 Bourdon tube

A Bourdon tube is a curved, hollow elastic element that converts a pressure difference into movement of its free end. A common form has an oval tube cross-section and a roughly C-shaped centreline. Fluid pressure is applied through the fixed end, while the other end is closed and free to move. WIKA describes the cross-section tending toward a more circular shape under internal pressure and the resulting end motion being transmitted to a pointer.^[ref]

In a Bourdon tube pressure gauge, the tube, linkage, gearing and pointer form a mechanical measuring chain. The sensing element undergoes elastic deformation; the movement converts a small displacement into a readable measurement indication. A steady pressure reading does not require continuous flow through the closed tube.

For an original small-range model, let free-end displacement be $x=K{p}_g$, with gauge pressure $p_g$ and stipulated $K=0.004\mathrm{mm}\mathrm{kP}{\mathrm{a}}^{-1}$. Let the linkage produce pointer angle $\theta =Gx$ with $G=500{}^{\circ }\mathrm{m}{\mathrm{m}}^{-1}$. At $p_g=100\mathrm{kPa}$,The combined response is $2{}^{\circ }\mathrm{kP}{\mathrm{a}}^{-1}$. These are illustrative coefficients, not a specification for a WIKA instrument. The actual response depends on tube geometry, material and movement.

The reference pressure belongs in the interpretation. With the outside of the element exposed to local atmosphere, the response measures gauge pressure, rather than absolute pressure. WIKA separately describes sealed reference arrangements for absolute-pressure instruments.^[ref]

For instrument calibration, connect the gauge and a suitable measurement standard to a common pressure source, allow equilibration, and compare several increasing and decreasing pressures within the intended range. Record the relative height of fluid-filled pressure ports because hydrostatic pressure can add a difference between them. Differences between increasing and decreasing readings can reveal hysteresis or backlash; a zero shift after loading can reveal a changed mechanical state. The original linear model alone does not establish the gauge's measurement uncertainty.