# My Air Mattress as a Pressure Vessel

In summary, to accurately model the whole air mattress, one must consider the number of cells, the shape of the mattress, and the material properties of the air cells, in order to calculate the maximum pressure the mattress can handle.
I wanted to make a free body diagram of my air mattress. The mattress is comprised of air cells. Each air cell is a 30 inches in length with a diameter of about 4 inches. Each cell is inflated to about 0.4 psi.

If I wanted to accurately model the whole bed (not just one individual cell), wouldn't I have to account for each cell as a thin-walled pressure vessel? That is, the whole bed doesn't have a reactive pressure of 0.4 necessarily right?

Say I wanted to find out the largest force the bed could handle. Wouldn't I be wrong to say that the limiting equation is P=F/A? That is, if my bed is 30 inches x 80 inches, and each air cell is filled to 0.4 psi, (and assuming a person is perfectly distributed), I would be wrong to say that my bed could support 960lbs?

The answer is yes, you would be wrong to say that your bed could support 960lbs. The limiting equation for pressure vessels is P = S x E x (D/t), where P is the maximum pressure, S is the allowable stress of the material, E is the modulus of elasticity, D is the outside diameter, and t is the wall thickness. In addition, the area of the vessel (A) must take into account the number of cells in the mattress, as well as the shape of the mattress, as the pressure is distributed across the entire mattress. Therefore, to accurately model the whole bed, you would need to take into account the number of cells, the shape of the mattress, and the material properties of the air cells, in order to accurately calculate the maximum pressure the mattress can handle.

## 1. What is a pressure vessel?

A pressure vessel is a container that is designed to hold fluids or gases at a pressure that is significantly higher than the ambient pressure. This can include air, water, steam, or other substances.

## 2. Is my air mattress considered a pressure vessel?

Yes, technically speaking, an air mattress can be considered a pressure vessel because it holds air at a higher pressure than the surrounding environment. However, it is not designed or regulated as a pressure vessel like those used in industrial or scientific applications.

## 3. How much pressure can an air mattress withstand?

The amount of pressure an air mattress can withstand varies depending on the material and design of the mattress. In general, most air mattresses can withstand pressures up to 10-15 psi, which is equivalent to about 1.4-2.1 pounds per square inch. However, it is important to follow the manufacturer's recommendations for maximum weight and pressure limits.

## 4. Can an air mattress burst like a traditional pressure vessel?

It is highly unlikely for an air mattress to burst like a traditional pressure vessel, as it is not designed to contain extremely high pressures. However, over-inflating the mattress or exposing it to sharp objects or extreme temperatures could potentially cause it to burst.

## 5. Are there any safety concerns when using my air mattress as a pressure vessel?

As long as the air mattress is used within its recommended weight and pressure limits, and is properly inflated and maintained, there should be no safety concerns. However, it is important to regularly check for any punctures or tears in the material and to follow all safety precautions provided by the manufacturer.

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