What is the Relationship Between Weight and Air Pressure?

[avoinvents]

Hi,

I hope you can help me please. I have an AA battery here that has a weight of 10 grams, I would like to know what 10 grams of weight is equals to in air pressure like mill bar or PSI, can you help please?
Many thanks in advance

Christopher

 

[Cyosis]

Not to be a nitpicker, but the battery has a mass of 10 grams its weight is 98mN, which is a force. Pressure is the force divided by the surface area it is acting on. Therefore there is no conversion from Newtons to bar or PSI.
Specify the surface area.

 

[avoinvents]

OK, so to get my pressure/force, I need to multiply 10 grams by 9.8066 = 98mN, is this correct? Then I need to divide 98mN by the surface area to give me my air pressure?

I have drawn 2 pictures I would like to show you, but I’m not sure how to upload them to you? May I have an email address for you please? The pictures are of two mats filled with air, one is 12” x 12” and the other mat is 24” x 24”, and both are attached to independent air pressure sensors. If I apply 98mN of force to both mats of air, will I get the same pressure reading from both sensors? What I’m trying to say is, even though the surface area on one mat is bigger than the other, the force 98mN is still the same being applied, so the pressure reading should be the same right?

 

[Cyosis]

I replied to your pm.

The air pressure would not be the same. Think about it this way. The same force will be spread over a larger surface. Therefore the force per meter^2 or in your case force per inch^2 will be less for the big mat. This is exactly what pressure is.

 

[avoinvents]

If I have a mat of air 12”x 12” with 98mN of force applied to it, I need to divide 98mN by 144 = 0.68. Would it be 0.68 PSI, millibar etc?

 

[Cyosis]

Newton is an SI unit so if you use Newtons you have to use square meters this results in pressure having Pascal as unit.

Edit: Since I never use the American/Imperial system myself I looked it up and if you want to divide by square inches you need to use pound force as the unit of force. This will result in psi being the unit of pressure.

 

[Redbelly98]

If I have a mat of air 12”x 12” with 98mN of force applied to it, I need to divide 98mN by 144 = 0.68. Would it be 0.68 PSI, millibar etc?

If you want to do the units correctly, then you don't actually divide by 144 -- you divide by 144 square inches. The area is 144 in², not just 144.

Since you are dividing 98 mN by 144 in² in this example, the answer is 0.68 mN/in². However, it's pretty unconventional to mix metric and non-metric units like that. You really should convert something, either mN into pounds-force, or inches² into m².

It's best to stick with one of the more commonly used force units:

PSI
N/m² = Pascals
Torr = mm Hg
atmospheres
bars
millibars
​

(Not sure if I left any out here.)

 

[avoinvents]

Sorry to be a pain, but i need further help with this and please bear in mind that i have never done this before.

I understand the part where i have to convert the weight into force but i have no idea on how to convert the force into air pressure. Could someone please try and explain to me step by step in plain english.

The measurement of 12 inches by 12 inches is incorrect it should be cm, but the square route is still 144. Even though the mat is 12 x12 i forgot to mention that it is also 4cm thick.

Could i please get step by step help, it would be very much appreciated.

Thank you all again in advance.

 

[Cyosis]

Pressure is given by $p=F/A$. In plain English, force divided by the area the force is acting on.

 

[Redbelly98]

... and the pressure units will be whatever units you used for the force per the units you used for the area.

 

[avoinvents]

10 grams = 0.093 Newton’s, 0.093 Newton’s = 0.142233433 PSI. Then I divide 0.142233433 by the surface of the mat with is which is 30cm x 30cm = 900 square cm. This would mean the pressure per cm is 0.000158. Can anyone confirm if I’m correct please?

I used this online converter to convert 10 gram/force direct to PSI:

http://www.translatorscafe.com/cafe...-per-square-centimeter-[N/cm^2]-to-psi-[psi]/

 

[Redbelly98]

No, I'm afraid that's still wrong. It's incorrect beginning with the conversion from grams to Newtons -- it should be 0.098 Newtons. And then, there is no way to convert from Newtons to PSI without being given an area. What exactly did you enter in the online converter?

Also, what units do you want the final pressure to be in? PSI? If so, you'll need to convert the weight into pounds(force), and also convert from cm into inches.

I will state what will be obvious to others, since it seems you are not quite grasping this yet: You must use pounds and inches in order to get pressure in pounds per square inch (PSI).

 

[avoinvents]

OK, with the online converter, I selected from 10 grams – forces /centimeter ^2 converts to 0.142233433 PSI, I then divide this into the surface area of the mat.
The final pressure needs to be in PSI.
So far is this correct. 10 grams = 0.098 Newton’s. Mat size is 12” x 12” = 144 square inches. Can you help me fill in the rest please?

 

[Cyosis]

So far is this correct. 10 grams = 0.098 Newton’s

This is correct. Now you need to convert 144 in^2 to square meters. Then you divide 0.098 by square meters and then you use the Pascal to PSI conversion.

 

[Redbelly98]

OK, with the online converter, I selected from 10 grams – forces /centimeter ^2 ...

Okay, that's the problem. The force here is 10 grams-force, not 10 grams-force/cm^2. At this point in the calculation it's appropriate to select Force, not Pressure, where it says "Select another converter"

The final pressure needs to be in PSI.
So far is this correct. 10 grams = 0.098 Newton’s. Mat size is 12” x 12” = 144 square inches. Can you help me fill in the rest please?

See Cyosis's recent post. You can choose Area at the online converter to convert in^2 to m^2. Be careful, you are not converting inches to meters, rather it's square inches to square meters.

Note, we haven't explicitly done the complete conversion for you because this is a homework problem, and we think you'll learn this better if you can work the details out.

 

[avoinvents]

Is this the correct answer?

0.000152995 psi

Please say it is.

thanks again

 

[Redbelly98]

Looks good!

 

[avoinvents]

Than you for all your help