(EDIT: What follows is a very good calculation based on a fundamental misconception of the type of motor used in a vacuum cleaner. Eventually I figured out the mistake and posted a link to the corrected calculation at the bottom of the discussions. But since then, this article continues to get more hits than any other blog page of mine, while the correction gets little attention. So I'm posting the link to the revised calculation here. But you should still enjoy the discussion below.)
They say the suction of a typical household vacuum cleaner is around 20 kPa, or 80 inches of water. That's an outrageous amount of suction! It comes to around twelve pounds on a typical vacuum hose. Like you could pick a gallon jug of milk with a vacuum cleaner? That's a lot of suction.
Here's how you do the calculation. First of all, every vacuum cleaner I've seen uses a centrifugal (squirrel-cage) blower. I think that's correct. Now, the pressure you get from such a blower is limited by the maximum speed of the blade tip, and that in turn is limited by centrifugal forces. It is a fascinating and little-known fact of material science that a solid disc of steel has a maximum peripheral speed of around 400 feet per second, beyond which the internal stresses exceed the tensile strength of steel. I actually know enough about these things to do the calculation, but I'm not going to do it today. I'm just going to use that 400 feet per second for my blower calculation.
(First a short digression: at 3600 rpm, you hit 400 feet per second with a rotor diameter of around 2 feet. That's a fundamental size limitation for things like big electric motors or generators, and in fact that limit is observed in practise, with some margin to spare.)
How do you convert this to air pressure? The governing equation is I think due to Bernoulli, and it is
Pressure = 1/2*rho*v^2
where rho is the gas pressure. I normally like to derive these things but today I just want to get the answer. The density of air is 1.3 kg/meter^3, and using 120 meters/sec for velocity, I get a pressure of 10 000 Pascals, or 10 kPa, which is just about half of what Wikipedia gives for the "typical" home vacuum cleaner. So what's my problem...isn't that pretty much in the ballpark?
The problem is: do you have a 2-foot diameter blower in your vacuum cleaner? I don't think so. Do you have four six-inch diameter blowers in cascaded in series? I've never seen cascaded blowers in a home vacuum cleaner. Do you have a 4-inch blower and a 20 000 rpm motor? I don't think so.
With a six-inch diameter blower at 3600 rpm (that's a huge blower), I make it around 2500 pascals, or about 10 inches of water. You can do some pretty cool stuff with 10 inches of water pressure, but 80 inches would be downright scary.
37 comments:
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Thanks, Kiwi. Nice website you've got. You know, I started out in Window Cleaning...did it right through university, and still take the odd job even now.But your van is nicer than mine. And your helpers are better looking.
Thanks for the good article. I think there may be one type-o in the last example. With a six-inch diameter blower at 3600 rpm my calculations give 2.07 inches of water. To get a pressure of 10 inches of water you would need 7907 rpm. PS - I am also assuming a density of air of 1.25 kg/m3.
Well, let's see what happens. 3600 rpm is 377 radians per second. With a 15 cm diameter (I'm going metric in anticipation of the density of air etc.) that is close to....ouch! I should be taking the radius! That's where I went wrong.
Okay, it's 30 meters per second tip velocity, and using 1/2*rho*v-squared, it's around 500 Pascals, which is fifty kilograms per meter squared, which is like you say, about two inches of water. Good call on your part.
On re-reading my article and thinking it over, I realize I did something a little more stupid after all. I actually calculated the correct pressure for a two-foot-diameter blower, and then instead of taking the pressure as quadratic in the diameter, I took it as linear! I'm pretty sure that I was thinking by analogy with v-squared-over-r, the equation for centrifugal force, where the quadratic factor in velocity is partially compensated by a linear factor on radius on the bottom, making the overall function linear. So for constant angular velocity the force is linear with the radius. But that same reasoning doesn't work for pressure. So I kind of out-smarted myself.
HI Marty,
Thanks for the info.
But many companies (not only wikipedia) are claiming 20KPa for their products.
LOGIK L16VRP12 Cylinder Bagless Vacuum Cleaner claims 26 KPa. Are they lying?
Thanks,
Manu.
Wow. I did not know that. Let's see if we can get to the bottom of this...I'm going to put up a new blogpost to flag this question. Thanks for the info. But I still say that's an insane amount of pressure.
marty
I work in the industrial vacuum and compressor market (that's not vacuum cleaners, that's vacuum pumps for industrial suction applications).
A few months ago based on a discussion I was having with a customer to get them to understand flow versus pressure I put one of my vacuum gauges on a domestic vacuum cleaner and it pulled -22kPa. If a domestic vacuum cleaner had a hose with a greater seal then it might get closer to that -26kPa as previously mentioned, but with leakage, that might have to start with a -30kPa ability and lose some pressure through leakage to achieve that.
Okay, that's a lot more than I can justify by calculation. Is that a central vac system or just a regular vacuum cleaner? Because I'm assuming its a centrifugal blower of 6 inch diameter going at 3600 rpm, and I don't get anywhere close to that kind of pressure. What kind of blower system do you think they use?
OK everyone...I was wrong! It really is 20 kPa...Wikipedia was right. I've set the record straight in my latest blogpost, which you can read here:
http://marty-green.blogspot.ca/2013/09/how-vacuum-cleaner-really-works.html
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Household Cleaners
It is easy to test if the pressure created by a vacuum cleaner is 80" of water. Just get a thin clear plastic tube that goes from a bucket of water to the next floor up and seal it to the vacuum cleaner. Typical ceilings are 8 feet or 96" I would have though you would easy lift that height with a modern vacuum cleaner,
Actually the vacuum cleaner does not lift anything. The vacuum cleaner just lowers the pressure and then it is the higher pressure everywhere else that does the work - so you could lift humungous amounts of water with a single vacuum cleaner if you construct a very strong container over sufficient surface area of water
All cheap household vacuum cleaners use a universal motor, so lot more than 3600rpm.
