32" fan blowing through 24" tube

Question

I currently have a 24" chimney fan rated at about 10000 CFM blowing through a 24" tube. If I were to make a cone so that I could install a 32" fan to blow through the same 24" tube, would that work? The 32" fan would be rated around 15000 CFM.

Answer 1

I answer these kinds of questions with a kind of elaborate, curated fashion so that they can be used as reference in future.

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We have two configurations:

1. Current Setup:

   • Fan Diameter: , 24"
   • Airflow: 10000 CFM
   • Tube Diameter: 24"

2. Proposed Setup:

   • Fan Diameter: 32"
   • Airflow: 15000 CFM
   • Tube Diameter: 24" (after coning down)

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Step 2: Air Velocity Calculation

The air velocity $ V $ can be determined using:

• $V = \frac{\text{CFM}}{A}$

where $ A $ is the cross-sectional area of the tube:

• $ A = \pi \left(\frac{D}{2}\right)^2 $

For the 24" tube:

$ A_{24} = \pi \left(\frac{24}{2}\right)^2 = \pi \times 144 \approx 452.39 \text{ in}^2 $

Velocity Calculations

Velocity for the current fan (10000 CFM):

$ V_{24}^{\text{old}} = \frac{10000}{452.39} \approx 22.1 \text{ ft/min} $

Velocity for the new fan (15000 CFM):

$ V_{24}^{\text{new}} = \frac{15000}{452.39} \approx 33.2 \text{ ft/min} $

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Step 3: Impact of Converging Cone

Transitioning airflow from a 32" fan into a 24" tube introduces losses due to turbulence. experience practices suggest a gradual transition angle (~6°) to minimize these losses.

Without proper tapering:

• Increased velocity leads to pressure drop.
• Turbulence reduces efficiency.
• Potential flow choking may occur.

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Step 4: Pressure Variation Analysis

Applying Bernoulli’s equation:

$ P_1 + \frac{1}{2} \rho V_1^2 = P_2 + \frac{1}{2} \rho V_2^2 $

where:

• $ P $ is static pressure,
• $ \rho $ is air density ,approx. 0.075 lb/ft³,
• $ V $ is velocity.

Velocity Before Constriction

Area of the 32" fan:

$ A_{32} = \pi \left(\frac{32}{2}\right)^2 = \pi \times 256 \approx 804.25 \text{ in}^2 $

Velocity of airflow from the 32" fan:

$ V_{32} = \frac{15000}{804.25} \approx 18.7 \text{ ft/min} $

Since the new velocity after constriction is:

$ V_{24} = 33.2 \text{ ft/min} $

Using Bernoulli’s equation:

$ P_{32} - P_{24} = \frac{1}{2} \rho \left( V_{24}^2 - V_{32}^2 \right) $

$ \Delta P = \frac{1}{2} (0.075) \left(33.2^2 - 18.7^2\right) $

$ = 0.0375 (1102.24 - 349.69) $

$ \approx 28.25 \text{ lb/ft}^2 $

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Conclusion: Considerations for Optimization

• Velocity increase may cause turbulent losses.
• Smooth tapering (~6° angle) minimizes inefficiencies.
• Potential pressure drop can reduce effective airflow.
• The system may not maintain 15000 CFM, as losses are dependent on design.

This is the basic calculation just for ilustration, FEM can do a better job, but I don't see under the hood!