In a refrigeration unit, the mechanic must replace a fan with a faster one. The old fan delivers 5,200 cubic feet per minute (CFM) and runs at 450 revolutions per minute (RPM). The new fan must deliver 6,500 CFM. Calculate the required new RPM. Round to the nearest whole number.
Use the formula: [tex]$\frac{C F M_{\text {new }}}{C F M_{\text {old }}}=\frac{R P M_{\text {new }}}{R P M_{\text {old }}}$[/tex]
A. 562 RPM
B. 563 PPM
C. 751 RPM
D. 320 RPM
Answer (2)
To find the new RPM for a fan that needs to increase its airflow from 5200 CFM to 6500 CFM, we use the proportional relationship between CFM and RPM. The calculations show that the new RPM is 563 after rounding. Thus, the final answer is 563 RPM.
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Substitute the given values into the formula: 5200 6500 = 450 RP M new .
Solve for RP M new : RP M new = 450 × 5200 6500 .
Calculate RP M new : RP M new = 562.5 .
Round to the nearest whole number: 563 .
Explanation
Problem Setup and Given Information We are given the formula CF M old CF M new = RP M old RP M new and the following information:
CF M old = 5200 CFM RP M old = 450 RPM CF M new = 6500 CFM
We need to find RP M new .
Rearranging the Formula We can rearrange the formula to solve for RP M new :
RP M new = RP M old × CF M old CF M new
Now, substitute the given values into the formula:
RP M new = 450 × 5200 6500
Calculating the New RPM Now, we calculate the value of RP M new :
RP M new = 450 × 5200 6500 = 450 × 1.25 = 562.5
Rounding to the Nearest Whole Number Since we need to round to the nearest whole number, we round 562.5 to 563.
Final Answer Therefore, the required new RPM is 563 RPM.
Examples
Imagine you're designing ventilation systems for a building. Knowing how fan speed (RPM) relates to air volume (CFM) allows you to select the right fan to ensure proper air circulation. If you need to increase the airflow, this calculation helps determine the necessary increase in fan speed. This principle applies to various engineering scenarios, from HVAC systems to industrial processes where airflow rates are critical.