But that change nothing in your calculation.
Thanks for the article.
Hi, I need to be able to lift a biscuit of size 5cm and 15g from a table. suction inlet would be 7cm in diameter.height of suction inlet would be 3cm high from the biscuit. I need to calculate the suction power to lift the biscuit
thanks
Aneeq Raheem
Hi, I need to be able to lift a biscuit of size 5cm and 15g from a table. suction inlet would be 7cm in diameter.height of suction inlet would be 3cm high from the biscuit. I need to calculate the suction power to lift the biscuit
thanks
Aneeq Raheem
good article. I am planning to build a saltwater distillation unit, and since water boils at a lower temperature with lower pressure, it will be economical to lower the pressure. But since boiling water, or steam creates pressure, I will probably need more volume than suction to keep the process going. Can a suction hose pick up a gallon jug of water? How would I know. I sweep the floor before vacuuming.
thanks a lot!!! as a student very important facts are here..
Marty Darling...
Universal motors as used in vacuum cleaners, blenders, routers (wood working), that are designed to run at high RPM, DO operate in the 15,000 - 30,000 RPM ranges, AND of all the vacuum cleaners I have dismantled, they all use alumium impellers, not steel, which while at 1/2 the strength, they have 1/3 the mass per unit volume...
How you done calculations can you please share any calculation data for increas my knowledge..
Thanks
ajadhav38@gmail.com
How you done calculations can you please share any calculation data or PDF document file anything for increas my knowledge..
Thanks
ajadhav38@gmail.com
How you done calculations can you please share any calculation data or PDF or documentsfor increas my knowledge..
Thanks
ajadhav38@gmail.com
I realized some time ago that there is a mistake in my analysis. It really is 20 kPa...Wikipedia was right. I've set the record straight in a subsequent blogpost, which you can read here:
http://marty-green.blogspot.ca/2013/09/how-vacuum-cleaner-really-works.html
Great post! Just wanted to give you a heads up. The term "squirrel cage" is normally used in forward curved centrifugal fans. While Vacuum cleaners use backward curved Centriugal fans due to a much higher static efficiency. Just a thought.
i think your understanding about pressure are wrong.. thats the problem.. the -20kpa make sense anyway.. and that 80inch of water, there is a calculation to convert it to pressure.. u can find your engineer friend to help...
Larry Finley
If you seal up your still, after expelling all the air with steam, you don't need to apply vacuum. The system pressure is determined by the vapour pressure of water at the condensing temperature. For example, if you are condensing at 50C (122F), the vapour pressure of water is 0.12 atm or 1.8psia. Watch out for your still imploding, though, as 1.8 psia inside a vessel equates to 14.7 - 1.8 = 12.9 psi of external pressure, which on a 1-ft diameter vessel top (pi * 144 / 4 = 113 sq.in)would exert a force of 1460 lbs
I came across this and I just wanted to point out that your error is assuming that the 400FPS does not scale with diameter. If you have a 2' diameter disc spinning your limit is correctly around 3600 RPM, due to the perimeter approaching 400FPS, however, angular velocity determines that with a 2" scroll cage blower, the distance a point on the end of the radius travels is 2*pi*Diameter per revolution, so with a 2" diameter scroll cage, you can easily spin up around 18,000RPM (as many performance blowers do) and still stay around 300FPS at the outer edge of the scroll cage.
No that wasn't my mistake. My mistake was assuming, on the basis of the limited speed increase of the fan when blocking the suction intake, that the motor was an ordinary induction motor rather than a high-speed series-wound motor. In fact, the reason the speed doesn't take off when you block the suction is that there is a built-in air bypass for cooling the motor. So the speed doesn't run away like it otherwise would.
You seem to know your motors well. Please give me some advice:
I need to provide a continuous vacuum for 8-10 hours a day every day.
What is the kind of vacuum cleaner motor generally that would withstand running constantly for 8-10 hours continuously on a daily basis? I was thinking of a vacuflo type, but perhaps a shop vac type might be cheaper. THis is for a DIY project and I wouldn’t mind replacing it yearly, say if they burnt out due to over-use.
> Because I'm assuming its a centrifugal blower of 6 inch diameter going at 3600 rpm
There's you're error; a common type of vacuum motor has about a 5" wheel and runs at 25,000 rpm.
Uh, no.
You might want to look at one...
Firstly, they use a universal motor spinning at a lot more than 3600rpm.
Secondly, they are usually two stage.
You object to "They say the suction of a typical household vacuum cleaner is around 20 kPa, or 80 inches of water. That's an outrageous amount of suction! It comes to around twelve pounds on a typical vacuum hose. Like you could pick a gallon jug of milk with a vacuum cleaner? That's a lot of suction."
But that seems about right to me. 20kPa is 3psi. The end of the pipe on mine is about an inch squared. So it should lift three pounds, which is a lemonade bottle with about 1.5 litres of water in it. It can almost do that.
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A perfect vacuum is about 407 inches of water. That is to say, a perfect vacuum could lift water about 407 inches = about 34 feet. So the 80-95 inches the best vacuums give is still only 15-23% of an atmosphere. But to get the weight that can be lifted (as some have mentioned) you multiply the pressure (weight per area) x area of contact with object being lifted = weight. So it depends greatly on the area over which the vacuum hose contacts.
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