Calculating the Suction Generated by a Shop-Vac

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The discussion focuses on the challenges of calculating the suction generated by a shop-vac for a design project involving kevlar fibers. The user has created a smaller 0.25" diameter attachment to enhance suction but struggles with the mathematical proof of its effectiveness. Experts emphasize the importance of understanding airflow velocity and the implications of scaling factors in pneumatic conveying. They caution against significant airflow restrictions, noting that reducing the nozzle size drastically affects airflow and could lead to motor cooling issues. A thorough description of the attachment and the method of fiber collection is necessary for accurate calculations.
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I am looking to determine the suction power generated by a shop-vac given differing attachment areas.
I am working on a design project where a shop-vac vacuum will be used to gather kevlar fibers in place for a cut to be made. Currently, the vacuum has a 1.25" diameter attachment. I have created a 0.25" diameter attachment that completes the task perfectly. However, I cannot figure out how to prove this mathematically. I have attached the vacuum specs below.

https://www.lowes.com/pd/Shop-Vac-6-Gallon-3-5-HP-Shop-Vacuum/1000351357

Air Flow (CFM) 145
Sealed Pressure (Inches) 58
 
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There are calculations to scale from a small experiment up to production size. The size of your numbers, and your background, indicates that you would be best off to run a full scale test.

If you are determined to calculate, you need to know exactly the minimum vacuum and/or air flow velocity and/or air flow rate to do what you want to do with the fibers. Then you need to understand if scaling factors apply. Search scaling factors pneumatic conveying for some idea of what scaling factors are and whether they apply to your situation.

I have over 20 years experience in handling materials ranging from tissue paper and paper towel stock to medical gauze using vacuum. We did a lot of testing.
 
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Be cautious about a major air flow restriction. You are restricting the hose cross section area by a factor of 25, less than 4% of design airflow. The Shop-Vac motor needs good airflow for cooling. Been there, done that. :cry:
 
Tom.G said:
Be cautious about a major air flow restriction. You are restricting the hose cross section area by a factor of 25, less than 4% of design airflow. The Shop-Vac motor needs good airflow for cooling. Been there, done that. :cry:

Shrinking the nozzle area by a factor of 25 does not decrease airflow by that same factor. The air velocity through the smaller nozzle will be much higher than through the large one. It will reduce flow rate somewhat as well, but the exact amount that it reduces it by will depend both on the shape of the nozzle and the characteristics of the fan and motor.
 
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You have given no information about the attachment that requires the mathematical model.
Start by describing the attachment.
How are you gathering the fibres by using an airflow?
How are the fibres arranged?
How long are the fibres?
What do you cut the fibres with?

You specify the vacuum cleaner you are using. A vacuum cleaner is designed with a centrifugal pump to generate a high volume airflow. If you obstruct the airflow, a greater pressure is dropped across the obstruction. The pump usually runs faster when obstructed, with lower air flow and a lower pump input pressure. Motor cooling can then becomes a problem.
 

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