Grumpy_Mike:
Without a resistor you can get up to 80V from those things which will damage your Arduino.As noted before it in not the pressure you are measuring but the change in pressure. For constant pressure you will get nothing. You only think you are getting something because you have charged up the input capacitor, it is a fake reading.
But the current is usually small, so the input protection diodes will generally protect from this, the
exception being high frequencies as the current goes up with frequency for an AC charge source.