Density and Pressure — Question 6

Question 6

A negative gauge reading can still mean positive absolute pressure

A sealed chamber has uniform absolute pressure $82\,\mathrm{kPa}$; outside pressure is $101\,\mathrm{kPa}$. A flat hatch of area $0.025\,\mathrm{m^2}$ separates them. Ignore its weight and hinge friction.

1. Find chamber gauge pressure and the net pressure force on the hatch, including direction.

2. Outside pressure later falls to $76\,\mathrm{kPa}$ while chamber pressure remains fixed. Find the new net force and explain what has reversed.

Question 6 - Solution

A negative gauge reading can still mean positive absolute pressure

(a) Derivation and calculation

Take outward as positive:$$p_g=p_{\mathrm{in}}-p_{\mathrm{out}}=82-101=\boxed{-19\,\mathrm{kPa}}.$$$$\boxed{F_{\mathrm{net}}=p_gA=(-19000)(.025)=-475\,\mathrm N}.$$The net force is 475 N inward although both absolute pressures are positive.

(b) Result and interpretation

After the outside pressure falls,$$\Delta p=82-76=+6\,\mathrm{kPa}.$$$$\boxed{F_{\mathrm{net}}=6000(.025)=+150\,\mathrm N\ \text{outward}}.$$The pressure ordering reverses; the chamber absolute pressure remains 82 kPa.

Physical check

A gauge value is a pressure difference, so a negative reading does not mean a negative absolute pressure.