Calculate change in air pressure (Physics 101 type Q)

[rdy4trvl]

I'd like to calculate the change in air pressure within a long tube - like the driveway hoses at gas stations.

The static pressure is zero, a vehicle drives over the hose and the increase in pressure activates a switch. I'm trying to determine the proper switch size (in PSI).

So, here is my attempt to start solving this (simple) problem...

• The hose is 1/2" (interior diameter) by 20 feet long. I calculate the cubic inches to be 47.1 (3.14 x 1/4 x 1/4 x 240 inches).
• If a vehicle drives over the hose, (say 12" of hose is compressed flat, for simplicity), then the cubic inches become 44.7 (3.14 x 1/4 x 1/4 x 228 inches). (If the two wheels don't hit at the same time, this could certainly change the results...but let's just keep it simple for now - one wheel, evenly compressed hose.)
• Volume of air decreases from 47.1 cubic in (CI) to 44.7 CI...how is this converted to a change in air pressure (assuming 47.1 was at 0 PSI)?

Thanks

 

[NobodySpecial]

At constant temperature the pressure * volume stays the same.
So if you decrease the volume by 10% the pressure goes up by 10%.

ps. The pressure in the pipe is 15psi - the same as outside air.
The 'gauge pressure' (PSG), ie the extra internal pressure, is zero.

 

[rdy4trvl]

Just to make sure I got this right...
In my example, the volume (of air in a tube capped at both ends) decreases from 47.1 to 44.7 or 5.1%...
Then the pressure would have increased 0.76 PSI (15PSI x 5.1%)
And I would need a switch able to detect < 1PSI increase in pressure.
...sounds logical...is it correct?

 

[NobodySpecial]

Correct
Ideally you would like to measure a rate-of-change of pressure, then you don't have to worry about the absolute pressure in the pipe changing with temperature or slow leaks etc.
The change in pressure with time as a car rolls over it should be pretty noticeable.

 

[rdy4trvl]

Great!
Thanks for the help...and additional considerations (temp., leaks, etc...had not considered...yet!).