Why do different sized syringes generate unequal pressures when equal force is applied to their plungers?

Question

Physics question. Here is scenario: 2 syringes filled with air; one a 10cc, the other a 30cc; plunger surface areas about 0.22 and 0.44sq inches respectively; syringes held back to back with plungers touching each other; I force the 10cc syringe against the 30cc syringe and measure STATIC pressures at the exit ports using digital manometers. Pressures are different. Why does Pasqal's law not apply? Example: 10cc syringe reads 20psi when the 30cc syring reading 20psi (air in 10cc syring appears considerably more compressed).

I'm an anesthesiologist trying to invent an intraneural injection pressure monitor for medical syringes. To numb a nerve I have to inject novacaine around it. If I accidentally inject into the nerve it will be damaged. I know the needle is in a nerve if the plunger on the syringe is hard to push (ie,>20psi=bad). I can measure pressure by having a pressure transducer in contact with the novacaine, but this contaminates the transducer and requires it be dicarded or resterilized for the next patient (expensive). My solution was to hook up a 10cc syringe full of air to a manometer and use it's pluger (in place of my finger) to push the plunger of the syringe with the novacaine in it. Unfortunately, the static pressures in the 2 syringes did not correlate even though equal pressure was being applied to both plungers. (I used an "in-line" hydlaulic manometer to test the novacaine syringe pressure.) How can I measure the injection pressure of the novacaine without contaminating it?

Answer 1

Well, as per your question, pressures are equal. But the load felt by you may be different because the smaller syringe presses more into your palm.

I think you should refine your experiment keeping in mind the objectives (which are not clear).

Answer 2

It depends upon area of the piston. Pressure = Force / area