Calculate water pressure in tube end when tube is compressed

[johboh]

Hello!

Background
I have a hobby in creating an automated home, controlling lights, reading temperatures, and so on from self build sensors and actuators. For a while I have had force sensing resistors under each leg of my bed so I can messaure my own weight every day, sleeping patterns and so on. This has been working quite good for a while, but the sensors does not stand the constant pressure and fails. I need a new solution.

Setup
Instead of a sensor under each leg, the bed will fully stand on a plastic tube filled with water. The tube will have a liquid pressure sensor in one end and a stop in the other end.

Problem
I need to know the pressure on the sensor so I can buy a suitable sensor for that working range.

Data

• The tube will have a diameter of about 10mm.
• The length of the tube will be around 10m to go around and under all legs of the bed.
• The pressure in total will be around (60+70+30) = 1600N.
• The bed stands only on the tube and the tube will be filled with water.

Question
In Bar, what will be the pressure applied on the sensor?

 

[xts]

Forget the idea!
You would have equip all the legs not with tubes (which get flattened under pressure), but rather with pistons with well knows area. Other problem is that such suspension for your bed is not stable - if the weight is not distributed centrally, some legs would totally collapse, while other stay lifted.
Better think about more robust tensometers.

 

[johboh]

If the tube is filled with water I think that this will not happen because water have a very low compressibility, right?

 

[xts]

Water has low compressibility, but the pipe must be ellastic (not quite predictably for plastic/rubber pipes), it suffers from ageing, water loss due to leaks and vapourisation, then you have thermal effects, and lots of others absolutely unpredictable.

Believe me - that is the worst possible tensometer you could design ;)

You can't beat the commercially available ones - just find a more robust one or think about proper shielding. I guess your tensometer got damaged not because of long term pressure (they are designed to withstand it), but because of lateral moves of bed legs, scratching it. Just think about shielding envelope made of hardened steel.

Just try your design to see its flaws - install such a tube without any pressure sensor and watch how it behaves as someone sits on your bed. Or as she rolls from one side to side.

 

[PJC01]

To calculate the water pressure in the tube end when the tube is compressed, we can use the equation P = F/A, where P is the pressure, F is the force applied, and A is the cross-sectional area of the tube. In this case, the force applied is 1600N and the area is the cross-sectional area of the tube, which we can calculate using the formula A = πr^2, where r is the radius (diameter/2) of the tube.

Using the given data, we can calculate the cross-sectional area to be A = π(10mm/2)^2 = 78.54 mm^2. Converting this to meters, we get A = 0.00007854 m^2.

Now, we can plug in the values into the equation P = F/A to get the pressure in Pa (Pascal). P = 1600N/0.00007854m^2 = 20,378,883 Pa.

To convert this to Bar, we can use the conversion 1 Bar = 100,000 Pa. Therefore, the pressure applied on the sensor would be 20,378,883/100,000 = 203.79 Bar.

It is important to note that this calculation assumes a completely rigid and uncompressible tube. If the tube has some flexibility or if the water is able to compress slightly, the pressure may be slightly different. Additionally, the pressure may also vary slightly depending on the height at which the sensor is placed within the tube. Overall, this calculation gives us an estimate of the pressure that can be used to select a suitable pressure sensor for the setup described.