Shape of the bubble tube surface The longitudinal profile (surface) of a level’s bubble tube is designed to be which geometric curve?

Introduction / Context:
Bubble tubes (spirit levels) rely on precise geometry to translate small tilts of the instrument into measurable bubble movements. The curve chosen for the internal surface directly controls the relationship between tilt angle and bubble displacement (sensitivity).

Given Data / Assumptions:

• The bubble resides in a liquid-filled, slightly curved glass tube.
• We consider the longitudinal (along-the-tube) shape.
• Small-angle behavior should be predictable and approximately linear.

Concept / Approach:

The inside surface of the tube is ground to a circular arc of very large radius. For small angular tilts, the arc length subtended is proportional to the angle (s ≈ R * α), giving a practical linear relationship between tilt and bubble travel over a limited range. This simplicity of design and predictable sensitivity are why a circular arc is used rather than more complex curves.

Step-by-Step Solution:

Verification / Alternative check:

Instrument design texts routinely derive sensitivity formulas from the circular-arc assumption and specify tube radii accordingly.

Why Other Options Are Wrong:

Straight, parabolic, elliptic, or hyperbolic surfaces would not provide the desired simple proportionality and manufacturability for standard levels.

Common Pitfalls:

Confusing the bubble tube’s external shape with the internal grinding; assuming “straight” because the tube appears nearly straight to the eye.

Final Answer:

Circular arc