \text{Total Vacuum Capacity} = \text{Vacuum Capacity for Patient Rooms} + \text{Vacuum Capacity for OR} $$
Substituting the values:
$$ \text{Total Vacuum Capacity} = 9.375 + 4.5 = 13.875 \text{ SCFM} $$
- Convert to cubic meters per hour
The conversion factor from SCFM to cubic meters per hour (m³/h) is approximately:
$$ 1 \text{ SCFM} \approx 1.699 \text{ m³/h} $$
Now, we convert:
$$ \text{Total Vacuum Capacity in m³/h} = 13.875 \times 1.699 = 23.578 \text{ m³/h} $$
The vacuum capacity required for the renovation of the hospital's vacuum system is approximately $23.578 \text{ m³/h}$.
More Information
The calculations are based on the specifications for vacuum terminals in patient and operating rooms. The SCFM (Standard Cubic Feet per Minute) value is converted into cubic meters per hour for clarity in a hospital setting.
Tips
- Miscalculating the number of rooms or terminals: Double-check the counts given in the problem.
- Incorrect application of the capacity factors: Ensure the right factors are used for the respective types of terminals.
- Forgetting to convert units: Always convert SCFM to cubic meters per hour for the final answer.
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