Vacuuming force of a vacuum cleaner calculate

[siddharth23]

I was wondering on what parameters the vacuum generated by a fan in a vacuum cleaner depends.
How can I calculate the vacuum created and the density of materials that it can suck in?

Thanks

 

[Aero51]

you are worried about not the force, but the pressure gradient between the ambient air and the vacuum cleaner itself. The most basic way to do this is with Bernoulli's equation.

http://en.wikipedia.org/wiki/Bernoulli's_principle

 

[siddharth23]

Righto. But the pressure gradient will determine the force. And how do I determine the gradient?

 

[UltrafastPED]

Break the problem down:

1. The fan moves so many cubic liters of air per second (or CFM if you must)- call this Q.
2. The geometry of the tubing provides a cross section which all of the incoming air must pass - you are interested in the "intake port" where the work is being done - label this cross sectional area A.
3. Now you need a formula which will provide the pressure - the simplest is the the Bernoulli equation: http://hyperphysics.phy-astr.gsu.edu/hbase/pber.html

4. The particles of dust and what not are now exposed to the pressure differential computed in step 3. If you know the size and mass of a particle you can calculate:
a. the gravitational force holding it down F=mg
b. the pressure force pulling it up P/cross section of size = lift force

If you only know the density of the stuff on the floor you will have to assume some geometry - this being a physics forum we will take the default and use "spherical cows": thus the density is m/(volume of sphere) and the cross sectional area is the area of circle of the same radius as the sphere.

You should be able to work out the rest, detail by detail.For a real vacuum cleaner there are more considerations; see http://home.howstuffworks.com/vacuum-cleaner.htm for a good start.

 

[Aero51]

In addition to Ultra's post you may be able to calculate the volumetric flow rate if you have the power output of the vacuum motor.

 

[256bits]

So what is being calculated here? Is it how high a column of water can be sucked up to get the vacuum pressure that the machine can achieve, and then relate that to the densities of materials that the hose can be immersed into.

Or is it the size of material and density that the vacuum can suck up. Certainly any vacuum that could suck up iron fillings might have some trouble with half inch or larger ball bearings even though the density is the same.